1. Vectors 
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 
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 
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 
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 
5.1 Introduction, 5.2 Introduction to co-ordinate system, 5.3 Cartesian co-ordinate 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 
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 
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 
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.