NOC:Mathematical Methods and its Applications


Lecture 1 - Introduction to linear differential equations


Lecture 2 - Linear dependence, independence and Wronskian of functions


Lecture 3 - Solution of second-order homogenous linear differential equations with constant coefficients - I


Lecture 4 - Solution of second-order homogenous linear differential equations with constant coefficients - II


Lecture 5 - Method of undetermined coefficients


Lecture 6 - Methods for finding Particular Integral for second-order linear differential equations with constant coefficients - I


Lecture 7 - Methods for finding Particular Integral for second-order linear differential equations with constant coefficients - II


Lecture 8 - Methods for finding Particular Integral for second-order linear differential equations with constant coefficients - III


Lecture 9 - Euler-Cauchy equations


Lecture 10 - Method of reduction for second-order linear differential equations


Lecture 11 - Method of variation of parameters


Lecture 12 - Solution of second order differential equations by changing dependent variable


Lecture 13 - Solution of second order differential equations by changing independent variable


Lecture 14 - Solution of higher-order homogenous linear differential equations with constant coefficients


Lecture 15 - Methods for finding Particular Integral for higher-order linear differential equations


Lecture 16 - Formulation of Partial differential equations


Lecture 17 - Solution of Lagrange’s equation - I


Lecture 18 - Solution of Lagrange’s equation - II


Lecture 19 - Solution of first order nonlinear equations - I


Lecture 20 - Solution of first order nonlinear equations - II


Lecture 21 - Solution of first order nonlinear equations - III


Lecture 22 - Solution of first order nonlinear equations - IV


Lecture 23 - Introduction to Laplace transforms


Lecture 24 - Laplace transforms of some standard functions


Lecture 25 - Existence theorem for Laplace transforms


Lecture 26 - Properties of Laplace transforms - I


Lecture 27 - Properties of Laplace transforms - II


Lecture 28 - Properties of Laplace transforms - III


Lecture 29 - Properties of Laplace transforms - IV


Lecture 30 - Convolution theorem for Laplace transforms - I


Lecture 31 - Convolution theorem for Laplace transforms - II


Lecture 32 - Initial and final value theorems for Laplace transforms


Lecture 33 - Laplace transforms of periodic functions


Lecture 34 - Laplace transforms of Heaviside unit step function


Lecture 35 - Laplace transforms of Dirac delta function


Lecture 36 - Applications of Laplace transforms - I


Lecture 37 - Applications of Laplace transforms - II


Lecture 38 - Applications of Laplace transforms - III


Lecture 39 - Z–transform and inverse Z-transform of elementary functions


Lecture 40 - Properties of Z-transforms - I


Lecture 41 - Properties of Z-transforms - II


Lecture 42 - Initial and final value theorem for Z-transforms


Lecture 43 - Convolution theorem for Z-transforms


Lecture 44 - Applications of Z-transforms - I


Lecture 45 - Applications of Z-transforms - II


Lecture 46 - Applications of Z-transforms - III


Lecture 47 - Fourier series and its convergence - I


Lecture 48 - Fourier series and its convergence - II


Lecture 49 - Fourier series of even and odd functions


Lecture 50 - Fourier half-range series


Lecture 51 - Parsevel’s Identity


Lecture 52 - Complex form of Fourier series


Lecture 53 - Fourier integrals


Lecture 54 - Fourier sine and cosine integrals


Lecture 55 - Fourier transforms


Lecture 56 - Fourier sine and cosine transforms


Lecture 57 - Convolution theorem for Fourier transforms


Lecture 58 - Applications of Fourier transforms to BVP - I


Lecture 59 - Applications of Fourier transforms to BVP - II


Lecture 60 - Applications of Fourier transforms to BVP - III