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Visvesvaraya Technological University VTU
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Page-1

- Fourier Series - ( 4 - 5 )
- Periodic function - ( 6 - 17 )
- Half-Range fourier series - ( 18 - 22 )
- Harmonic Analysis - ( 23 - 27 )
- Fourier Transforms - ( 28 - 34 )
- Fourier sine,cosine and Z transforms - ( 35 - 51 )
- Difference equation - ( 52 - 55 )
- Statistical Methods, Curves Fitting, Numerical Method - ( 56 - 77 )
- Finite Difference, Numerical Integration - ( 78 - 84 )
- Interpolation - ( 85 - 96 )
- Numerical Integration - ( 97 - 99 )
- Vector Integration, Calculus Of Variation - ( 100 - 108 )

Topic:

ENGINEERING MATHEMATICS-III
15MAT31
SYLLABUS
ENGINEERING MATHEMATICS-III
SUB CODE: 15MAT31
Hrs/Week: 04
Total Hrs: 50
IA Marks:20
Exam Hrs: 03
Exam Marks: 80
MODULE-I
Fourier Series:
Periodic functions, Dirichlet’s condition, Fourier Series of Periodic functions with period
2π and with arbitrary period 2c, Fourier series of even and odd functions, Half range
Fourier Series, practical Harmonic analysis. Complex Fourier series.
MODULE-II:
Fourier Transforms: Infinite Fourier transforms, Fourier Sine and Cosine transforms,
Inverse transform.
Z-transform: Difference equations, basic definition, z-transform-definition, Standard ztransforms, Damping rule, Shifting rule, Initial value and final value theorems (without
proof) and problems, Inverse z-transform. Applications of z-transforms to solve
difference equations.
MODULE- III
Statistical Methods: Correlation and rank Correlation coefficients, Regression and
Regression coefficients, lines of regression -problems
Curve fitting: Curve fitting by the method of least squares, fitting of the curves of the
form,
y
ax b y
ax 2
bx c y
aebx y
axb
Numerical Methods: Numerical solution of algebraic and transcendental equations by:
Regular-falsi method, Secant method, Newton -Raphsonmethod and Graphical method.
MODULE IV
Finite differences: Forward and backward differences,Newton’s forward and backward
interpolation formulae. Divided differences-Newton’s divided difference formula.
Lagrange’s interpolation formula and inverse interpolation formula. Central DifferenceStirling’sand Bessel’s formulae (all formulae without proof)-Problems.
Numerical integration: Simpson’s 1/3, 3/8 rule, Weddle’s rule (without proof ) –
Problems
MODULE-V
Vector integration:
Line integrals-definition and problems, surface and volume integrals-definition, Green’s
theorem in a plane, Stokes and Gauss divergence theorem (without proof) and problems.
Calculus of Variations: Variation of function and Functional, variation problems,
Euler’s equation, Geodesics, minimal surface of revolution, hanging chain, problems
DEPT OF MATHEMATICS,SJBIT
Page 1

ENGINEERING MATHEMATICS-III
15MAT31
Course Outcomes: On completion of this course, students are able to
know the use of periodic signals and Fourier series to analyze
circuits
explain the general linear system theory for continuous-time
signals and systems using the Fourier Transform
analyze discrete-time systems using convolution and the z-transform
use appropriate numerical methods to solve algebraic and
transcendental equations and also to calculate a definite integral
Use curl and divergence of a vector function in three dimensions,
as well as apply the Green's Theorem, Divergence Theorem and
Stokes' theorem in various applications
Solve the simple problem of the calculus of variations
DEPT OF MATHEMATICS,SJBIT
Page 2

ENGINEERING MATHEMATICS-III
15MAT31
Engineering Mathematics – III
Module 1: Fourier Series
Module 2: Fourier Transforms & Z Transforms…………………………28-55
Module 3;
Module 4: Finite Difference, Numerical Integration ……………….78-99
Module 5: Vector Integration, Calculus of Variation ……………………100-108
……………………………4-27
Statistical Methods, Curve Fitting, Numerical Method ….56-77
DEPT OF MATHEMATICS,SJBIT
Page 3

ENGINEERING MATHEMATICS-III
15MAT31
MODULE- I
FOURIER SERIES
CONTENTS:
Introduction
Periodic function
Trigonometric series and Euler’s formulae
Fourier series of period 2
Fourier series of even and odd functions
Fourier series of arbitrary period
Half range Fourier series
Complex form of Fourier series
Practical Harmonic Analysis
DEPT OF MATHEMATICS,SJBIT
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