Syllabus for

Academic Year  (2024)

This course on embedded systems provides the necessary theoretical background to understand and develop practical applications using the Arduino environment. It covers the basics of general embedded systems, standard peripherals and communication, operating systems and Arduino development environment and its applications. This course prepares students to acquire skills for their employability and also entrepreneurship in the future. Unit III caters to national and global needs. 

Introduction, Comparison between embedded systems and general computing system, Major components of an embedded system, Block diagram, Processor embedded into a system, embedded hardware units in a system, Classification of embedded systems, applications, Case study of Digital thermometer, air conditioner, digital Camera,Pacemaker as embedded systems.

Classification of I/Os- synchronous serial input, synchronous serial output, Asynchronous serial input, Asynchronous serial output, parallel port on bit input, parallel port on bit output, parallel port input, parallel port output. Serial communication devices-basics of operating modes, Serial bus communication protocols. Fundamentals of I2C, CAN, USB and firewire (IEEE 1394) protocols, SPI and SCI. Basics of timer and counting devices.

Introduction, Comparison between embedded systems and general computing system, Major components of an embedded system, Block diagram, Processor embedded into a system, embedded hardware units in a system, Classification of embedded systems, applications, Case study of Digital thermometer, air conditioner, digital Camera,Pacemaker as embedded systems.

Classification of I/Os- synchronous serial input, synchronous serial output, Asynchronous serial input, Asynchronous serial output, parallel port on bit input, parallel port on bit output, parallel port input, parallel port output. Serial communication devices-basics of operating modes, Serial bus communication protocols. Fundamentals of I2C, CAN, USB and firewire (IEEE 1394) protocols, SPI and SCI. Basics of timer and counting devices.

Operating system- services of an OS. User and supervisory mode structure, layers at the structure in the system, Kernel and process management function. Introduction to the real-time operating system (RTOS), Basic functions in RTOS, examples of RTOS, Hard real-time and soft real-time operations. Structural units and activities of an RTOS.

Introduction to Arduino environment, features, advantages, Programming overview, variables, logical and math operators. Digital and analog I/O functions, time functions, math functions, Control structure- for, while, case. Arduino IDE, basic program examples. Arduino hardware- types of boards, comparison of specifications, Arduino Uno board- specifications, basic architecture of AVR core, features of Atmega microcontroller.

Operating system- services of an OS. User and supervisory mode structure, layers at the structure in the system, Kernel and process management function. Introduction to the real-time operating system (RTOS), Basic functions in RTOS, examples of RTOS, Hard real-time and soft real-time operations. Structural units and activities of an RTOS.

Introduction to Arduino environment, features, advantages, Programming overview, variables, logical and math operators. Digital and analog I/O functions, time functions, math functions, Control structure- for, while, case. Arduino IDE, basic program examples. Arduino hardware- types of boards, comparison of specifications, Arduino Uno board- specifications, basic architecture of AVR core, features of Atmega microcontroller.

Interfacing of I/O devices, simple analogue and digital input reading with a switch, reading analogue value, getting input from sensors- detecting light (LDR), movement (PIR sensor), sound (microphone, amplifier LM 386), heat (LM 35). Interface for visual output- LED, 7 segments LED and LCD module. Circuit and program examples for each.  Basics of motor driver circuit- H Bridge. Basics of stepper motor, Micro Servo motor interfacing and control programs.

Introduction to ARM processors, specifications, applications in embedded systems design Concept of IOT, basics of IOT architecture and applications.

Interfacing of I/O devices, simple analogue and digital input reading with a switch, reading analogue value, getting input from sensors- detecting light (LDR), movement (PIR sensor), sound (microphone, amplifier LM 386), heat (LM 35). Interface for visual output- LED, 7 segments LED and LCD module. Circuit and program examples for each.  Basics of motor driver circuit- H Bridge. Basics of stepper motor, Micro Servo motor interfacing and control programs.

Introduction to ARM processors, specifications, applications in embedded systems design Concept of IOT, basics of IOT architecture and applications.

[2]. Prasad, K V K K,( 2004).Embedded/real-Time Systems: Concepts, Design and Programming: The Ultimate Reference, Wiley India.

[3]. Bailey, Oliver, (2005). Embedded Systems Design, Dream Tech Press.

[4]. Massimo Banzi, Michael Shiloh, (2007).Make Getting Started With Arduino, (3rd Edition.),.Shroff Publishers & Distributors.

[2]. Michael Margolis, (2011). Arduino Cookbook, O’Reilly Media Inc.

[3]. John Nussey, (2005). Arduino For Dummies, John Wiley & Sons Inc (Sea) Pvt Ltd, 

[4]. Dream Tech Software Team, (2002). Programming for Embedded Systems, Create Tomorrows Embedded Systems Today, Wiley India

Optical fiber communication systems have revolutionized our global telecommunications network. With their very high data rates and capacity, optical fiber systems link continents, countries, cities and end-users. They have enabled the internet and changed our society. This paper provides comprehensive coverage of the field of electronic communication and various technologies using fibre optics. The principles of operation and properties of optoelectronic components, as well as the signal guiding characteristics of glass fibres, are discussed. Units I to III caters to local and regional needs. 

Classification of photonic devices, Interaction of matter and radiations, LED, construction, heterojunction structures, materials, working, characteristics and applications, Semiconductor diode laser, condition for amplification, laser cavity, construction details, characteristics & applications, photodetectors, photoconductors, PIN photodiode, avalanche photodiode, metal-semiconductor-metal (MSM) photo-detector photo-transistor, photomultiplier tube, comparison of photo-detectors.

Classification of photonic devices, Interaction of matter and radiations, LED, construction, heterojunction structures, materials, working, characteristics and applications, Semiconductor diode laser, condition for amplification, laser cavity, construction details, characteristics & applications, photodetectors, photoconductors, PIN photodiode, avalanche photodiode, metal-semiconductor-metal (MSM) photo-detector photo-transistor, photomultiplier tube, comparison of photo-detectors.

Introduction, Historical development, General OFC system, need for lightwave communication, advantages, disadvantages and applications of optical fiber communication, optical fiber waveguides, Ray transmission theory, cylindrical fiber, Types of rays, optical fiber modes and configurations, fiber profiles, cut-off wavelength, and mode field diameter. Optical fiber materials, plastic optical fiber, Speciality optical fiber, photonic crystal fiber, fiber optic cables. Indoor and Outdoor fiber optic cables

Optical amplifiers, Block diagram. Basic applications and types. Semiconductor optical amplifiers (SDA). EDFA (Erbium-doped fiber amplifier). Introduction to optical networks. Network topologies. Introduction to synchronous optical network/synchronous digital hierarchy (SONET/SDH)

Introduction, Historical development, General OFC system, need for lightwave communication, advantages, disadvantages and applications of optical fiber communication, optical fiber waveguides, Ray transmission theory, cylindrical fiber, Types of rays, optical fiber modes and configurations, fiber profiles, cut-off wavelength, and mode field diameter. Optical fiber materials, plastic optical fiber, Speciality optical fiber, photonic crystal fiber, fiber optic cables. Indoor and Outdoor fiber optic cables

Optical amplifiers, Block diagram. Basic applications and types. Semiconductor optical amplifiers (SDA). EDFA (Erbium-doped fiber amplifier). Introduction to optical networks. Network topologies. Introduction to synchronous optical network/synchronous digital hierarchy (SONET/SDH)

Introduction, Attenuation, absorption, scattering losses, bending loss, dispersion, Intra modal dispersion, and Intermodal dispersion. Introduction to couplers & connectors, fiber alignment and joint loss, single-mode fiber joints, fiber splices, fiber connectors and fiber couplers. Optical Receiver Operation, receiver sensitivity, quantum limit, coherent detection, Analog receivers & Digital receivers, Analog links, Introduction, an overview of analogue links, carrier noise ratio (CNR), multichannel transmission techniques,  Digital links – Introduction, Overview of digital links.

Introduction, Attenuation, absorption, scattering losses, bending loss, dispersion, Intra modal dispersion, and Intermodal dispersion. Introduction to couplers & connectors, fiber alignment and joint loss, single-mode fiber joints, fiber splices, fiber connectors and fiber couplers. Optical Receiver Operation, receiver sensitivity, quantum limit, coherent detection, Analog receivers & Digital receivers, Analog links, Introduction, an overview of analogue links, carrier noise ratio (CNR), multichannel transmission techniques,  Digital links – Introduction, Overview of digital links.

[2]. John M. Senior, (2013). Optical fiber communications- Principles & Practice, (3^rd Edition), Pearson.

 [2]. J.Wilson, J.F.B . Hawkes(2010.). Optoelectronics-An Introduction, (2^nd Edition), PHI.

This Paper will enable the students to get a thorough knowledge of measuring instruments and their measuring techniques. Any instrument consists of an input sensing element or transducer, signal conditioner and display unit. So the basic principles and applications of the transducers, signal conditioners, data acquisition systems and digital instruments are covered. The students are introduced to biomedical instrumentation as it is an emerging area of instrumentation and pc based on instrumentation. Units II and III caters to regional and national needs.

Introduction, Basic concepts of measurement, Block diagram of a measurement system, Performance characteristics: static and dynamic Errors in measurement, Types of errors, sources of errors, dynamic characteristics.

 Electrical transducers,  Selecting a transducer, classification of transducers-, Resistive, capacitive and inductive transducers- Strain gauge- types- un-bonded, bonded metal wire, foil and semiconductor types, Thermistor - temp characteristics, Thermocouple, IC temperature sensors LM 34/35 Resistance thermometer,  Inductive transducers-Reluctance type- Linear variable differential transformer (LVDT), Capacitive transducer, Pressure transducer, Photoelectric transducers, Piezoelectric transducer.

Introduction, Basic concepts of measurement, Block diagram of a measurement system, Performance characteristics: static and dynamic Errors in measurement, Types of errors, sources of errors, dynamic characteristics.

 Electrical transducers,  Selecting a transducer, classification of transducers-, Resistive, capacitive and inductive transducers- Strain gauge- types- un-bonded, bonded metal wire, foil and semiconductor types, Thermistor - temp characteristics, Thermocouple, IC temperature sensors LM 34/35 Resistance thermometer,  Inductive transducers-Reluctance type- Linear variable differential transformer (LVDT), Capacitive transducer, Pressure transducer, Photoelectric transducers, Piezoelectric transducer.

Introduction, Block diagram of signal conditioning, Voltage to Current converter, Current to Voltage converter, and the expression for output. Practical integrator and differentiator circuit, frequency response, Logarithmic amplifier, circuit description and output expression.Basic Instrumentation amplifier- important features, basic instrumentation amplifier- block diagram, realization using 3 op-amps, differential instrumentation amplifier using transducer Bridge, output voltage derivation.

Introduction, general data acquisition system (DAS), the objective of DAS, Single-channel and multi-channel DAS block diagrams qualitative description, Functional blocks of a data acquisition configuration, Digital to Analog converter- R-2R ladder and binary-weighted ladder circuits, brief analysis, D to A using op-amp summing amplifier, Analog to Digital converter- Successive approximation method, Flash ADC, block diagram explanation, Introduction to Lab view.

Introduction, Block diagram of signal conditioning, Voltage to Current converter, Current to Voltage converter, and the expression for output. Practical integrator and differentiator circuit, frequency response, Logarithmic amplifier, circuit description and output expression.Basic Instrumentation amplifier- important features, basic instrumentation amplifier- block diagram, realization using 3 op-amps, differential instrumentation amplifier using transducer Bridge, output voltage derivation.

Introduction, general data acquisition system (DAS), the objective of DAS, Single-channel and multi-channel DAS block diagrams qualitative description, Functional blocks of a data acquisition configuration, Digital to Analog converter- R-2R ladder and binary-weighted ladder circuits, brief analysis, D to A using op-amp summing amplifier, Analog to Digital converter- Successive approximation method, Flash ADC, block diagram explanation, Introduction to Lab view.

Digital voltmeter, performance characteristics, ramp type and dual slope type digital voltmeters, Digital multimeter, resolution and sensitivity of digital multimeter. LCR Meter, Signal generator, Function generator, CRT, vertical and horizontal deflection, Storage Oscilloscopes- analogue and digital, Bio-Medical instrumentation- Bioelectric potentials, ECG, EEG, EMG.                                                                                                 The general form of PC based instrumentation system Data acquisition using serial interfaces, serial connection formats, serial communication modes, serial interface standards (RS 232), Features of USB, i2c, spi BUS type of communication protocols.

Digital voltmeter, performance characteristics, ramp type and dual slope type digital voltmeters, Digital multimeter, resolution and sensitivity of digital multimeter. LCR Meter, Signal generator, Function generator, CRT, vertical and horizontal deflection, Storage Oscilloscopes- analogue and digital, Bio-Medical instrumentation- Bioelectric potentials, ECG, EEG, EMG.                                                                                                 The general form of PC based instrumentation system Data acquisition using serial interfaces, serial connection formats, serial communication modes, serial interface standards (RS 232), Features of USB, i2c, spi BUS type of communication protocols.

[2]. W.D. Cooper, A.D. Helfrick, (2008). Electronic Instrumentation and Measuring Techniques, 3^rd Edition, PHI.

[2]. C.S.Rangan, G.R.Sarma, VSV Mani, (2008).Instrumentation devices and systems,(2^nd Edition.), TMH.

[3]. N. Mathivanan (2011).PC based instrumentation, (3^rd Edition.), PHI.

This paper is designed to understand the fundamentals of signals, systems and digital signal processing. Digital and analogue signals are introduced, followed by their processing through various mathematical techniques. Basic concepts for continuous-time and discrete-time signals in the time and frequency domains are also covered. Electronic systems are introduced with the relation between the output and the input. The mathematical modelling of different types of systems is also detailed.

Introduction and Classification of signals: Definition of signal and systems, communication and control systems as examples. Sampling of analogue signals, Continuous-time and discrete-time signals, Classification of signals as even, odd, periodic and non-periodic, deterministic and non-deterministic, energy and power. Elementary signals/Functions: exponential, sine, impulse, step and its properties, ramp, rectangular, triangular, signum, sync functions. Operations on signals: Amplitude scaling, addition, multiplication, differentiation, integration, time scaling, time-shifting and time folding.

Introduction and Classification of signals: Definition of signal and systems, communication and control systems as examples. Sampling of analogue signals, Continuous-time and discrete-time signals, Classification of signals as even, odd, periodic and non-periodic, deterministic and non-deterministic, energy and power. Elementary signals/Functions: exponential, sine, impulse, step and its properties, ramp, rectangular, triangular, signum, sync functions. Operations on signals: Amplitude scaling, addition, multiplication, differentiation, integration, time scaling, time-shifting and time folding.

Signal sensing and acquisition: Basic Architectural features, DSP Computational Building Blocks, Bus Architecture and Memory, Data Addressing Capabilities, Address Generation Unit, Programmability and Program Execution, Speed Issues, Hardware looping, Interrupts, Stacks, Relative Branch support, Pipelining and Performance, Pipeline Depth, Interlocking, Branching effects, Interrupt effects, Pipeline Programming models.

Signal sensing and acquisition: Basic Architectural features, DSP Computational Building Blocks, Bus Architecture and Memory, Data Addressing Capabilities, Address Generation Unit, Programmability and Program Execution, Speed Issues, Hardware looping, Interrupts, Stacks, Relative Branch support, Pipelining and Performance, Pipeline Depth, Interlocking, Branching effects, Interrupt effects, Pipeline Programming models.

Commercial Digital signal-processing Devices, Data Addressing modes of TMS320C67XX DSPs, Data Addressing modes of TMS320C6713 Processor, Memory space of the Processor, Program Control, instructions and Programming, On-Chip Peripherals, Interrupts of the processor, Pipeline Operations. Qualitative transformations on signals - Fourier transformations (qualitative).

Commercial Digital signal-processing Devices, Data Addressing modes of TMS320C67XX DSPs, Data Addressing modes of TMS320C6713 Processor, Memory space of the Processor, Program Control, instructions and Programming, On-Chip Peripherals, Interrupts of the processor, Pipeline Operations. Qualitative transformations on signals - Fourier transformations (qualitative).

 [2]. A. Anand Kumar, (2013). Signals and Systems (3^rd Edition), PHI.

 [3]. P. Ramesh Babu, (2014). Digital Signal Processing, 6^th Edition, Scitech.

 [2]. Taan S. ElAli, (2012). Discrete Systems and Digital Signal Processing with Matlab, (2^nd Edition.), Taylor and Francis.

This practical course covers the study of the Arduino development platform, writing the programs and implementing practical applications using Arduino Uno.

The course has a provision for conducting all the experiments virtually using an online tool in tinkercad.com. This course focusses on electronics design skills for employment and entrepreneurship.

1. Installation and setting up of Arduino

2. Uploading and running sample programs

3. Interfacing of LED

4. Fading of LED using PWM

5. Reading analog voltage using Potentiometer

6. Interfacing of Pushbuttons

7. Interfacing of a Photo Resistor (LDR)

8. Interfacing of a Relay

9. Interfacing of a dc Motor

10. Interfacing of a Single Servo

11. Interfacing Liquid crystal display (LCD) module

12. Interfacing Ultra sound Sensor for distance measurement

1. Installation and setting up of Arduino

2. Uploading and running sample programs

3. Interfacing of LED

4. Fading of LED using PWM

5. Reading analog voltage using Potentiometer

6. Interfacing of Pushbuttons

7. Interfacing of a Photo Resistor (LDR)

8. Interfacing of a Relay

9. Interfacing of a dc Motor

10. Interfacing of a Single Servo

11. Interfacing Liquid crystal display (LCD) module

12. Interfacing Ultra sound Sensor for distance measurement

[2].Michael Margolis, (2011).Arduino Cookbook, O’Reilly Media Inc.

This course describes the technical features and specifications of the optical fiber communication training kit. Students will be able to perform different types of experiments to understand basic fiber optical communications. The kit demonstrates the properties of fiber optic transmitters and receivers, characteristics of fiber optic cables, different types of modulation and demodulation techniques, and PC to PC communication via fiber optic link using the RS232 interface. It can also be used to demonstrate various digital communication techniques via fiber-optic links.

1.     Setting up an Analog and Digital fiber link

2.     Measurement of Propagation or Attenuation Loss in the optical fiber

3.     Study of bending loss in optical fiber

4.     Calculation of Numerical Aperture of optical fiber

5.     Study of V I characteristics of Light-emitting diode

6.     Study the characteristics of Photodiode and phototransistor

7.     Study of voice transmission through fiber optic link

8.     PC to PC communications through fiber optic link

 9.     Study of modulation techniques (AM, FM, and PWM)

1.     Setting up an Analog and Digital fiber link

2.     Measurement of Propagation or Attenuation Loss in the optical fiber

3.     Study of bending loss in optical fiber

4.     Calculation of Numerical Aperture of optical fiber

5.     Study of V I characteristics of Light-emitting diode

6.     Study the characteristics of Photodiode and phototransistor

7.     Study of voice transmission through fiber optic link

8.     PC to PC communications through fiber optic link

 9.     Study of modulation techniques (AM, FM, and PWM)

[2]. John M. Senior, (2013). Optical fiber communications- Principles & Practice, (3^rd Edition), Pearson.

[3]. Scientech 2501 optical fiber communication trainer kit reference manual and tutorials.

[4]. Opti system 17.1 user’s manual and tutorials (www.optiwave.com).

[2]. J.Wilson, J.F.B . Hawkes (2010.). Optoelectronics-An Introduction, (2^nd Edition), PHI.

This course provides laboratory hours that allow students the opportunity to enhance their understanding of how to construct, analyse and troubleshoot basic signal conditioning and instrumentation amplifier circuits using basic ICs and discrete components. These topics will enhance their basic skills which in turn can be useful for global industrial requirements.

1.     Op-amp Integrator –Frequency response & waveforms.

2.     Op-amp Differentiator –Frequency response & waveforms.

3.     Capacitance Meter using IC 555

4.     Instrumentation amplifier.

5.     DAC with binary-weighted resistors 

6.     Study of DAC using IC 0804

7.     Interfacing of an ADC to a Computer port

8.     Flash ADC – IC Quad op-amp

9.     Frequency counter

10.  Familiarization with basic transducers by using a trainer kit.

11.  Characteristics of a phototransistor

12.  Acquisition of temperature sensor data through bridge circuit and Instrumentation amplifier.

1.     Op-amp Integrator –Frequency response & waveforms.

2.     Op-amp Differentiator –Frequency response & waveforms.

3.     Capacitance Meter using IC 555

4.     Instrumentation amplifier.

5.     DAC with binary-weighted resistors 

6.     Study of DAC using IC 0804

7.     Interfacing of an ADC to a Computer port

8.     Flash ADC – IC Quad op-amp

9.     Frequency counter

10.  Familiarization with basic transducers by using a trainer kit.

11.  Characteristics of a phototransistor

12.  Acquisition of temperature sensor data through bridge circuit and Instrumentation amplifier.

[1]. H.S.Kalsi,(2010). Electronic Instrumentation, (2^nd Edition), TMH,.

[2]. W.D. Cooper, A.D. Helfrick, (2008). Electronic Instrumentation and Measuring Techniques, 3^rd Edition, PHI.

[1]. A.K. Sawhney, Dhanpat Rai & sons, (2008). A Course in Electrical, Electronics Measurement and Instrumentation, BPB publications.

[2]. C.S.Rangan, G.R.Sarma, VSV Mani, (2008).Instrumentation devices and systems,(2^nd Edition.), TMH.

[3]. N. Mathivanan (2011).PC-based instrumentation, (3^rd Edition.), PHI.

This practical course covers the fundamentals of signals and systems. Basic simulation of signals and systems and signal processing through various mathematical techniques using GNU Octave /MATLAB/Python will be carried out. 

1. Introduction to Octave

2. Plotting Elementary signals

3. Plotting of continuous-time and discrete-time signals

4. Sampling of signals

5. Periodic and non-periodic signals

6. Even and odd signals

7. Operations on signals for the independent variable

8. Operations on signals for the dependent variable

9. Modulation of signals

1. Introduction to Octave

2. Plotting Elementary signals

3. Plotting of continuous-time and discrete-time signals

4. Sampling of signals

5. Periodic and non-periodic signals

6. Even and odd signals

7. Operations on signals for the independent variable

8. Operations on signals for the dependent variable

9. Modulation of signals

[1]. Alan V. Oppenheim, Alan S.Willsky, S.Hamid Nawab, (2015).Signals and Systems, (62nd Edition), Peason.

[2]. A. Anand Kumar, (2013).Signals and Systems, (3^rd Edition.), PHI.

[3]. Nagoor Kani, (2010).Signals and Systems, (2^nd Edition.), McGraw Hill Education.

[1]. Alan V. Oppenheim, Alan S.Willsky, S.Hamid Nawab, (2015).Signals and Systems, (62nd Edition), Peason.

[2]. A. Anand Kumar, (2013).Signals and Systems, (3^rd Edition.), PHI.

[3]. Nagoor Kani, (2010).Signals and Systems, (2^nd Edition.), McGraw Hill Education.

Course Description:

This course aims at developing the ability to write the mathematical proofs. It helps the students to understand and appreciate the beauty of the abstract nature of mathematics and also to develop a solid foundation of theoretical mathematics.

Course Objectives : This course will help the learner to

COBJ1. understand the theory of matrices, concepts in vector spaces and Linear Transformations.

COBJ2. gain problems solving skills in solving systems of equations using matrices, finding eigenvalues and eigenvectors, vector spaces and linear transformations.

Elementary row operations, rank, inverse of a matrix using row operations, Echelon forms, normal forms, system of homogeneous and non-homogeneous equations, Cayley Hamilton theorem, eigenvalues and eigenvectors, diagonalization of square matrices.

Elementary row operations, rank, inverse of a matrix using row operations, Echelon forms, normal forms, system of homogeneous and non-homogeneous equations, Cayley Hamilton theorem, eigenvalues and eigenvectors, diagonalization of square matrices.

Elementary row operations, rank, inverse of a matrix using row operations, Echelon forms, normal forms, system of homogeneous and non-homogeneous equations, Cayley Hamilton theorem, eigenvalues and eigenvectors, diagonalization of square matrices.

Elementary row operations, rank, inverse of a matrix using row operations, Echelon forms, normal forms, system of homogeneous and non-homogeneous equations, Cayley Hamilton theorem, eigenvalues and eigenvectors, diagonalization of square matrices.

Elementary row operations, rank, inverse of a matrix using row operations, Echelon forms, normal forms, system of homogeneous and non-homogeneous equations, Cayley Hamilton theorem, eigenvalues and eigenvectors, diagonalization of square matrices.

Elementary row operations, rank, inverse of a matrix using row operations, Echelon forms, normal forms, system of homogeneous and non-homogeneous equations, Cayley Hamilton theorem, eigenvalues and eigenvectors, diagonalization of square matrices.

Elementary row operations, rank, inverse of a matrix using row operations, Echelon forms, normal forms, system of homogeneous and non-homogeneous equations, Cayley Hamilton theorem, eigenvalues and eigenvectors, diagonalization of square matrices.

Vector space-examples and properties, subspaces-criterion for a subset to be a subspace, linear span of a set, linear combination, linear independent and dependent subsets, basis and dimensions, and standard properties.

Vector space-examples and properties, subspaces-criterion for a subset to be a subspace, linear span of a set, linear combination, linear independent and dependent subsets, basis and dimensions, and standard properties.

Vector space-examples and properties, subspaces-criterion for a subset to be a subspace, linear span of a set, linear combination, linear independent and dependent subsets, basis and dimensions, and standard properties.

Vector space-examples and properties, subspaces-criterion for a subset to be a subspace, linear span of a set, linear combination, linear independent and dependent subsets, basis and dimensions, and standard properties.

Vector space-examples and properties, subspaces-criterion for a subset to be a subspace, linear span of a set, linear combination, linear independent and dependent subsets, basis and dimensions, and standard properties.

Vector space-examples and properties, subspaces-criterion for a subset to be a subspace, linear span of a set, linear combination, linear independent and dependent subsets, basis and dimensions, and standard properties.

Vector space-examples and properties, subspaces-criterion for a subset to be a subspace, linear span of a set, linear combination, linear independent and dependent subsets, basis and dimensions, and standard properties.

Linear transformations, properties, matrix of a linear transformation, change of basis, range and kernel, rank and nullity, rank-nullity theorem, non-singular linear transformation, eigenvalues and eigenvectors of a linear transformation.

Linear transformations, properties, matrix of a linear transformation, change of basis, range and kernel, rank and nullity, rank-nullity theorem, non-singular linear transformation, eigenvalues and eigenvectors of a linear transformation.

Linear transformations, properties, matrix of a linear transformation, change of basis, range and kernel, rank and nullity, rank-nullity theorem, non-singular linear transformation, eigenvalues and eigenvectors of a linear transformation.

Linear transformations, properties, matrix of a linear transformation, change of basis, range and kernel, rank and nullity, rank-nullity theorem, non-singular linear transformation, eigenvalues and eigenvectors of a linear transformation.

Linear transformations, properties, matrix of a linear transformation, change of basis, range and kernel, rank and nullity, rank-nullity theorem, non-singular linear transformation, eigenvalues and eigenvectors of a linear transformation.

Linear transformations, properties, matrix of a linear transformation, change of basis, range and kernel, rank and nullity, rank-nullity theorem, non-singular linear transformation, eigenvalues and eigenvectors of a linear transformation.

Linear transformations, properties, matrix of a linear transformation, change of basis, range and kernel, rank and nullity, rank-nullity theorem, non-singular linear transformation, eigenvalues and eigenvectors of a linear transformation.

2. V. Krishnamurthy, V. P. Mainra, and J. L. Arora, An introduction to linear algebra. New Delhi, India: Affiliated East East-West Press Pvt Ltd., 2003.

2. S. Lang, Introduction to Linear Algebra, 2nd ed., New York: Springer-Verlag, 2005.

3. S. H. Friedberg, A. Insel, and L. Spence, Linear algebra, 4th ed., Pearson, 2015.

4. Gilbert Strang, Linear Algebra and its Applications, 4th ed., Thomson Brooks/Cole, 2007.

5. K. Hoffmann and R. A. Kunze, Linear algebra, 2nd ed., PHI Learning, 2014.

Course Description: This course aims at providing a solid foundation upon the fundamental theories on Fourier and Laplace transforms.

Course objectives​: This course will help the learner to

COBJ1. gain familiarity in fundamental theories of the Fourier series, Fourier Integrals, Fourier and Laplace transforms.
COBJ2. acquire problem solving skills in using Fourier Series, Fourier and Laplace transforms.

Fourier series and Fourier transform of some common functions. The Fourier integral, complex Fourier transforms, basic properties, transform of the derivative, convolution theorem, and Parseval’s identity. The applications of Fourier transform to ordinary differential equations.

Fourier series and Fourier transform of some common functions. The Fourier integral, complex Fourier transforms, basic properties, transform of the derivative, convolution theorem, and Parseval’s identity. The applications of Fourier transform to ordinary differential equations.

Fourier series and Fourier transform of some common functions. The Fourier integral, complex Fourier transforms, basic properties, transform of the derivative, convolution theorem, and Parseval’s identity. The applications of Fourier transform to ordinary differential equations.

Fourier series and Fourier transform of some common functions. The Fourier integral, complex Fourier transforms, basic properties, transform of the derivative, convolution theorem, and Parseval’s identity. The applications of Fourier transform to ordinary differential equations.

Fourier series and Fourier transform of some common functions. The Fourier integral, complex Fourier transforms, basic properties, transform of the derivative, convolution theorem, and Parseval’s identity. The applications of Fourier transform to ordinary differential equations.

Fourier cosine and sine transforms with examples, properties of Fourier Cosine and Sine Transforms, applications of Fourier sine and cosine transforms with examples.

Fourier cosine and sine transforms with examples, properties of Fourier Cosine and Sine Transforms, applications of Fourier sine and cosine transforms with examples.

Fourier cosine and sine transforms with examples, properties of Fourier Cosine and Sine Transforms, applications of Fourier sine and cosine transforms with examples.

Fourier cosine and sine transforms with examples, properties of Fourier Cosine and Sine Transforms, applications of Fourier sine and cosine transforms with examples.

Fourier cosine and sine transforms with examples, properties of Fourier Cosine and Sine Transforms, applications of Fourier sine and cosine transforms with examples.

Laplace Transform of standard functions, Laplace transform of periodic functions, Inverse Laplace transform, solution of ordinary differential equation with constant coefficient using Laplace transform, solution of simultaneous Ordinary differential equations.

Laplace Transform of standard functions, Laplace transform of periodic functions, Inverse Laplace transform, solution of ordinary differential equation with constant coefficient using Laplace transform, solution of simultaneous Ordinary differential equations.

Laplace Transform of standard functions, Laplace transform of periodic functions, Inverse Laplace transform, solution of ordinary differential equation with constant coefficient using Laplace transform, solution of simultaneous Ordinary differential equations.

Laplace Transform of standard functions, Laplace transform of periodic functions, Inverse Laplace transform, solution of ordinary differential equation with constant coefficient using Laplace transform, solution of simultaneous Ordinary differential equations.

Laplace Transform of standard functions, Laplace transform of periodic functions, Inverse Laplace transform, solution of ordinary differential equation with constant coefficient using Laplace transform, solution of simultaneous Ordinary differential equations.

Course Description: This course is concerned with the fundamentals of mathematical modeling. It deals with finding solution to real world problems by transforming into mathematical models using differential equations. The coverage includes mathematical modeling through first order, second order and system of ordinary differential equations.

 Course objectives​: This course will help the learner to

This course will help the learner to

COBJ1.  interpret the real-world problems in the form of first and second order differential equations. 

COBJ2.  familiarize with some classical linear and nonlinear models. 

COBJ3.  analyse the solutions of systems of differential equations by phase portrait method.

Population Dynamics, Carbon dating, Newtons law of cooling, Epidemics, Economics, Medicine, mixture problem, electric circuit problem, Chemical reactions, Terminal velocity, Continuously compounding of interest.

Population Dynamics, Carbon dating, Newtons law of cooling, Epidemics, Economics, Medicine, mixture problem, electric circuit problem, Chemical reactions, Terminal velocity, Continuously compounding of interest.

Population Dynamics, Carbon dating, Newtons law of cooling, Epidemics, Economics, Medicine, mixture problem, electric circuit problem, Chemical reactions, Terminal velocity, Continuously compounding of interest.

Population Dynamics, Carbon dating, Newtons law of cooling, Epidemics, Economics, Medicine, mixture problem, electric circuit problem, Chemical reactions, Terminal velocity, Continuously compounding of interest.

Population Dynamics, Carbon dating, Newtons law of cooling, Epidemics, Economics, Medicine, mixture problem, electric circuit problem, Chemical reactions, Terminal velocity, Continuously compounding of interest.

Population Dynamics, Carbon dating, Newtons law of cooling, Epidemics, Economics, Medicine, mixture problem, electric circuit problem, Chemical reactions, Terminal velocity, Continuously compounding of interest.

Population Dynamics, Carbon dating, Newtons law of cooling, Epidemics, Economics, Medicine, mixture problem, electric circuit problem, Chemical reactions, Terminal velocity, Continuously compounding of interest.

The vibrations of a mass on a spring, free damped motion, forced motion, resonance phenomena, electric circuit problem, Nonlinear-Pendulum.

The vibrations of a mass on a spring, free damped motion, forced motion, resonance phenomena, electric circuit problem, Nonlinear-Pendulum.

The vibrations of a mass on a spring, free damped motion, forced motion, resonance phenomena, electric circuit problem, Nonlinear-Pendulum.

The vibrations of a mass on a spring, free damped motion, forced motion, resonance phenomena, electric circuit problem, Nonlinear-Pendulum.

The vibrations of a mass on a spring, free damped motion, forced motion, resonance phenomena, electric circuit problem, Nonlinear-Pendulum.

The vibrations of a mass on a spring, free damped motion, forced motion, resonance phenomena, electric circuit problem, Nonlinear-Pendulum.

The vibrations of a mass on a spring, free damped motion, forced motion, resonance phenomena, electric circuit problem, Nonlinear-Pendulum.

Phase plane analysis: Phase Portrait for Linear and Non-Linear Systems, Stability Analysis of Solution, Applications, Predator prey model: Lotka-Volterra Model, Kermack-McKendrick Model, Predator-Prey Model and Harvesting Analysis, Competitive-Hunter Model, Combat models: Lanchester Model, Battle of IWO Jima, Battle of Vietnam, Battle of Trafalgar., Mixture Models, Epidemics-SIR model, Economics.

Phase plane analysis: Phase Portrait for Linear and Non-Linear Systems, Stability Analysis of Solution, Applications, Predator prey model: Lotka-Volterra Model, Kermack-McKendrick Model, Predator-Prey Model and Harvesting Analysis, Competitive-Hunter Model, Combat models: Lanchester Model, Battle of IWO Jima, Battle of Vietnam, Battle of Trafalgar., Mixture Models, Epidemics-SIR model, Economics.

Phase plane analysis: Phase Portrait for Linear and Non-Linear Systems, Stability Analysis of Solution, Applications, Predator prey model: Lotka-Volterra Model, Kermack-McKendrick Model, Predator-Prey Model and Harvesting Analysis, Competitive-Hunter Model, Combat models: Lanchester Model, Battle of IWO Jima, Battle of Vietnam, Battle of Trafalgar., Mixture Models, Epidemics-SIR model, Economics.

Phase plane analysis: Phase Portrait for Linear and Non-Linear Systems, Stability Analysis of Solution, Applications, Predator prey model: Lotka-Volterra Model, Kermack-McKendrick Model, Predator-Prey Model and Harvesting Analysis, Competitive-Hunter Model, Combat models: Lanchester Model, Battle of IWO Jima, Battle of Vietnam, Battle of Trafalgar., Mixture Models, Epidemics-SIR model, Economics.

Phase plane analysis: Phase Portrait for Linear and Non-Linear Systems, Stability Analysis of Solution, Applications, Predator prey model: Lotka-Volterra Model, Kermack-McKendrick Model, Predator-Prey Model and Harvesting Analysis, Competitive-Hunter Model, Combat models: Lanchester Model, Battle of IWO Jima, Battle of Vietnam, Battle of Trafalgar., Mixture Models, Epidemics-SIR model, Economics.

Phase plane analysis: Phase Portrait for Linear and Non-Linear Systems, Stability Analysis of Solution, Applications, Predator prey model: Lotka-Volterra Model, Kermack-McKendrick Model, Predator-Prey Model and Harvesting Analysis, Competitive-Hunter Model, Combat models: Lanchester Model, Battle of IWO Jima, Battle of Vietnam, Battle of Trafalgar., Mixture Models, Epidemics-SIR model, Economics.

Phase plane analysis: Phase Portrait for Linear and Non-Linear Systems, Stability Analysis of Solution, Applications, Predator prey model: Lotka-Volterra Model, Kermack-McKendrick Model, Predator-Prey Model and Harvesting Analysis, Competitive-Hunter Model, Combat models: Lanchester Model, Battle of IWO Jima, Battle of Vietnam, Battle of Trafalgar., Mixture Models, Epidemics-SIR model, Economics.

Course Description: This course is an introductory course to the basic concepts of Graph Theory. This includes a definition of graphs, types of graphs, paths, circuits, trees, shortest paths, and algorithms to find shortest paths.

Course objectives: This course will help the learner to

COBJ 1. gain conceptual knowledge on terminologies used in graph theory.

COBJ 2. understand the results on graphs and their properties.

COBJ 3. gain proof writing and algorithm writing skills.

Graphs, connected graphs, classes of graphs, regular graphs, degree sequences, matrices, isomorphic graphs.

Graphs, connected graphs, classes of graphs, regular graphs, degree sequences, matrices, isomorphic graphs.

Graphs, connected graphs, classes of graphs, regular graphs, degree sequences, matrices, isomorphic graphs.

Graphs, connected graphs, classes of graphs, regular graphs, degree sequences, matrices, isomorphic graphs.

Graphs, connected graphs, classes of graphs, regular graphs, degree sequences, matrices, isomorphic graphs.

Graphs, connected graphs, classes of graphs, regular graphs, degree sequences, matrices, isomorphic graphs.

Graphs, connected graphs, classes of graphs, regular graphs, degree sequences, matrices, isomorphic graphs.

Bridges, trees, minimum spanning trees, cut-vertices, blocks, traversability, Eulerian and Hamiltonian graphs, digraphs. 

Bridges, trees, minimum spanning trees, cut-vertices, blocks, traversability, Eulerian and Hamiltonian graphs, digraphs. 

Bridges, trees, minimum spanning trees, cut-vertices, blocks, traversability, Eulerian and Hamiltonian graphs, digraphs. 

Bridges, trees, minimum spanning trees, cut-vertices, blocks, traversability, Eulerian and Hamiltonian graphs, digraphs. 

Bridges, trees, minimum spanning trees, cut-vertices, blocks, traversability, Eulerian and Hamiltonian graphs, digraphs. 

Bridges, trees, minimum spanning trees, cut-vertices, blocks, traversability, Eulerian and Hamiltonian graphs, digraphs. 

Bridges, trees, minimum spanning trees, cut-vertices, blocks, traversability, Eulerian and Hamiltonian graphs, digraphs. 

Matching, factorizations, decompositions, graceful labeling, planar graphs, Embedding graphs on surfaces.

Matching, factorizations, decompositions, graceful labeling, planar graphs, Embedding graphs on surfaces.

Matching, factorizations, decompositions, graceful labeling, planar graphs, Embedding graphs on surfaces.

Matching, factorizations, decompositions, graceful labeling, planar graphs, Embedding graphs on surfaces.

Matching, factorizations, decompositions, graceful labeling, planar graphs, Embedding graphs on surfaces.

Matching, factorizations, decompositions, graceful labeling, planar graphs, Embedding graphs on surfaces.

Matching, factorizations, decompositions, graceful labeling, planar graphs, Embedding graphs on surfaces.

Course Description​: This course aims to enlighten students with the fundamental concepts of vectors, geometry of space, partial differentiation and vector analysis such as gradient, divergence, curl, and the evaluation of line, surface and volume integrals. The three classical theorems, viz., Green’s theorem, Gauss divergence theorem and Stoke’s theorem are also covered.

Course objectives​: This course will help the learner to 

COBJ 1. gain familiarity with the fundamental concepts of vectors and geometry of space  Curves.

COBJ 2. illustrates and interprets differential and integral calculus of vector fields 

COBJ 3. demonstrate the use Green’s Theorem, Stokes Theorem, and Gauss’ divergence Theorem

Fundamentals: Three-dimensional coordination systems, Vectors and vector operations, Line and planes in space, Curves in space and their tangents, Integrals of vector functions, Arc length in space, Curvature and normal vectors of a space, TNB frame, Directional derivatives and gradient  vectors, Divergence and curl of vector valued functions.

Fundamentals: Three-dimensional coordination systems, Vectors and vector operations, Line and planes in space, Curves in space and their tangents, Integrals of vector functions, Arc length in space, Curvature and normal vectors of a space, TNB frame, Directional derivatives and gradient  vectors, Divergence and curl of vector valued functions.

Fundamentals: Three-dimensional coordination systems, Vectors and vector operations, Line and planes in space, Curves in space and their tangents, Integrals of vector functions, Arc length in space, Curvature and normal vectors of a space, TNB frame, Directional derivatives and gradient  vectors, Divergence and curl of vector valued functions.

Fundamentals: Three-dimensional coordination systems, Vectors and vector operations, Line and planes in space, Curves in space and their tangents, Integrals of vector functions, Arc length in space, Curvature and normal vectors of a space, TNB frame, Directional derivatives and gradient  vectors, Divergence and curl of vector valued functions.

Fundamentals: Three-dimensional coordination systems, Vectors and vector operations, Line and planes in space, Curves in space and their tangents, Integrals of vector functions, Arc length in space, Curvature and normal vectors of a space, TNB frame, Directional derivatives and gradient  vectors, Divergence and curl of vector valued functions.

Double Integrals- Areas, Moments, and Centres of Mass – Double Integrals in Polar Form –Triple Integrals in Rectangular Coordinates, Masses and Moments in Three Dimensions, Triple Integrals in Cylindrical and Spherical Coordinates, Substitutions in Multiple Integrals.

Double Integrals- Areas, Moments, and Centres of Mass – Double Integrals in Polar Form –Triple Integrals in Rectangular Coordinates, Masses and Moments in Three Dimensions, Triple Integrals in Cylindrical and Spherical Coordinates, Substitutions in Multiple Integrals.

Double Integrals- Areas, Moments, and Centres of Mass – Double Integrals in Polar Form –Triple Integrals in Rectangular Coordinates, Masses and Moments in Three Dimensions, Triple Integrals in Cylindrical and Spherical Coordinates, Substitutions in Multiple Integrals.

Double Integrals- Areas, Moments, and Centres of Mass – Double Integrals in Polar Form –Triple Integrals in Rectangular Coordinates, Masses and Moments in Three Dimensions, Triple Integrals in Cylindrical and Spherical Coordinates, Substitutions in Multiple Integrals.

Double Integrals- Areas, Moments, and Centres of Mass – Double Integrals in Polar Form –Triple Integrals in Rectangular Coordinates, Masses and Moments in Three Dimensions, Triple Integrals in Cylindrical and Spherical Coordinates, Substitutions in Multiple Integrals.

Line Integrals, Vector Fields, Work, Circulation and Flux, Path Independence, Potential Functions, and Conservative Fields, Green’s Theorem in the Plane, Surface Area and Surface  Integrals, Parametrized Surfaces, Stokes’ Theorem, The Divergence Theorem.

Line Integrals, Vector Fields, Work, Circulation and Flux, Path Independence, Potential Functions, and Conservative Fields, Green’s Theorem in the Plane, Surface Area and Surface  Integrals, Parametrized Surfaces, Stokes’ Theorem, The Divergence Theorem.

Line Integrals, Vector Fields, Work, Circulation and Flux, Path Independence, Potential Functions, and Conservative Fields, Green’s Theorem in the Plane, Surface Area and Surface  Integrals, Parametrized Surfaces, Stokes’ Theorem, The Divergence Theorem.

Line Integrals, Vector Fields, Work, Circulation and Flux, Path Independence, Potential Functions, and Conservative Fields, Green’s Theorem in the Plane, Surface Area and Surface  Integrals, Parametrized Surfaces, Stokes’ Theorem, The Divergence Theorem.

Line Integrals, Vector Fields, Work, Circulation and Flux, Path Independence, Potential Functions, and Conservative Fields, Green’s Theorem in the Plane, Surface Area and Surface  Integrals, Parametrized Surfaces, Stokes’ Theorem, The Divergence Theorem.

Course description: Operations research deals with the problems on optimization or decision making that are affected by certain constraints / restrictions in the environment. This course aims at teaching solution techniques of solving linear programming models, simple queuing model, two-person zero sum games and Network models.

Course objectives: This course will help the learner to

COBJ1. gain an insight executing the algorithms for solving linear programming problems including transportation and assignment problems.

COBJ2. learn about the techniques involved in solving the two person zero sum game.

COBJ3. calculate the estimates that characteristics the queues and perform desired analysis on a network.

Introduction to simplex algorithm –Special cases in the Simplex Method –Definition of the Dual Problem – Primal Dual relationships – Dual simplex methods. Transportation Models: Determination of the starting solution – iterative computations of the transportation algorithm. Assignment Model: The Hungarian Method.

Introduction to simplex algorithm –Special cases in the Simplex Method –Definition of the Dual Problem – Primal Dual relationships – Dual simplex methods. Transportation Models: Determination of the starting solution – iterative computations of the transportation algorithm. Assignment Model: The Hungarian Method.

Introduction to simplex algorithm –Special cases in the Simplex Method –Definition of the Dual Problem – Primal Dual relationships – Dual simplex methods. Transportation Models: Determination of the starting solution – iterative computations of the transportation algorithm. Assignment Model: The Hungarian Method.

Introduction to simplex algorithm –Special cases in the Simplex Method –Definition of the Dual Problem – Primal Dual relationships – Dual simplex methods. Transportation Models: Determination of the starting solution – iterative computations of the transportation algorithm. Assignment Model: The Hungarian Method.

Introduction to simplex algorithm –Special cases in the Simplex Method –Definition of the Dual Problem – Primal Dual relationships – Dual simplex methods. Transportation Models: Determination of the starting solution – iterative computations of the transportation algorithm. Assignment Model: The Hungarian Method.

Introduction to simplex algorithm –Special cases in the Simplex Method –Definition of the Dual Problem – Primal Dual relationships – Dual simplex methods. Transportation Models: Determination of the starting solution – iterative computations of the transportation algorithm. Assignment Model: The Hungarian Method.

Introduction to simplex algorithm –Special cases in the Simplex Method –Definition of the Dual Problem – Primal Dual relationships – Dual simplex methods. Transportation Models: Determination of the starting solution – iterative computations of the transportation algorithm. Assignment Model: The Hungarian Method.

Elements of a queuing Model – Pure Birth Model – Pure Death Model –Specialized Poisson Queues – Steady state Models: (M/M/1):(GD/∞/∞) – (M/M/1):(FCFS/∞/∞) - (M/M/1):(GD/N/∞) – (M/M/c):(GD/∞/∞) –  (M/M/∞):(GD/∞/∞).

Game Theory: Optimal solution of two person zero-sum games – Solution of Mixed strategy Games (only Linear programming solution).

Elements of a queuing Model – Pure Birth Model – Pure Death Model –Specialized Poisson Queues – Steady state Models: (M/M/1):(GD/∞/∞) – (M/M/1):(FCFS/∞/∞) - (M/M/1):(GD/N/∞) – (M/M/c):(GD/∞/∞) –  (M/M/∞):(GD/∞/∞).

Game Theory: Optimal solution of two person zero-sum games – Solution of Mixed strategy Games (only Linear programming solution).

Elements of a queuing Model – Pure Birth Model – Pure Death Model –Specialized Poisson Queues – Steady state Models: (M/M/1):(GD/∞/∞) – (M/M/1):(FCFS/∞/∞) - (M/M/1):(GD/N/∞) – (M/M/c):(GD/∞/∞) –  (M/M/∞):(GD/∞/∞).

Game Theory: Optimal solution of two person zero-sum games – Solution of Mixed strategy Games (only Linear programming solution).

Elements of a queuing Model – Pure Birth Model – Pure Death Model –Specialized Poisson Queues – Steady state Models: (M/M/1):(GD/∞/∞) – (M/M/1):(FCFS/∞/∞) - (M/M/1):(GD/N/∞) – (M/M/c):(GD/∞/∞) –  (M/M/∞):(GD/∞/∞).

Game Theory: Optimal solution of two person zero-sum games – Solution of Mixed strategy Games (only Linear programming solution).

Elements of a queuing Model – Pure Birth Model – Pure Death Model –Specialized Poisson Queues – Steady state Models: (M/M/1):(GD/∞/∞) – (M/M/1):(FCFS/∞/∞) - (M/M/1):(GD/N/∞) – (M/M/c):(GD/∞/∞) –  (M/M/∞):(GD/∞/∞).

Game Theory: Optimal solution of two person zero-sum games – Solution of Mixed strategy Games (only Linear programming solution).

Elements of a queuing Model – Pure Birth Model – Pure Death Model –Specialized Poisson Queues – Steady state Models: (M/M/1):(GD/∞/∞) – (M/M/1):(FCFS/∞/∞) - (M/M/1):(GD/N/∞) – (M/M/c):(GD/∞/∞) –  (M/M/∞):(GD/∞/∞).

Game Theory: Optimal solution of two person zero-sum games – Solution of Mixed strategy Games (only Linear programming solution).

Elements of a queuing Model – Pure Birth Model – Pure Death Model –Specialized Poisson Queues – Steady state Models: (M/M/1):(GD/∞/∞) – (M/M/1):(FCFS/∞/∞) - (M/M/1):(GD/N/∞) – (M/M/c):(GD/∞/∞) –  (M/M/∞):(GD/∞/∞).

Game Theory: Optimal solution of two person zero-sum games – Solution of Mixed strategy Games (only Linear programming solution).

Linear programming formulation of the shortest-route Problem. Maximal Flow model:- Enumeration of cuts – Maximal Flow Algorithm – Linear Programming Formulation of Maximal Flow Model. CPM and PERT:- Network Representation – Critical path computations – Construction of the Time Schedule – Linear Programming formulation of CPM – PERT calculations.

Linear programming formulation of the shortest-route Problem. Maximal Flow model:- Enumeration of cuts – Maximal Flow Algorithm – Linear Programming Formulation of Maximal Flow Model. CPM and PERT:- Network Representation – Critical path computations – Construction of the Time Schedule – Linear Programming formulation of CPM – PERT calculations.

Linear programming formulation of the shortest-route Problem. Maximal Flow model:- Enumeration of cuts – Maximal Flow Algorithm – Linear Programming Formulation of Maximal Flow Model. CPM and PERT:- Network Representation – Critical path computations – Construction of the Time Schedule – Linear Programming formulation of CPM – PERT calculations.

Linear programming formulation of the shortest-route Problem. Maximal Flow model:- Enumeration of cuts – Maximal Flow Algorithm – Linear Programming Formulation of Maximal Flow Model. CPM and PERT:- Network Representation – Critical path computations – Construction of the Time Schedule – Linear Programming formulation of CPM – PERT calculations.

Linear programming formulation of the shortest-route Problem. Maximal Flow model:- Enumeration of cuts – Maximal Flow Algorithm – Linear Programming Formulation of Maximal Flow Model. CPM and PERT:- Network Representation – Critical path computations – Construction of the Time Schedule – Linear Programming formulation of CPM – PERT calculations.

Linear programming formulation of the shortest-route Problem. Maximal Flow model:- Enumeration of cuts – Maximal Flow Algorithm – Linear Programming Formulation of Maximal Flow Model. CPM and PERT:- Network Representation – Critical path computations – Construction of the Time Schedule – Linear Programming formulation of CPM – PERT calculations.

Linear programming formulation of the shortest-route Problem. Maximal Flow model:- Enumeration of cuts – Maximal Flow Algorithm – Linear Programming Formulation of Maximal Flow Model. CPM and PERT:- Network Representation – Critical path computations – Construction of the Time Schedule – Linear Programming formulation of CPM – PERT calculations.

Course description: This course aims at providing hands on experience in using Python functions to illustrate the notions vector space, linear independence, linear dependence, linear transformation and rank.

Course objectives: This course will help the learner to

COBJ1. The built in functions required to deal with vectors and Linear Transformations.

COBJ2. Python skills to handle vectors using the properties of vector spaces and linear transformations

1. Operations on matrices
2. Finding rank of matrices
   
3. Reducing a matrix to Echelon form
4. Inverse of a matrix by different methods
5. Solving system of equations using various methods
6. Finding eigenvalues and eigenvectors of a matrix
7. Expressing a vector as a linear combination of given set of vectors
8. Linear span, linear independence and linear dependence
9. Linear transformations and plotting of linear transformations
10. Applications of Rank-Nullity Theorem

1. Operations on matrices
2. Finding rank of matrices
   
3. Reducing a matrix to Echelon form
4. Inverse of a matrix by different methods
5. Solving system of equations using various methods
6. Finding eigenvalues and eigenvectors of a matrix
7. Expressing a vector as a linear combination of given set of vectors
8. Linear span, linear independence and linear dependence
9. Linear transformations and plotting of linear transformations
10. Applications of Rank-Nullity Theorem

1. Operations on matrices
2. Finding rank of matrices
   
3. Reducing a matrix to Echelon form
4. Inverse of a matrix by different methods
5. Solving system of equations using various methods
6. Finding eigenvalues and eigenvectors of a matrix
7. Expressing a vector as a linear combination of given set of vectors
8. Linear span, linear independence and linear dependence
9. Linear transformations and plotting of linear transformations
10. Applications of Rank-Nullity Theorem

1. Operations on matrices
2. Finding rank of matrices
   
3. Reducing a matrix to Echelon form
4. Inverse of a matrix by different methods
5. Solving system of equations using various methods
6. Finding eigenvalues and eigenvectors of a matrix
7. Expressing a vector as a linear combination of given set of vectors
8. Linear span, linear independence and linear dependence
9. Linear transformations and plotting of linear transformations
10. Applications of Rank-Nullity Theorem

1. Operations on matrices
2. Finding rank of matrices
   
3. Reducing a matrix to Echelon form
4. Inverse of a matrix by different methods
5. Solving system of equations using various methods
6. Finding eigenvalues and eigenvectors of a matrix
7. Expressing a vector as a linear combination of given set of vectors
8. Linear span, linear independence and linear dependence
9. Linear transformations and plotting of linear transformations
10. Applications of Rank-Nullity Theorem

1. Operations on matrices
2. Finding rank of matrices
   
3. Reducing a matrix to Echelon form
4. Inverse of a matrix by different methods
5. Solving system of equations using various methods
6. Finding eigenvalues and eigenvectors of a matrix
7. Expressing a vector as a linear combination of given set of vectors
8. Linear span, linear independence and linear dependence
9. Linear transformations and plotting of linear transformations
10. Applications of Rank-Nullity Theorem

1. Operations on matrices
2. Finding rank of matrices
   
3. Reducing a matrix to Echelon form
4. Inverse of a matrix by different methods
5. Solving system of equations using various methods
6. Finding eigenvalues and eigenvectors of a matrix
7. Expressing a vector as a linear combination of given set of vectors
8. Linear span, linear independence and linear dependence
9. Linear transformations and plotting of linear transformations
10. Applications of Rank-Nullity Theorem

This course will help students to gain skills in using Python to illustrate Fourier transforms, Laplace transforms for some standard functions and implementing Laplace transforms in solving ordinary differential equations of first and second order with constant coefficient.

Course Objectives​: This course will help the learner to

COBJ1. code python language using jupyter interface.

COBJ2. use built in functions required to deal with Fourier and Laplace transforms.

COBJ3. calculate Inverse Laplace transforms and the inverse Fourier transforms of standard functions using sympy.integrals

1.  Fourier series using sympy and numpy.
2.  Practical harmonic analysis using math, sympy and numpy.
3.  Fourier cosine and Fourier sine transforms using sympy and math.
4.  Discrete Fourier transform using Python.
5.  Laplace transforms using sympy, sympy.integrals and sympy.abc.
6.  Inverse Laplace transforms using sympy, sympy.integrals and sympy.abc.
7. Inverse Fourier transforms using sympy, sympy.integrals and sympy.abc.

1.  Fourier series using sympy and numpy.
2.  Practical harmonic analysis using math, sympy and numpy.
3.  Fourier cosine and Fourier sine transforms using sympy and math.
4.  Discrete Fourier transform using Python.
5.  Laplace transforms using sympy, sympy.integrals and sympy.abc.
6.  Inverse Laplace transforms using sympy, sympy.integrals and sympy.abc.
7. Inverse Fourier transforms using sympy, sympy.integrals and sympy.abc.

1.  Fourier series using sympy and numpy.
2.  Practical harmonic analysis using math, sympy and numpy.
3.  Fourier cosine and Fourier sine transforms using sympy and math.
4.  Discrete Fourier transform using Python.
5.  Laplace transforms using sympy, sympy.integrals and sympy.abc.
6.  Inverse Laplace transforms using sympy, sympy.integrals and sympy.abc.
7. Inverse Fourier transforms using sympy, sympy.integrals and sympy.abc.

1.  Fourier series using sympy and numpy.
2.  Practical harmonic analysis using math, sympy and numpy.
3.  Fourier cosine and Fourier sine transforms using sympy and math.
4.  Discrete Fourier transform using Python.
5.  Laplace transforms using sympy, sympy.integrals and sympy.abc.
6.  Inverse Laplace transforms using sympy, sympy.integrals and sympy.abc.
7. Inverse Fourier transforms using sympy, sympy.integrals and sympy.abc.

1.  Fourier series using sympy and numpy.
2.  Practical harmonic analysis using math, sympy and numpy.
3.  Fourier cosine and Fourier sine transforms using sympy and math.
4.  Discrete Fourier transform using Python.
5.  Laplace transforms using sympy, sympy.integrals and sympy.abc.
6.  Inverse Laplace transforms using sympy, sympy.integrals and sympy.abc.
7. Inverse Fourier transforms using sympy, sympy.integrals and sympy.abc.

Course description: This course provides students with an understanding of the practical and theoretical aspects of mathematical models involving ordinary differential equations (ODEs) using Python programming.

Course objectives:

This course will help the learner to 

COBJ1. various models spanning disciplines such as physics, biology, engineering, and finance. 

COBJ2. develop the basic understanding of differential equations and skills to implement numerical algorithms to solve mathematical problems using Python.

1. Growth of a population – Linear growth, Exponential growth, Logistic growth
2. Decay Model - Radioactive Decay
3. Numerical Methods
4. A Simple Pendulum
5. Spreading of a Disease
6. Mixture problems
7. Trajectory of a ball
8. Spring mass system
9. Electrical Circuits

1. Growth of a population – Linear growth, Exponential growth, Logistic growth
2. Decay Model - Radioactive Decay
3. Numerical Methods
4. A Simple Pendulum
5. Spreading of a Disease
6. Mixture problems
7. Trajectory of a ball
8. Spring mass system
9. Electrical Circuits

1. Growth of a population – Linear growth, Exponential growth, Logistic growth
2. Decay Model - Radioactive Decay
3. Numerical Methods
4. A Simple Pendulum
5. Spreading of a Disease
6. Mixture problems
7. Trajectory of a ball
8. Spring mass system
9. Electrical Circuits

1. Growth of a population – Linear growth, Exponential growth, Logistic growth
2. Decay Model - Radioactive Decay
3. Numerical Methods
4. A Simple Pendulum
5. Spreading of a Disease
6. Mixture problems
7. Trajectory of a ball
8. Spring mass system
9. Electrical Circuits

1. Growth of a population – Linear growth, Exponential growth, Logistic growth
2. Decay Model - Radioactive Decay
3. Numerical Methods
4. A Simple Pendulum
5. Spreading of a Disease
6. Mixture problems
7. Trajectory of a ball
8. Spring mass system
9. Electrical Circuits

1. Growth of a population – Linear growth, Exponential growth, Logistic growth
2. Decay Model - Radioactive Decay
3. Numerical Methods
4. A Simple Pendulum
5. Spreading of a Disease
6. Mixture problems
7. Trajectory of a ball
8. Spring mass system
9. Electrical Circuits

1. Growth of a population – Linear growth, Exponential growth, Logistic growth
2. Decay Model - Radioactive Decay
3. Numerical Methods
4. A Simple Pendulum
5. Spreading of a Disease
6. Mixture problems
7. Trajectory of a ball
8. Spring mass system
9. Electrical Circuits

Course description: The course graph theory using Python is aimed at enabling the students to appreciate and understand core concepts of graph theory with the help of technological tools. It is designed with a learner-centric approach wherein the students will understand the concepts of graph theory using programming tools and develop computational skills.

Course objectives: This course will help the learner to

COBJ1. gain familiarity in Python language using jupyter interface and NetworkX package

COBJ2. construct graphs and analyze their structural properties.

COBJ3. implement standard algorithms for shortest paths, minimal spanning trees and graph searching..

1. Introduction to NetworkX package
2. Construction of graphs
3. Degree and distance related parameters
4. In-built functions for different graph classes
5. Computation of graph parameters using in-built functions
6. Graph Operations and Graph Connectivity
7. Customization of Graphs
8. Digraphs
9. Matrices and Algorithms of Graphs
10. Graph as models.

1. Introduction to NetworkX package
2. Construction of graphs
3. Degree and distance related parameters
4. In-built functions for different graph classes
5. Computation of graph parameters using in-built functions
6. Graph Operations and Graph Connectivity
7. Customization of Graphs
8. Digraphs
9. Matrices and Algorithms of Graphs
10. Graph as models.

1. Introduction to NetworkX package
2. Construction of graphs
3. Degree and distance related parameters
4. In-built functions for different graph classes
5. Computation of graph parameters using in-built functions
6. Graph Operations and Graph Connectivity
7. Customization of Graphs
8. Digraphs
9. Matrices and Algorithms of Graphs
10. Graph as models.

1. Introduction to NetworkX package
2. Construction of graphs
3. Degree and distance related parameters
4. In-built functions for different graph classes
5. Computation of graph parameters using in-built functions
6. Graph Operations and Graph Connectivity
7. Customization of Graphs
8. Digraphs
9. Matrices and Algorithms of Graphs
10. Graph as models.

1. Introduction to NetworkX package
2. Construction of graphs
3. Degree and distance related parameters
4. In-built functions for different graph classes
5. Computation of graph parameters using in-built functions
6. Graph Operations and Graph Connectivity
7. Customization of Graphs
8. Digraphs
9. Matrices and Algorithms of Graphs
10. Graph as models.

1. Introduction to NetworkX package
2. Construction of graphs
3. Degree and distance related parameters
4. In-built functions for different graph classes
5. Computation of graph parameters using in-built functions
6. Graph Operations and Graph Connectivity
7. Customization of Graphs
8. Digraphs
9. Matrices and Algorithms of Graphs
10. Graph as models.

1. Introduction to NetworkX package
2. Construction of graphs
3. Degree and distance related parameters
4. In-built functions for different graph classes
5. Computation of graph parameters using in-built functions
6. Graph Operations and Graph Connectivity
7. Customization of Graphs
8. Digraphs
9. Matrices and Algorithms of Graphs
10. Graph as models.

Course description: The course calculus of several variables using python is aimed at enabling the students to explore and study the calculus with several variables in a detailed manner with the help of the mathematical packages available in Python. This course is designed with a learner-centric approach wherein the students will acquire mastery in understanding multivariate calculus using Python modules.

Course objectives: This course will help the learner to gain a familiarity with

COBJ1. skills to implement Python language in calculus of several variables

COBJ2. the built-in functions available in library to deal with problems in multivariate calculus

1. Introduction to basic commands and plotting of graph using matplotlib
2. Vectors-dot and cross products, plotting lines in two and three-dimensional space, planes and surfaces.
3. Arc length, curvature and normal vectors.
4. Curves in sphere: Tangent vectors and velocity- circular helix with velocity vectors.
5. Functions of two and three variables: graphing numerical functions of two Variables.
6. Graphing numerical functions in polar coordinates. Partial derivatives and the directional derivative.
7. The gradient vector and level curves- the tangent plane -the gradient vector field.
8. Vector fields: Normalized vector fields- two-dimensional plot of the vector field.
9. Double Integrals: User defined function for calculating double integrals - area properties with double integrals.
10. Line integrals – Curl and Green’s theorem, divergence theorem.

1. Introduction to basic commands and plotting of graph using matplotlib
2. Vectors-dot and cross products, plotting lines in two and three-dimensional space, planes and surfaces.
3. Arc length, curvature and normal vectors.
4. Curves in sphere: Tangent vectors and velocity- circular helix with velocity vectors.
5. Functions of two and three variables: graphing numerical functions of two Variables.
6. Graphing numerical functions in polar coordinates. Partial derivatives and the directional derivative.
7. The gradient vector and level curves- the tangent plane -the gradient vector field.
8. Vector fields: Normalized vector fields- two-dimensional plot of the vector field.
9. Double Integrals: User defined function for calculating double integrals - area properties with double integrals.
10. Line integrals – Curl and Green’s theorem, divergence theorem.

1. Introduction to basic commands and plotting of graph using matplotlib
2. Vectors-dot and cross products, plotting lines in two and three-dimensional space, planes and surfaces.
3. Arc length, curvature and normal vectors.
4. Curves in sphere: Tangent vectors and velocity- circular helix with velocity vectors.
5. Functions of two and three variables: graphing numerical functions of two Variables.
6. Graphing numerical functions in polar coordinates. Partial derivatives and the directional derivative.
7. The gradient vector and level curves- the tangent plane -the gradient vector field.
8. Vector fields: Normalized vector fields- two-dimensional plot of the vector field.
9. Double Integrals: User defined function for calculating double integrals - area properties with double integrals.
10. Line integrals – Curl and Green’s theorem, divergence theorem.

1. Introduction to basic commands and plotting of graph using matplotlib
2. Vectors-dot and cross products, plotting lines in two and three-dimensional space, planes and surfaces.
3. Arc length, curvature and normal vectors.
4. Curves in sphere: Tangent vectors and velocity- circular helix with velocity vectors.
5. Functions of two and three variables: graphing numerical functions of two Variables.
6. Graphing numerical functions in polar coordinates. Partial derivatives and the directional derivative.
7. The gradient vector and level curves- the tangent plane -the gradient vector field.
8. Vector fields: Normalized vector fields- two-dimensional plot of the vector field.
9. Double Integrals: User defined function for calculating double integrals - area properties with double integrals.
10. Line integrals – Curl and Green’s theorem, divergence theorem.