From the course: Complete Guide to Differential Equations Foundations for Data Science

Unlock this course with a free trial

Join today to access over 25,300 courses taught by industry experts.

Fourier series with partial differential equations

Fourier series with partial differential equations

From the course: Complete Guide to Differential Equations Foundations for Data Science

Start my 1-month free trial Buy for my team

Fourier series with partial differential equations

“

- [Instructor] Let's wrap up partial differential equations by exploring how Fourier series show up in them. You may have noticed some of these appear along the way, but let's take a moment to focus on how they're helpful when solving partial differential equations. Remember, a Fourier series represents a periodic function, f of x, with a period of two capital L as an infinite sum of sine and cosine values. If you are dealing with just even functions, then you'll have a Fourier cosine series where you'll have f of x equals f of negative x. If you're dealing with just odd functions, then you'll have a Fourier sine series where you'll have f of x equals negative f of negative x. Let's review the Fourier series formulas. For your general Fourier series, you have f of x equals a of zero divided by two, plus the sum of n equals one to infinity of capital A of n, multiplied by cosine of n, multiplied by pi, multiplied by x, divided by capital L, and then multiply that by capital B of n…

Contents