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

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Fourier series with boundary value problems

Fourier series with boundary value problems

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

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Fourier series with boundary value problems

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- [Instructor] Let's wrap up boundary value problems by exploring how Fourier Series show up in them. You have probably noticed these series show up along the way. But let's take a moment to focus on them and how they will become helpful when solving partial differential equations along with other boundary value problems. Fourier Series are similar to Taylor series where they help you express complicated functions in simpler terms in the form of a series. Fourier Series are different from Taylor series though since they always converge on the same interval if a function converges, meaning the interval does not depend on the function. They also don't have powers of the functions, but instead are a series of different arguments involving the series solution. 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. This allows you to express complex functions as a summation of simple trigonometric terms with sine…

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