10MAT31 Engineering Maths III syllabus for IS


Part A
Unit-1 FOURIER SERIES 7 hours

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 2π and arbitrary period, half range Fourier series. Complex form of
Fourier Series. Practical harmonic analysis.

Unit-2 FOURIER TRANSFORMS 6 hours

Infinite Fourier transform, Fourier Sine and Cosine transforms, properties,Inverse transforms

Unit-3 APPLICATIONS OF PDE 6 hours

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.

Unit-4 CURVE FITTING AND OPTIMIZATION 7 hours

Curve fitting by the method of least squares- Fitting of curves of the form
y=ax+b, y=ax2+bx+c, y=aebx , y=axb
Optimization: Linear programming, mathematical formulation of linear programming problem (LPP),
Graphical method and simplex method.

Part B
Unit-5 NUMERICAL METHODS - 1 6 hours

Numerical Solution of algebraic and transcendental equations: Regula-falsimethod, Newton - Raphson method. Iterative methods of solution of a systemof equations: Gauss-seidel and Relaxation methods. Largest eigen value andthe corresponding eigen vector by Rayleigh’s power method.

Unit-6 NUMERICAL METHODS – 2 7 hours

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)

Unit-7 NUMERICAL METHODS – 3 7 hours

Numerical solutions of PDE – finite difference approximation to derivatives,Numerical solution of
two dimensional Laplace’s equation, one dimensional heat and wave equations

Unit-8 DIFFERENCE EQUATIONS AND Z-TRANSFORMS 6 hours

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.

Note: * In the case of illustrative examples, questions are not to be set.

Last Updated: Tuesday, January 24, 2023