Calculus books dealing with Fourier series

In summary, a Fourier series is a mathematical representation of a periodic function as an infinite sum of sine and cosine functions, used for analyzing and approximating complex periodic functions in calculus. They are important for breaking down complex functions into simpler components and have practical applications in various fields such as physics and engineering. Some limitations include only being applicable to periodic functions and slow convergence for some functions. Recommended books for learning about Fourier series in calculus include "Fourier Series and Boundary Value Problems" by Ruel V. Churchill, "An Introduction to Fourier Series and Integrals" by Robert T. Seeley, and "The Fourier Transform and Its Applications" by Ronald N. Bracewell, as well as consulting with a calculus professor or online resources for additional guidance
  • #1
Electrophy6
18
0
Hey all,
I am looking for **calculus**(and not all these books of Advanced Engineerigng Math or etc...) books dealing with Fourier Series ,its expansions , half reange extensions etc...
I have found that "Stewart'c calculus" includes a chapter dealing generally with Fourier Series but *not * with its expansions

Thanks in advance!
 
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  • #2
One of the easiest books concerning Fourier Series is Boyce and Diprima's "Elementary Differential Equations and Boundary Value Problems". I think it should count as calculus.
 
  • #3
Like Micromass said, any book in differential equations will deal with Fourier Series at a basic level.
 

Related to Calculus books dealing with Fourier series

1. What is a Fourier series?

A Fourier series is a mathematical representation of a periodic function as an infinite sum of sine and cosine functions. It is used to analyze and approximate complex periodic functions.

2. Why are Fourier series important in calculus?

Fourier series are important in calculus because they allow us to break down complex functions into simpler components, making it easier to analyze and understand them. They also have many practical applications in physics, engineering, and other fields.

3. How are Fourier series used in real-life applications?

Fourier series have a wide range of applications in real-life, including signal processing, image and sound compression, and solving differential equations. They are also used in fields such as acoustics, electromagnetism, and finance.

4. Are there any limitations to using Fourier series?

Yes, there are some limitations to using Fourier series. They are only applicable to periodic functions, and the convergence of the series may be slow for some functions. Additionally, they may not accurately represent functions with sharp discontinuities or singularities.

5. What are some recommended books for learning about Fourier series in calculus?

Some popular books on Fourier series include "Fourier Series and Boundary Value Problems" by Ruel V. Churchill, "An Introduction to Fourier Series and Integrals" by Robert T. Seeley, and "The Fourier Transform and Its Applications" by Ronald N. Bracewell. It is also recommended to consult with a calculus professor or check online resources for additional guidance and practice problems.

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