Fourier analysis - prerequisites

[conjectures]

I was wondering at what point most students encounter Fourier analysis and what the prerequisites are considered to be?

 

[micromass]

I'd say you have to know calculus and linear algebra fairly well. With that knowledge, you can already do quite a bit of Fourier analysis.

If you want to do more theoretical things, then following a course in real analysis and functional analysis seems necessary.

 

[Chunkysalsa]

Most students (at my school) encounter Fourier Analysis in Partial Differential Equations if they are math majors and Circuit Analysis II (with more use in a Systems and Signals course) if they are EE majors.

To use the techniques from Fourier Analysis, you need integration as well as a good working knowledge of complex numbers and trigonometric functions. Understanding it requires Linear Algebra.

Thats as far as I know. This is coming from a EE who just took linear algebra.

 

[conjectures]

Thanks for the replies.

I suspect it's the complex numbers / trigonometry that I should be working on further. Any recommended resources?

My background is primarily economics so have some [perhaps passable] calculus and linear algebra.

I'm at one of those points where I feel I get/can follow something, but not deeply enough to replicate independently in an applied context.

 

[Matrix0]

Fourier analysis is a mathematical tool used to decompose a complex signal or function into simpler components, called Fourier series or Fourier transforms. It has a wide range of applications in various fields, including physics, engineering, and signal processing.

In most undergraduate programs, students encounter Fourier analysis in their advanced calculus or differential equations courses. These courses typically have calculus and linear algebra as prerequisites, as Fourier analysis involves concepts such as integration, differentiation, and vector spaces.

In addition, a strong understanding of trigonometry and complex numbers is also essential for understanding Fourier analysis. These concepts are usually covered in high school math courses, but students may also encounter them in introductory college courses.

Moreover, having a solid understanding of basic calculus concepts such as limits, derivatives, and integrals will greatly aid in grasping the concepts of Fourier analysis. Some knowledge of differential equations is also helpful, as Fourier analysis is often used to solve these types of equations.

Overall, a strong foundation in mathematics is crucial for understanding Fourier analysis. Students should have a good understanding of calculus, linear algebra, trigonometry, and complex numbers before delving into this topic. With the right prerequisites and a dedicated approach to learning, students can successfully master Fourier analysis and its applications.