10MAT31Maths VTU Syllabus

	III SEMESTER
	ENGINEERING MATHEMATICS – III
Sub Code	:	10MAT31	IA Marks	:	25
Hrs/ Week	:	04	Exam Hours	:	03
Total Hrs.	:	52	Exam Marks	:	100

PART-A

UNIT-1Fourier 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-2

Fourier Transforms

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

6 Hours

UNIT-3 Application 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 equat ion.

6 Hours

UNIT-4

Curve Fitting and Optimisation

Curve fitting by the method of least squares- Fitting of curves of the form y =ax +b, y = a x2 + b x + c, y = a ebx , y = axb

Optimization: Linear programming, mathematical formulation of linear programming problem (LPP), Graphical method and simplex method.

7 Hours

PART-B

UNIT-5

Numerical Methods - 1

Numerical Solution of algebraic and transcendental equations: Regula-falsimethod, 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-6

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-7

Numerical Methods – 3

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

7 Hours

UNIT-8

Difference Equations and Z-Transorms

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.

REFERENCE BOOKS:

1.B.V. Ramana, Higher Engineering Mathematics, Latest edition, Tata Mc. Graw Hill Publications.

2.Peter V. O’Neil, Engineering Mathematics, CENGAGE Learning India Pvt Ltd.Publishers.