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**Maths - III - MAT31 VTU notes**

# 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 TRANSFORM**S

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 |

FOURIER SERIES | Prof. A T Eshwar, PESCE, Mandya Prof. N R Srinath, RNSIT, B'lore Prof. P R Hampiholi, GIT, Belgaum | |

CALCULUS OF VARIATIONS | ||

LINEAR ALGEBRA | ||

FOURIER TRANSFORMS | ||

Numerical Analysis | ||

Partial Differential Equations | ||

Interpolation |

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