WITH EFFECT FROM THE ACADEMIC YEAR 2010 - 2011

MT 201

MATHEMATICS-III

(Common to all Branches)

Instruction                                                                                              4 Periods per week

Duration of University Examination                                                      3 Hours

University Examination                                                                        75 Marks

Sessional                                                                                               25 Marks

UNIT – I

Partial differential Equations:  Formation of partial differential equations of first order, Lagrange’s solution.  Standard types.  Charpit’s & Jacobi’s method of solution, Partial differential equations of higher order, Monge’s method.

UNIT-II

Fourier Series:  Expansion of a function in Fourier series for a given range, half range sine and cosine expansion, odd and even functions of Fourier series, change of interval, complex form of Fourier Series.

UNIT-III

Partial differential Equations: Solution of wave equation, heat equation and Laplace’s equation by the method of separation of variables, and their use in problems of vibrating string, one and two dimensional wave and heat flow and examples thereon.

UNIT-IV

Z-Transforms:  Introduction.  Basic theory of Z-Transforms.  Z-Transform of some standard sequences.  Existence of Z-Transform, Linearity property, Translational Theorem, Scaling property, Initial and Final Value Theorems, Differentiation of Z-Transform, Convolution Theorem, Solution of Difference equations using Z-Transforms.

UNIT-V:

Numerical Methods:  Solution of linear system of equations.  Gauss elimination method Gauss-Seidel iterative method, ill-conditioned equations and refinement of solutions, Interpolation, Lagrange Interpolation, Newton’s divided difference interpolation, Newtons’s Forward and Backward difference Interpolation Formulas.  Numerical differentiation and integration (Trapezoidal and Simpson’s formulas) Solution of Differential equations by Runge Kutta Method.

Suggested Reading

1. E. Kreyszig.  Advanced Engineering Mathematics, Wiley Eastern Ltd., 8^th Edition, New Delhi, 2006.
2. R.K. Jain and S.R.K. Iyengar, Advanced Engineering Mathematics, Narosa 

            Publications, 2005.

3. B.V. Ramana, Higher Engineering Mathematics, Core Engineering Series, Tata  

            McGraw Hill Publishing Company Ltd., New Delhi, 2007.

4. B.S. Grewal,  Higher Engineering Mathematics, Khanna Publications, 34^th Edition, 1998.