Introduction to Methods of Applied Mathematics

Introduction:

The course "Introduction to Methods of Applied Mathematics" is an essential course for final year undergraduate and graduate students in engineering, physics and applied mathematics. The course is designed to introduce learners to the very important and essential topics used by almost all branches of science and engineering. The course is taught by two highly experienced professors - Prof. Vivek K. Aggarwal from the Department of Applied Mathematics, DTU Delhi and Prof. Mani Mehra from the Department of Mathematics, IIT Delhi. This course is highly applicable in various industries such as Goldman Sachs, FinMachenics, Deutsche Bank and other finance companies.

In this article, we will provide a comprehensive summary of the course outline and its topics, as well as the instructors' background and the intended audience. We will also discuss our experience as a teaching assistant (TA) and how we conducted one hour Interaction session per week for the learners.

Course Outline:

The course is divided into twelve weeks, with each week covering a specific topic. The following is a brief summary of each week's topics:

Week 1: Introduction to first-order linear and non-linear ordinary differential equations (ODE) and Riccati equation.

Week 2: Solving second-order ODE.

Week 3: Introduction 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 shortcomings 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.

Intended Audience:

The course is aimed at final year undergraduate and graduate students in engineering, physics and applied mathematics. The course is designed to provide learners with a comprehensive understanding of the essential topics used in various branches of science and engineering. The course is also highly applicable in various industries such as Goldman Sachs, FinMachenics, Deutsche Bank and other finance companies.

Instructor Background:

The course is taught by two highly experienced professors - Prof. Vivek K. Aggarwal from the Department of Applied Mathematics, DTU Delhi and Prof. Mani Mehra from the Department of Mathematics, IIT Delhi. Prof. Mani Mehra is presently working as an Associate Professor in the department of Mathematics, IIT Delhi. She earned her PhD from IIT Kanpur in 2005. Prof. Vivek Kumar Aggarwal is presently worked as an Assistant Professor dept. of Applied Mathematics, DTU Delhi. He earned his PhD in Mathematics from IIT Kanpur in 2005. Their extensive knowledge and experience in the field of mathematics make them the perfect instructors for this course.

TA Experience:

As a teaching assistant for this course, we were responsible for conducting one hour Interaction session per week for the learners. Our goal was to provide additional support to the learners and answer any questions they had about the course material. We conducted these sessions via video conferencing, which allowed us to interact with the learners and provide a more personalized learning experience. During these sessions, we also provided additional practice problems to the learners to help them reinforce their understanding of the course material.

Conclusion:

In conclusion, the course "Introduction to Methods of Applied Mathematics" is an essential course for final year undergraduate and graduate students in engineering, physics and applied mathematics. The course covers the very important and essential topics used