Maths - III - MAT31 VTU notes

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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.

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Maths - III - MAT31

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dec 06 and jan 07

JUNE.JULY-2008

JUNE.JULY-2008(2)

JUNE JULY -2007

JUNE JULY-2006

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DEC.07 and JAN 08

DEC 07 and JAN 08(2)

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