NOC:Transform Calculus and its applications in Differential Equations


Lecture 1 - Introduction to Integral Transform and Laplace Transform


Lecture 2 - Existence of Laplace Transform


Lecture 3 - Shifting Properties of Laplace Transform


Lecture 4 - Laplace Transform of Derivatives and Integration of a Function - I


Lecture 5 - Laplace Transform of Derivatives and Integration of a Function - II


Lecture 6 - Explanation of properties of Laplace Transform using Examples


Lecture 7 - Laplace Transform of Periodic Function


Lecture 8 - Laplace Transform of some special Functions


Lecture 9 - Error Function, Dirac Delta Function and their Laplace Transform


Lecture 10 - Bessel Function and its Laplace Transform


Lecture 11 - Introduction to Inverse Laplace Transform


Lecture 12 - Properties of Inverse Laplace Transform


Lecture 13 - Convolution and its Applications


Lecture 14 - Evaluation of Integrals using Laplace Transform


Lecture 15 - Solution of Ordinary Differential Equations with constant coefficients using Laplace Transform


Lecture 16 - Solution of Ordinary Differential Equations with variable coefficients using Laplace Transform


Lecture 17 - Solution of Simultaneous Ordinary Differential Equations using Laplace Transform


Lecture 18 - Introduction to Integral Equation and its Solution Process


Lecture 19 - Introduction to Fourier Series


Lecture 20 - Fourier Series for Even and Odd Functions


Lecture 21 - Fourier Series of Functions having arbitrary period - I


Lecture 22 - Fourier Series of Functions having arbitrary period - II


Lecture 23 - Half Range Fourier Series


Lecture 24 - Parseval's Theorem and its Applications


Lecture 25 - Complex form of Fourier Series


Lecture 26 - Fourier Integral Representation


Lecture 27 - Introduction to Fourier Transform


Lecture 28 - Derivation of Fourier Cosine Transform and Fourier Sine Transform of Functions


Lecture 29 - Evaluation of Fourier Transform of various functions


Lecture 30 - Linearity Property and Shifting Properties of Fourier Transform


Lecture 31 - Change of Scale and Modulation Properties of Fourier Transform


Lecture 32 - Fourier Transform of Derivative and Integral of a Function


Lecture 33 - Applications of Properties of Fourier Transform - I


Lecture 34 - Applications of Properties of Fourier Transform - II


Lecture 35 - Fourier Transform of Convolution of two functions


Lecture 36 - Parseval's Identity and its Application


Lecture 37 - Evaluation of Definite Integrals using Properties of Fourier Transform


Lecture 38 - Fourier Transform of Dirac Delta Function


Lecture 39 - Representation of a function as Fourier Integral


Lecture 40 - Applications of Fourier Transform to Ordinary Differential Equations - I


Lecture 41 - Applications of Fourier Transform to Ordinary Differential Equations - II


Lecture 42 - Solution of Integral Equations using Fourier Transform


Lecture 43 - Introduction to Partial Differential Equations


Lecture 44 - Solution of Partial Differential Equations using Laplace Transform


Lecture 45 - Solution of Heat Equation and Wave Equation using Laplace Transform


Lecture 46 - Criteria for choosing Fourier Transform, Fourier Sine Transform, Fourier Cosine Transform in solving Partial Differential Equations


Lecture 47 - Solution of Partial Differential Equations using Fourier Cosine Transform and Fourier Sine Transform


Lecture 48 - Solution of Partial Differential Equations using Fourier Transform - I


Lecture 49 - Solution of Partial Differential Equations using Fourier Transform - II


Lecture 50 - Solving problems on Partial Differential Equations using Transform Techniques


Lecture 51 - Introduction to Finite Fourier Transform


Lecture 52 - Solution of Boundary Value Problems using Finite Fourier Transform - I


Lecture 53 - Solution of Boundary Value Problems using Finite Fourier Transform - II


Lecture 54 - Introduction to Mellin Transform


Lecture 55 - Properties of Mellin Transform


Lecture 56 - Examples of Mellin Transform - I


Lecture 57 - Examples of Mellin Transform - II


Lecture 58 - Introduction to Z-Transform


Lecture 59 - Properties of Z-Transform


Lecture 60 - Evaluation of Z-Transform of some functions