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In this course you will learn :
Week 1 : Introduction to first order linear and non-linear ordinary differential equations (ODE), Riccati equation
Week 2 : Solving second order ODE
Week 3 : Introductions to Green’s functions for second order linear ODE
Week 4 : Introduction to Adjoint operators and their Green’s functions
Week 5 : Laplace Transforms and its properties
Week 6 : Application of Laplace Transforms to solve ODE
Week 7 : Introduction to Fourier Series
Week 8 : Fourier integrals and Fourier Transform and properties
Week 9 : Riesz bases, frames and orthonormal bases and shortcoming of Fourier Series
Week 10: Shortcomings of Fourier transforms, Gabor transform, Window Fourier Transform, Multiresolution Analysis
Week 11: Daubechies wavelet, wavelet series and wavelet transform and different properties of wavelets
Week 12: Revision and Problem-solving sessions
