Mathematical Physics
Mathematical Physics
1st Order Differential Equation (Introduction, conditions of a unique solution, homogeneous, exact, inexact and linear differential equations, integrating factor, Bernoulli's theorem): Link
2nd Order Differential Equation (Conditions of a unique solution, linear homogeneous ODE with constant coefficients, Wronskian, non-homogeneous ODE, particular integral): Link
Applications of Differential Equations (1st order and 2nd order linear ordinary differential equations with constant coefficients): Link
Coordinate system (Rectangular, plane polar, cylindrical and spherical coordinate system, orthogonal transformation, Jacobian): Link
Curvilinear Coordinates (Introduction, orthogonal curvilinear coordinates, arc length, surface and volume elements, gradient, divergence, curl and Laplacian in orthogonal curvilinear coordinates): Link
Vector Integration (Line, surface and volume integrals of vector fields, flux of a vector field, Gauss divergence, Green's and Stokes theorems): Link
Matrices (Introduction to different types of matrices, properties of matrix, matrix transformation, eigen-values and eigenvectors, Cayley-Hamilton theorem, diagonalization, solutions of coupled linear homogeneous ODE): Link
Introduction to probability (Independent random variables, Sample space and Probability distribution functions. Binomial, Gaussian, and Poisson distribution with examples, mean and variance): Link
Dirac Delta function and its properties (Definition of Dirac delta function, representation as limit of a Gaussian function and rectangular function properties of Dirac delta function): Link