SHRI SHANKARACHARYA TECHNICAL CAMPUS
SHRI SHANKARACHARYA GROUP OF INSTITUTIONS
BHILAI
(An Autonomous Institute affiliated to CSVTU,Bhilai)
Scheme of Examination and Syllabus 2021
Second Year B. Tech. (Common to All
rd Branches)
Subject Code
Evaluation Scheme
3 semester
d
SEMESTER
APPLIED MATHEMATICSIII
ESE
100
Course Objectives
L=3
T=1
P=0
Credits = 4
CT
20
TA
30
Total
150
ESE Duration
3 Hours
Course Outcomes
The objective of this course is to familiarize the On successful completion of the course, the
prospective engineers with techniques in calculus of student will be able to:
multivariable and infinite series expansion of CO 1. To have a thorough knowledge of PDE which arise in
continuous function as well as some statistical mathematical descriptions of situations in Engineering.
treatment of discrete functions. More precisely, the CO 2. To make the students understand that Fourier series
objectives are:
analysis is powerful methods where the formulas are integrals
• To instigate a thorough knowledge of partial and to have knowledge of expanding periodic functions that
differential equations which arise in mathematical explore variety of applications of Fourier series.
descriptions of situations in engineering.
CO3. To provide knowledge of Laplace transform of elementary
• To develop the tool of Fourier series for learning functions including its properties and applications to solve ordinary
advanced Engineering Mathematics.
differentials equations.
• To provide knowledge of Laplace transform of CO4. To study about a quantity that may take any of a given
elementary functions including its properties and range of values that can’t be predicted as it is but can be
applications to solve ordinary differential equations.
described in terms of their probability
• To originate a thorough study about random CO5. To provide a sound background of complex analysis to
quantities and their description in terms of their perform a thorough investigation of major theorems of complex
probability.
analysis and to apply these ideas to a wide range of problems that
• To introduce the tools of differentiation and include the evaluation of both complex line integrals and real
integration of functions of complex variable that is integrals..
used in various techniques dealing engineering
problems.
UNIT – I Partial differential equation: Formation, Solution by direct integration method,
Linear equation of first order, Homogeneous linear equation with constant coefficients, Nonhomogeneous linear equations, Method of separation of variables; Equation of vibrating string
(wave equation).
[8 Hrs]
UNIT – II Fourier Series- Euler’s formula; Functions having point of discontinuity; Change
of interval; Even and Odd function; Half range series; Harmonic Analysis.
[10Hrs]
UNIT – III Laplace transform: Definition; Transform of elementary functions; Properties of
Laplace transform; Inverse Laplace Transform (Method of partial fraction, Using properties and
Convolution theorem); Transform of Unit step function and Periodic functions; Application to the
solution of ordinary differential equations.
[10Hrs]
UNIT – IV Probability distributions: Random variable; Discrete and continuous probability
distributions; Mathematical expectation; Mean, Variance and Moments; Moment generating
functions; Probability distribution (Binomial, Poisson and Normal distributions).
[10Hrs]
Chairman (AC)
Chairman (BoS)
October 2020
Date of Release
1.00
Version
Applicable for
AY 2020-21 Onwards
SHRI SHANKARACHARYA TECHNICAL CAMPUS
SHRI SHANKARACHARYA GROUP OF INSTITUTIONS
BHILAI
(An Autonomous Institute affiliated to CSVTU,Bhilai)
Scheme of Examination and Syllabus 2021
Second Year B. Tech. (Common to All
rd Branches)
Subject Code
Evaluation Scheme
3 semester
d
SEMESTER
APPLIED MATHEMATICS-II
ESE
100
L=3
CT
20
T=1
TA
30
P=0
Total
150
Credits = 4
ESE Duration
3 Hours
UNIT – V Complex
CO5
Analysis
Analytic functions; Cauchy-Riemann equations and its applications to flow problems; Complex
integration; Cauchy theorem (without proof), Cauchy Integral formula (without proof);
Expansion of complex functions (Taylor’s and Laurent’s series); Cauchy Residue theorem
(without proof) and its application in evaluation of real definite integrals.
[10Hrs]
Text Books:
S.
No.
1)
2)
3)
4)
Title
Authors
Higher Engineering
Mathematics
Advanced Engineering
Mathematics
Advanced Engineering
Mathematics
Applied Engineering
Mathematics
Linear Algebra: A Modern
Introduction
Reference Books:
5)
S.
No.
1)
2)
3)
4)
Title
Calculus and Analytic
geometry
Engineering
Mathematics
for first year
Higher Engineering
Mathematics
A text book of Engineering
Mathematics
Edition
Publisher
Khanna
Publishers
th
28 Edition
S. Chand
H. K. Dass
2012
Publication
John Wiley &
Erwin Kreyszig 9th Edition2006 Sons
B.S. Grewal
44rd Edition 2017
Madan Mohan nd
BS Publications
2 Edition 2016
Singh
D. Poole
Authors
G. B. Thomas
and
R. L. Finney
T. Veerarajan
B. V. Ramana
N.P. Bali and
Manish Goyal
2nd Edition, 2005 Brooks/Cole
Edition
9th Edition
2002
2008
11thReprint
2010
Reprint, 2010.
Publisher
Pearson, Reprint
Tata McGrawHill, New Delhi
Tata McGraw
Hill New Delhi
Laxmi
Publications
Dr. M M Singh, Chairman(BOS)
Chairman (AC)
Chairman (BoS)
October 2020
Date of Release
1.00
Version
Applicable for
AY 2020-21 Onwards