Chapter 1. Co-ordinate Systems and Partial Differential Equations....................7
A. Co-ordinate Systems
1.1 Review of Cartesian, spherical and cylindrical co-ordinates
1.2 Transformation equation
1.3 General Curvilinear co-ordinate system: Co-ordinate surface,
co-ordinate lines, length, surfaces.
1.4 Expressions for gradient, divergence, Laplacian, and curl.
B. Partial Differential Equations
1.5 General methods for solving second order PDE
1.6 Method of separation of variables in Cartesian, Spherical polar and cylindrical co-ordinate system (2D Laplace’s equation, 1D Wave equation)
1.7 Singular points (x = x0, x= ∞)
1.8 Solution of differential equation-Statement of Fuch’s theorem, Frobenius method of series solution (Legendre’s Equation).
Problem Solving

Chapter 2. Special Theory of Relativity............................85
2.1 Introduction
2.2
Newtonian relativity
2.3 Galilean transformation equation
2.4 Michelson-Morley experiment
2.5 Postulates of special theory of relativity
2.6 Lorentz transformations
2.7 Kinematic effects of Lorentz transformation, Length contraction,
Proper time
Problem
Solving

Chapter 3. Special Functions and Fourier Series................................122
Part A: Special Functions
3.0 Introduction.
3.1 Generating function for Legendre Polynomials: Pn (x).
3.2 Properties of Legendre Polynomials.
3.3 Generating function for Hermite Polynomials: Hn (x)
3.4 Properties of Hermite Polynomials.
3.5 Bessel function of first kind: Jn (x)
3.6 Properties of Bessel function of first kind.
3.7 Applications of Special Functions in Physics.
Problem solving.
Part B: Fourier Series
3.8 Introduction to Fourier Series
3.9 Dirichlet’s Conditions for a Fourier Series
3.10 Determination of Fourier coefficients a0, an & bn
3.11 Simple problems (Odd function, even function, x,x2, e+x, e-x) on
finding a Fourier Series with continuous interval only
3.12 Advantages or applications of Fourier Series
Problem Solving