Introduction to Laplace Transforms
Properties of Laplace Transforms
Properties of Laplace Transforms - Contd.
Properties of Laplace Transforms - Contd.
Laplace transforms of Derivatives - Intro. To Inverse Laplace transforms
Problems on Finding Inverse Laplace Transforms.
Problems on Finding Inverse Laplace Transforms - Contd.
Practice problems - Laplace Transform of an Integral
Practice problems - Introduction to Convolution Theorem
Impulse response function - Convolution theorem - problems
Problems on Convolution theorem
Discussion of test questions
Laplace transforms of Periodic functions
Problems on Laplace transforms of Periodic functions & Unit step functions
Problems on Second Shifting theorem
Discussion of Homework problems.
Solving an ODE using Laplace transforms
More problems on solving an ODE using Laplace Transforms
Solving systems of ODE using Laplace Transforms
Solving LCR circuit problems using Laplace transforms
Solving Problems on Mass-Spring Damping systems using Laplace transforms
Discussion of Test 1 on Laplace Transforms
Introduction to Fourier Series
Problems on Fourier Series
Fourier series of odd and even functions
Fourier series of odd and even functions - Contd.
Fourier series of odd and even functions - Contd.
Introduction of Half Range Fourier Series of functions
Discussion of homework problems
Introduction to Fourier Series in Complex form
Introduction to Harmonic analysis using Fourier coefficients.
Introduction to RMS value and Parseval's Identity
Discussion of problems on Fourier Series
Introduction to Analytic functions
Properties of Analytic functions and related problems
Introduction to Harmoninc conjugates and Milne Thomson method
Necessary conditions for Analyticity and problems on Transformation of functions
Problems on Simple Transformations
Analysis of Standard Transformations
Analysis of Standard Transformations - Contd.
Introduction to Bilinear Transformations
Problems on Bilinear Transformations
Problems on Bilinear Transformations - Contd.
General revision on Unit 3
Introduction to Complex Integration
Problems on Line Integrals
Introduction to Cauchy's theorem for analytic functions
Cauchy's theorem for analytic functions - problems
Introduction to Power series expansion of a function and standard expansions
Taylor's series and Laurent's series expansion of fucntions
More problems on Laurent's series expansion of functions
Introduction to Singularities of a complex function
Introduction to the Residue of a complex function at a singularity
Evaluation of Real improper integrals using Cauchy's Residue theorem
Evaluation of Real improper integrals using Cauchy's Residue theorem - Contd.
Evaluation of Real improper integrals using Cauchy's Residue theorem - Contd.
General revision on Unit 4
