10 MAT 31 IA ENGINEERING MATHEMATICS – III Visvesvaraya Technological University Syllabus

ENGINEERING MATHEMATICS – III

CODE: 10 MAT 31 IA Marks: 25

Hrs/Week: 04 Exam Hrs: 03

Total Hrs: 52 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
y = ax+b, y =a x2 + b x + c, , y
bx b
y = a e = 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: Gaussseidel
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.
2
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.
Reference Book:
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