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Module I: Ordinary differential equations (16 hours)
A brief review of the method of solutions first order equations - Separable, homogeneous and linear types
– Exact equations - Orthogonal trajectories – General linear second order equations - homogeneous linear
equation of the second order with constant coefficients – Fundamental system of solutions – Method of
variation of parameters – Cauchy’s equation.

Module II: Laplace transforms (17 hours)
Gamma and Beta functions – Definition and simple properties – Laplace transform - Inverse transform –
Laplace transform of derivatives and integrals – Shifting theorems – Differentiation and integration of
transforms - Transforms of unit step function and impulse function – Transforms of periodic functions –
Solutions of ordinary differential equations using Laplace transforms.


Module III: Vector differential calculus (18 hours)
Functions of more than one variable – Idea of partial differentiation – Euler’s theorem for homogeneous
functions – Chain rule of partial differentiation – Application in errors and approximations. Vector function
of single variable – Differentiation of vector functions – Scalar and vector fields – Gradient of a scalar field
– Divergence and curl of vector fields – Their physical meanings – Relation between the vector differential
operators.

Periodic functions – Trigonometric series – Euler formulae – Even and odd functions - Functions having
arbitrary period – Half range expansions – Numerical method for determining Fourier coefficients -
Harmonic analysisModule IV: Fourier series and harmonic analysis (15 hours)

Attached Files

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