Mathematics 1

Differential Calculus:

•  function; 
• limit of a function;
•  continuity and differentiability of functions; 
• successive differentiation;
•  physical applications of first and second order derivatives; 
• Leibnitz’s theorem; expansion of functions; 
• Rolle’s theorem; 
• mean value theorem; 
• Taylor’s theorem and Maclaurins theorem (proof not required);
• maxima and minima for functions of one and two variables; 
• functions of several variables; 
• partial differentiation; 
• tangent; 
• normal and curvature.  

Integral Calculus:

• Review of indefinite integrals; 
• definite integrals;
•  properties of definite integrals; 
• gamma and beta functions;
  integration by reduction, 
• integrals with several variables; 
• rectification; 
• quadrature; 
• surface areas and volumes of revolution.

Matrices

• Introduction; 
• transpose of matrix;      
• adjoint and inverse of a matrix;       
• solution of linear equations by matrices;
• rank of a matrix;                
• symmetric and skew – symmetric matrix;            
• Hermitian matrix;             
• orthogonal matrix.

Mathematics 2

• Differential Equations:
  Definition;        
• types of differential equations;         
• formation of differential equations;         
• solution of first order and first degreee quations; 
• solution of linear differential equations of second and higher orders with constant coefficients;
•  method of variation of parameters;
• solution of homogeneous linear equations;
• solution of differential equations in series (Frobenius method);
• Co-ordinate geometry:
  Co-ordinates of a point in space; 
• distance between two points;
•  direction cosines and direction ratios of a straight line; 
• angle between two straight lines;
• condition of perpendicularity and parallelism of two straight lines, sphere and conicoid;

Numerical analysis: 

• solution of algebraic and transcendental equations; 
• interpolation and extrapolation; 
• numerical differentiation and integration; 
• numerical solution of ordinary differential equations

Mathematics 3

• Fourier series & Fourier integrals:
  Trigonometric series;
•  the Euler-Fourier formula; 
• expansion of functions into Fourier series; 
• half range expansions; the Fourier integrals; 
• Fourier series.

Legendre polynomial:

• Legendre polynomial from Legendre equation; 
• recurrence formula for Legendre polynomial, Rodrigues formula; 
• Orthogonality of Legendre polynomial; 
• generating function.

• Bessel’s functions:
• Derivation of Bessel’s function from the solution of Bessel’s equation; 
• recurrence formula for Bessels functions; 
• orthogonal properties of Bessel’s functions.

Vector calculus:

• Scalar & vector functions; gradient of a scalar function; 
• curl & divergence of a vector function; 
• Green’s theorem; 
• Gauss’s divergence theorem and Stokes theorem

Engineering physics 

• General Properties of matter:
  Elasticity,         surface tension         viscosity.
  Heat and Thermodynamics:
• First law of thermodynamics and its applications, 
• different kinds of thermo-dynamical changes, 
• interrelation between pressure, 
• volume and temperature.
•  Second law of thermodynamics; 
• reversible and irreversible processes, 
• heat engine and Carnot’s cycle.

Electricity and Magnetism

• Current and resistance, 
• Kirchhoff’s laws on distribution of current. 
• Magnetic induction due to current,
  Ampere’s law, 
• Biot-Savartlaw. 
• Electromagnetic induction, 
• Henry-Faraday’slaw, inductance, L-Rcircuits.
  Nuclear Physics and Electronics:
  Nuclear physics – Atomic and nuclear structure,
•  radio activity,
•  decay law, 
• half life, 
• nuclear fission and fusion, 
• uses of radio isotopes

Practical