BAS203 : ENGINEERING MATHEMATICS-II

Course Objectives:
The objective of this course is to familiarize the prospective engineers with techniques in ordinary
differential equations, Laplace transform, sequence and series,Fourier series and complex
variables. It aims to equip the students to deal with advanced level of mathematics and applications
that would be essential for their disciplines.
The students will learn:
• The effective mathematical tools for the solutions of differential equations that model
physical processes.
• The basic knowledge of Laplace transform and its applications in solving differential
equations.
• The tool for convergence of series and expansion of function using Fourier series for
learning advanced Engineering Mathematics.
• The tools of differentiation of functions of complex variables that are used in various
techniques dealing with engineering problems.
• The tools of integration of functions of complex variables that are used in various
techniques dealing with engineering problems.
Contact
Content
Hours
Unit -1: Ordinary Differential Equation of Higher Order 8
Linear differential equation of nth order with constant coefficients, Simultaneous
linear differential equations, Second order linear differential equations with variable
coefficients, Solution by changing independent variable, Method of variation of
parameters, Cauchy-Euler equation, Application of differential equations in solving
engineering problems.
Unit-2: Laplace Transform 10
Laplace transform, Existence theorem, Properties of Laplace Transform, Laplace
transform of derivates and integrals, Unit step function, Laplace transform of
periodic function, Inverse Laplace transform, Convolution theorem. Application of
Laplace Transform to solve ordinary differential equations and simultaneous
differential equations.
Unit-3: Sequence and Series 8

Definition of Sequence and series with examples, Convergence of series, Tests for
convergence of series, Ratio test, D’ Alembert’s test, Raabe’s test, Comparison test.
Fourier series, Half range Fouriersine and cosine series.

Unit-4: Complex Variable–Differentiation 8

Functions of complex variable, Limit, Continuity and differentiability, Analytic
functions, Cauchy- Riemann equations (Cartesian and Polar form), Harmonic
function, Method to find Analytic functions, Milne’s Thompson Method, Conformal
mapping, Mobius transformation and their properties.
Unit-5: Complex Variable –Integration 8
Complex integration, Cauchy- Integral theorem, Cauchy integral formula, Taylor’s
and Laurent’s series, singularities and itsclassification, zeros of analytic functions,
Residues, Cauchy’s Residue theorem and its application.

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Course Outcomes:

Course Outcome (CO) Bloom’s

Level
At the end of this course, the students will be able to:

CO 1 Remember the concept differentiation to evaluate LDE of nth order with constant K1 &K5
coefficient and LDE with variable coefficient of 2nd order.

CO 2 Understand and apply the concept of Laplace Transform to evaluate differential K2 ,K3 & K5
equations

CO 3 Understand the concept of convergence to analyze the convergence of series and K2 & K4
expansion of the function for Fourier series.

CO 4 Apply the concept of analyticity, Harmonic function and create theimage of K3, K6& K3
function applying conformal transformation
Apply the concept of Cauchy Integral theorem, Cauchy Integralformula, K3& K5
CO 5 singularity and calculus of residue to evaluate integrals
K1 – Remember, K2 – Understand, K3 – Apply, K4 – Analyze, K5 – Evaluate, K6 – Create

Text Books:
1. B. V. Ramana, Higher Engineering Mathematics, Tata McGraw-Hill Publishing Company
Ltd., 2008.
2. B. S. Grewal, Higher Engineering Mathematics, Khanna Publisher, 2005.
3. R. K. Jain & S. R. K. Iyenger, Advance Engineering Mathematics , Narosa Publishing -
House, 2002

Reference Books:
1. E. Kreyszig, Advance Engineering Mathematics, John Wiley & Sons, 2005.
2. Peter V. O’Neil, Advance Engineering Mathematics, Thomson (Cengage) Learning, 2007.
3. Maurice D. Weir, Joel Hass, Frank R.Giordano, Thomas, Calculus, Eleventh Edition,
Pearson.
4. G.B Thomas, R L Finney, Calculus and Analytical Geometry, Ninth Edition Pearson, 2002.
5. James Ward Brown and Ruel V Churchill, Fourier Series and Boundary Value Problems,
8th Edition-McGraw-Hill
6. D. Poole, Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/Cole, 2005.
7. Veerarajan T., Engineering Mathematics for first year, McGraw-Hill, New Delhi, 2008.
8. Charles E Roberts Jr, Ordinary Diffrential Equations, Application, Model and Computing,
CRC Press T&F Group.
9. Ray Wylie C and Louis C Barret, Advanced Engineering Mathematics, 6thEdition, McGraw-
Hill.
10. James Ward Brown and Ruel V Churchill, Complex Variable and Applications, 8th Edition,
McGraw-Hill.
11. P. Sivaramakrishna Das and C. Vijayakumari, Engineering Mathematics, 1st Edition,
Pearson India Education Services Pvt. Ltd.
12. Advanced Engineering Mathematics By Chandrika Prasad, Reena Garg Khanna Publishing
House, Delhi.
13. Laplace Transforms by Schaum’s series, 2005 Edition, Spiegel Publicaiton.

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BEE101 / BEE201: FUNDAMENTALS OF ELECTRICAL ENGINEERING

Contact
Content
Hours

Unit -1: DC Circuits 6

Electrical circuit elements (R, L and C), Concept of active and passive elements,
voltage and current sources, concept of linearity, unilateral and bilateral elements.
Kirchhoff‟s laws, Mesh and nodal methods of analysis.

Unit-2: : Steady State Analysis of Single Phase AC Circuits 6

Representation of Sinusoidal waveforms – Average and effective values, Form and

peak factors.
Analysis of single phase AC Circuits consisting R-L-C combination (Series and
Parallel) Apparent, active & reactive power, Power factor. Concept of Resonance in
series & parallel circuits, bandwidth and quality factor.
Three phase balanced circuits, voltage and current relations in star and delta
connections.

Unit-3: Transformers 6

Magnetic circuits, ideal and practical transformer, equivalent circuit, losses in

transformers, regulation and efficiency.

Unit-4: Electrical machines 8

DC machines: Principle & Construction, Types, EMF equation of generator and

torque equation of motor, applications of DC motors (simple numerical problems)
Three Phase Induction Motor: Principle & Construction, Types, Slip-torque
characteristics, Applications (Numerical problems related to slip only)
Single Phase Induction motor: Principle of operation and introduction to methods of
starting, applications.
Three Phase Synchronous Machines: Principle of operation of alternator and
synchronous motor and their applications.

Unit-5: Electrical Installations 4

Introduction of Switch Fuse Unit (SFU), MCB, ELCB, MCCB, ACB. Types of Wires,
Cables and Bus-bars. Fundamentals of earthing and lightning protection. Types of
Batteries

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Course Outcomes:

Course Outcome (CO)

CO 1 Apply the concepts of KVL/KCL and network theorems in solving DC circuits.
CO 2 Analyze the steady state behavior of single phase and three phase AC electrical circuits.
Identify the application areas of a single phase two winding transformer as well as an auto
CO 3 transformer and calculate their efficiency. Also identify the connections of a three phase
transformer.
Illustrate the working principles of induction motor, synchronous machine as well as DC
CO 4
machine and employ them in different area of applications.
Describe the components of low voltage electrical installations and perform elementary
CO 5
calculations for energy consumption.

Text Books:
1. Ritu Sahdev, “Basic Electrical Engineering”, Khanna Publishing House, 2018.
2. P.V. Prasad, S.Sivanagaraju,“Electrical Engineering:Concepts and Applications” Cengage, 2018
3. D. P. Kothari and I. J. Nagrath, “Basic Electrical Engineering”, Tata McGraw Hill, 2010.
4. D. C. Kulshreshtha, “Basic Electrical Engineering”, McGraw Hill, 2009.

Reference Books:
1. E. Hughes, “Electrical and Electronics Technology”, Pearson, 2010.
2. L. S. Bobrow, “Fundamentals of Electrical Engineering”, Oxford University Press, 2011.
3. V. D. Toro, “Electrical Engineering Fundamentals”, Pearson India, 1989.

Spoken Tutorial (MOOCs):

1. AC DC Circuit Analysis using NgSpice, Open Source Software (http://spoken-tutorial.org)

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BEC101 / BEC201 : FUNDAMENTALS OF ELECTRONICS ENGINEERING

Topics Contact
Hours

Unit-1 8

Semiconductor Diode: Depletion layer, V-I characteristics, ideal and practical Diodes,
Diode Equivalent Circuits, Zener Diodes breakdown mechanism (Zener and avalanche)
Diode Application: Diode Configuration, Half and Full Wave rectification, Clippers,
Clampers, Zener diode as shunt regulator, Voltage-Multiplier Circuits
Special Purpose two terminal Devices: Light-Emitting Diodes, Photo Diodes, Varactor
Diodes, Tunnel Diodes.

Unit-2 8

Bipolar Junction Transistor: Transistor Construction, Operation, Amplification

action. Common Base, Common Emitter, Common Collector Configuration
Field Effect Transistor: Construction and Characteristic of JFETs. Transfer
Characteristic. MOSFET (MOS) (Depletion and Enhancement) Type, Transfer
Characteristic.

Unit-3 8

Operational Amplifiers: Introduction, Op-Amp basic, Practical Op-Amp Circuits

(Inverting Amplifier, Non-inverting Amplifier, Unit Follower, Summing Amplifier,
Integrator, Differentiator).Differential and Common-Mode Operation, Comparators.

Unit-4 8

Digital Electronics: Number system & representation, Binary arithmetic, Introduction of

Basic and Universal Gates, using Boolean algebra simplification of Boolean function. K Map
Minimization upto 6 Variables.

Unit-5 8

Fundamentals of Communication Engineering: Basics of signal representation and

analysis, Electromagnetic spectrum Elements of a Communication System, Need of
modulation and typical applications, Fundamentals of amplitude modulation and
demodulation techniques.
Introduction to Wireless Communication: Overview of wireless communication,
cellular communication, different generations and standards in cellular communication
systems, Fundamentals of Satellite & Radar Communication.

Course Outcomes:
At the end of this course students will demonstrate the ability to:
1. Describe the concept of PN Junction and devices.
2. Explain the concept of BJT, FET and MOFET.
3. Apply the concept of Operational amplifier to design linear and non-linear applications.
4. Perform number systems conversions, binary arithmetic and minimize logic functions.
5. Describe the fundamentals of communication technologies.

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