2023 2024 MBA - Visvesvaraya Technological University VTU Engineering Mathematics III Syllabus

You are searching for the Visvesvaraya Technological University Engineering Mathematics 3rd semester Syllabus. Here I am providing you the syllabus of VTU Engineering Mathematics 3rd semester:

PART – A

UNIT 1:
Fourier Series
Periodic functions, Fourier expansions, Half range expansions, Complex
form of Fourier series, Practical harmonic analysis.

UNIT 2:
Fourier Transforms
Finite and Infinite Fourier transforms, Fourier sine and consine transforms,
properties. Inverse transforms.

UNIT 3:
Partial Differential Equations (P.D.E)
Formation of P.D.E Solution of non homogeneous P.D.E by direct
integration, Solution of homogeneous P.D.E involving derivative with
respect to one independent variable only (Both types with given set of
conditions) Method of separation of variables. (First and second order
equations) Solution of Lagrange’s linear P.D.E. of the type P p + Q q = R.

UNIT 4:
Applications of P.D.E
Derivation of one dimensional wave and heat equations. Various possible
solutions of these by the method of separation of variables. D’Alembert’s
solution of wave equation. Two dimensional Laplace’s equation – various
possible solutions. Solution of all these equations with specified boundary
conditions. (Boundary value problems).

PART – B

UNIT 5:
Numerical Methods
Introduction, Numerical solutions of algebraic and transcendental equations:-
Newton-Raphson and Regula-Falsi methods. Solution of linear simultaneous
equations : - Gauss elimination and Gauss Jordon methods. Gauss - Seidel
iterative method. Definition of eigen values and eigen vectors of a square
matrix. Computation of largest eigen value and the corresponding eigen
vector by Rayleigh’s power method.

UNIT 6:
Finite differences (Forward and Backward differences) Interpolation,
Newton’s forward and backward interpolation formulae. Divided differences
– Newton’s divided difference formula. Lagrange’s interpolation and inverse
interpolation formulae. Numerical differentiation using Newton’s forward
and backward interpolation formulae. Numerical Integration – Simpson’s
one third and three eighth’s value, Weddle’s rule.
(All formulae / rules without proof)

UNIT 7:
Calculus of Variations
Variation of a function and a functional Extremal of a functional, Variational
problems, Euler’s equation, Standard variational problems including
geodesics, minimal surface of revolution, hanging chain and Brachistochrone
problems.

UNIT 8:
Difference Equations and Z-transforms
Difference equations – Basic definitions. Z-transforms – Definition,
Standard Z-transforms, Linearity property, Damping rule, Shifting rule,
Initial value theorem, Final value theorem, Inverse Z-transforms.
Application of Z-transforms to solve difference equations.

Text Book:
Higher Engineering Mathematics by Dr. B.S. Grewal (36th Edition – Khanna Publishers)

Reference Books:
1. Higher Engineering Mathematics by B.V. Ramana (Tata- Macgraw Hill).
2. Advanced Modern Engineering Mathematics by Glyn James – Pearson Education.