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# How to study this subject:

III SEMESTER
ENGINEERING MATHEMATICS � III
CODE: 10 MAT 31
Hrs/Week: 04
Total Hrs: 52
IA Marks: 25
Exam Hrs: 03
Exam Marks:100
PART-A
Unit-I: FOURIER SERIES
Convergence and divergence of infinite series of positive terms, definition
and illustrative examples*
Periodic functions, Dirichlet�s conditions, Fourier series of periodic functions
of period
and arbitrary period, half range Fourier series. Complex form of
Fourier Series. Practical harmonic analysis.
[7 hours]
Unit-II: FOURIER TRANSFORMS
Infinite Fourier transform, Fourier Sine and Cosine transforms, properties,
Inverse transforms
[6 hours]
Unit-III: APPLICATIONS OF PDE
Various possible solutions of one dimensional wave and heat equations, two
dimensional Laplace�s equation by the method of separation of variables,Solution of all these equations with specified boundary conditions.
D�Alembert�s solution of one dimensional wave equation.
[6 hours]
Unit-IV: CURVE FITTING AND OPTIMIZATION
Curve fitting by the method of least squares- Fitting of curves of the form
bx
b
y = ax + b, y = a x 2 + b x + c, y = a e , y = ax
Optimization: Linear programming, mathematical formulation of linear
programming problem (LPP), Graphical method and simplex method.
[7 hours]
PART-B

Unit-V: NUMERICAL METHODS - 1
Numerical Solution of algebraic and transcendental equations: Regula-falsi
method, Newton - Raphson method. Iterative methods of solution of a system
of equations: Gauss-seidel and Relaxation methods. Largest eigen value and
the corresponding eigen vector by Rayleigh�s power method.
[6 hours]
Unit-VI: NUMERICAL METHODS � 2
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.
Numerical integration: Simpson�s one-third, three-eighth and Weddle�s rules
(All formulae/rules without proof)
[7 hours]
Unit-VII: NUMERICAL METHODS � 3
Numerical solutions of PDE � finite difference approximation to derivatives,
Numerical solution of two dimensional Laplace�s equation, one dimensional
heat and wave equations
[7 hours]
Unit-VIII: DIFFERENCE EQUATIONS AND Z-TRANSFORMS

Difference equations: Basic definition; Z-transforms � definition, standard Z-
transforms, damping rule, shifting rule, initial value and final value theorems.
Inverse Z-transform. Application of Z-transforms to solve difference
equations.
[6 hours]
Note: * In the case of illustrative examples, questions are not to be set.
Text Books:
1. B.S. Grewal, Higher Engineering Mathematics, Latest edition,
Khanna Publishers
2. Erwin Kreyszig, Advanced Engineering Mathematics, Latest
edition, Wiley Publications.

# Official Notes

Maths - III - MAT31

 e-Notes Topic Subject Matter Experts Click here FOURIER SERIES Prof. A T Eshwar, PESCE, MandyaProf. N R Srinath, RNSIT, B'lore Prof. P R Hampiholi, GIT, Belgaum Click here CALCULUS OF VARIATIONS Click here LINEAR ALGEBRA Click here FOURIER TRANSFORMS Click here Numerical Analysis Click here Partial Differential Equations Click here Interpolation

# Notes from other sources

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# Model question paper

dec 06 and jan 07

JUNE.JULY-2008

JUNE.JULY-2008(2)

JUNE JULY -2007

# Previous year question paper

DEC.07 and JAN 08

# Useful links

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