NPTEL - Mathematical methods and its applications 

offered by IIT Roorkee

Introduction to linear differential equations

Linear dependence

Independence and Wronskian of functions

Solution of second-order homogeneous linear differential equations with constant coefficients-I

Solution of second-order homogeneous linear differential equations with constant coefficients-II

Method of undetermined coefficients

Methods for finding Particular Integral for second-order linear differential equations with constant coefficients-I

Methods for finding Particular Integral for second-order linear differential equations with constant coefficients-II

Methods for finding Particular Integral for second-order linear differential equations with constant coefficients-III

Euler-Cauchy equations

Method of reduction for second-order

Linear differential equations

Method of variation of parameters

Solution of second order differential equations by changing dependent variable

Solution of second order differential equations by changing independent variable

Solution of higher-order homogenous linear differential equations with constant coefficients

Methods for finding Particular Integral for higher-order linear differential equations

Formulation of Partial differential equations

Solution of Lagrange's equation-I

Solution of Lagrange's equation-II

Solution of first order nonlinear equations-I

Solution of first order nonlinear equations--II

Solution of first order nonlinear equations-III

Solution of first order nonlinear equations-IV

Introduction to Laplace transforms

Laplace transforms of some standard functions

Existence theorem for Laplace transforms

Properties of Laplace transforms--I

Properties of Laplace transforms--II

Properties of Laplace transforms--III

Properties of Laplace transforms--IV

Convolution theorem for Laplace transforms--I

Convolution theorem for Laplace transforms--II

Initial and final value theorems for Laplace transforms

Laplace transforms of periodic functions

Laplace transforms of Heaviside unit step function

Laplace transforms of Dirac delta function

Applications of Laplace transforms-I

Applications of Laplace transforms-II

Applications of Laplace transforms-III

Z -transform and inverse Z-transform of elementary functions

Properties of Z-transforms-I

Properties of Z-transforms-II

Initial and final value theorem for Z-transforms

Convolution theorem for Z- transforms

Applications of Z- transforms--I

Applications of Z- transforms-II

Applications of Z- transforms--III

Fourier series and its convergence--I

Fourier series and its convergence--II

Fourier series of even and odd functions

Fourier half-range series

Parsevel's Identity

Complex form of Fourier series

Fourier integrals

Fourier sine and cosine integrals

Fourier transforms

Fourier sine and cosine transforms

Convolution theorem for Fourier transforms

Applications of Fourier transforms to BVP-I

Applications of Fourier transforms to BVP-II

Applications of Fourier transforms to BVP-III