Introduction to Methods of Applied Mathematics

This course is aimed at final year undergraduate and graduate students in engineering, physics and applied mathematics. This will cover the very important and essential topics used by almost all branches of Science and engineering.INTENTED AUDIENCE : Any Interested LearnersPREREQUISITES : Some basic knowledge of Calculus, Differential Equations, Topics related to Mathematics – I, II will be an advantage.

Week 1 : Introduction to first order linear and non-linear ordinary differentialequations (ODE), Riccati equationWeek 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 waveletsWeek 12: Revision and Problem-solving sessions