Basic Understanding of Fourier Series and Transforms for AI

Welcome to this course on Fourier Series. This is a part of Engineering Maths. I am Suman Mathews, math educator and tutor.

I have a double master's in Maths and I have taught Math for three decades to college and High school students. By taking this Course on Fourier Series, you will learn the basics of Analytical Mathematics.

In this course, you are introduced to the Euler's formula and basic formulas of integration which involve integrals of the product of the exponential and trigonometric functions. You learn how to write the Fourier series of a function. You learn about odd and even functions in different contexts, not just the traditional definition. Different aspects of odd and even functions are explained with examples.

The Fourier series of odd and even functions is explained. You will understand how to calculate the Fourier coefficients in different intervals for different functions. You understand the trick of solving identities using the Fourier series.There is a brief introduction to the role of periodic functions in evaluating the Fourier series.

You learn how to evaluate the Fourier series of the exponential, trigonometric, algebraic, modulus functions and more.The course concludes with half range Fourier Series

You will also learn how to calculate the cosine series and the sine series of a function. A number of problems are completely solved with steps clearly explained. The last assignment covers all the properties learnt in this course together with an understanding of the Fourier half series.

As a bonus, you will learn about Harmonic Analysis and how to calculate the 1st and 2nd harmonic for a function.  Also learn how to calculate Harmonic coefficients for different types of intervals.

Learn Essential Concepts in Demystifying Fourier Transforms. You'll learn how to calculate Fourier Sine and Cosine Transforms and how to evaluate their Inverse. Also learn the technique of differentiating under the integral while solving problems.

Learn about Partial Derivatives and the Chain Rule for Differentiating them.

So let's start learning!