3CH1(MA)-Mathematics-III |
Units: I |
Differential Equations & Fourier Series : Ordinary differential equations of second order
with variable coefficients; Method of variation of parameters; Power series methods;
Partial differential equations of first order Lagrange’s method, standard forms, Fourier
series and Harmonic analysis
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Units: II |
Legendre’s function of first and second kinds; simple recurrence relations; Rodrigues’
formula; orthogonal property, and Bessel’s differential equation, Bessel functions of first
and second kind, simple recurrence relations, orthogonal property of Bessel function. |
Units: III |
Laplace Transforms with its simple properties; applications to the solution of ordinary
differential equations, method of separation of variables, applications to the solution of
wave equations in one dimension, Laplace’s equation in two dimensions, diffusion
equation in one dimension.
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Units: IV |
Numerical Analysis: Finite differences- Forward, Backward, and Central differences,
Newton’s forward and backward difference interpolation formulae, Stirling’s formula.
Numerical differentiation, Numerical Integration – Trapezoidal rule, Simpson’s one-third
and three-eighth rule. Introduction to numerical solution of ordinary differential equations.
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Units: V |
Tensor Analysis: Definition of a tensor, Transformation of co-ordinates. Contravariant
and co-variant vectors, addition and multiplication of tensors, contraction of tensors, inner
product, fundamental tensor, Christoffel symbols, co-variant differentiation.
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Text/ Reference Books |
1. Grewal, B.S., “Higher Engineering Mathematics”, Khanna Publishers, New Delhi.
2. Gaur, Y.N. and Koul, C.L., “Higher Engineering Mathematics”, Book1 & 2, Jaipur
Publishing House, Jaipur.
3. Sastry, S.S., “Introductory Methods of Numerical Analysis”, Prentice-Hall of India,
1988.
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