1. Vectors..............................................................1
1.1 Introduction, 1.2 Scalar product of two vectors (or dot product of two
vectors), 1.3 Vector product of two vectors (or cross product of two vectors),
1.4 Scalar Triple Product, 1.5 Vector Triple product, 1.6 Differentiation of vector

2. Vector Analysis I.............................................47
2.1 Scalar and Vector Fields, 2.2 Differentiation of a Vector, 2.3 Vector
Differential Operator, 2.4 Gradient of a Scalar, 2.5 Divergence of a Vector,
2.6 The Curl of a Vector, 2.7 Laplacian Operator, 2.8 Vector Integration,
2.9 Gauss’s Divergence theorem, 2.10 Stoke’s Theorem

3. Vector Analysis II.........................................84
3.1 Introduction, 3.2 Revision, 3.3 Gauss’s divergence theorem, 3.4 Green’s first
and second theorem, 3.5 Stokes’ Theorem, 3.6 Green’s theorem in plane
4. Ordinary Differential Equation......................................................108
4.1 Introduction, 4.2 Differential Equations, 4.3 Types of Differential Equations,
4.4 Degree of Differential Equation, 4.5 Order of Differential Equation, 4.6 Linear
Differential Equations, 4.7 Non-linear Differential Equations, 4.8 Homogeneous
Differential Equations, 4.9 Non – Homogeneous or Inhomogeneous Differential
Equations, 4.10 First order homogeneous differential equations with constant
coefficients, 4.11 Second order homogeneous differential equations with constant
coefficients, 4.12 Use of differential equations in Physics

5. Differential Equations .....................................131
5.1 Introduction, 5.2 Introduction to co-ordinate system, 5.3 Cartesian coordinate
system (x, y, z), 5.4 Spherical Polar Co-ordinate System (r, θ, φ),
5.5 Cylindrical Co-ordinate System, 5.6 Differential Equation, 5.7 Partial
differential equations occurring frequently while studying physics, 5.8 Methods
to solve second order partial differential equations, 5.9 Separation of variables
method to solve Laplace’s equation, 5.10 Separation of variables method to
solve wave equation, 5.11 Singular points of differential equations, 5.12 Series
solution of differential equation

6. Special Functions ..........................................199
6.1 Introduction, 6.2 Generating Function for Legendre Polynomials : Pn (x),
6.3 Properties of Legendre Polynomials, 6.4 Hermite Polynomials : Hn(x),
6.5 Properties of Hermite Polynomials, 6.6 Bessel Function of First Kind :
Jn(x), 6.7 Properties of Bessel function of first kind

7. Complex Analysis.......................................212
7.1 Introduction, 7.2 Complex number and Conjugate of complex number,
7.3 Basic Mathematical operations with complex numbers, 7.4 Polar form
of a complex number, 7.5 Exponential form of complex numbers, 7.6 Euler’s
formula, 7.7 Graphical representation of complex numbers : Argand diagram,
7.8 De-Moiver’s theorem, 7.9 Powers and Roots of a complex number,
7.10 Logarithmic form of complex number, 7.11 Trigonometric functions,
7.12 Hyperbolic functions, 7.13 Application of complex number to determine
velocity and acceleration, 7.14 Functions of Complex Variables, 7.15 Analyticity
and Cauchy - Riemann conditions, 7.16 Singular functions (Singularity of a
function)

8. Special Theory of Relativity...........................266
8.1 Introduction, 8.2 Concept of frame of reference, 8.3 Newtonian Relativity,
8.4 Galilean Transformations, 8.5 Michelson-Morley experiment, 8.6 Postulates
of special theory of relativity, 8.7 Lorent’z transformation equations, 8.8 Length
contraction, 8.9 Time dilation, 8.10 Relativity of simultaneity, 8.11 Addition
of velocities, 8.12 Variation of mass with velocity, 8.13 Mass-energy relation,
8.14 Energy momentum relation.