# Books for Laplace and Fourier transforms

• yoran
In summary, the conversation is about a computer science student who needs resources for learning about Laplace and Fourier transforms for an electric engineering course. Some recommended books for understanding these transforms include "Who is Fourier: a mathematical adventure" for a quick derivation, "Digital Signal Processing" by Steven Smith for an intuitive understanding, "Schaum's Outline of Laplace Transforms" for application examples, "Linear Signals and Systems" by B.P Lathi for application in signals and systems, and "Advanced Engineering Mathematics" by Zill and Cullen for a deeper understanding. The main differences between Fourier and Laplace transforms, as well as their uses and conditions, are also discussed.
yoran
Hi,

I'm a computer science student but I'm taking electric engineering courses. One of those courses is called "System Theory and Control Theory". The course assumes knowledge of Laplace and Fourier transforms. All the electric engineers have had an analysis course that covers those topics but I haven't. Do you know any books which cover Laplace and Fourier transforms, by preference books intended for engineers?

Thanks

A quick easy derivation of Fourier series and transform (continuous), is "Who is Fourier: a mathematical adventure". It is cartoonish but is real easy to read and is a good derivation. A good easy intuitive book on La Place transforms is: Digital Signal Processing by Steven Smith. (it is free on the web). Look at the last chapter. Neither book will help you solve problems but you will have a good solid feel for what these important transforms really are.

Ok thanks. I checked out Digital Signal Processing by Steven Smith and it's really great. Not too much detail but it covers a lot of stuff. Exactly what I need :-). Thanks!

You can also pick up a copy of Schaum's Outline of Laplace Transforms. You can also see how Laplace and Fourier transforms are applied by picking up a book relating to Signals and Systems. For this I would recommend Linear Signals and Systems by B.P Lathi.

Advanced Engineering Mathematics by Zill and Cullen.

For deeper undersatnding into Fourier Series look up Fourier Transform and Its Applications by Ronald Bracewell

what are the main differences between the Fourier and laplace transform.and when and where we used these transformation also conditions for Fourier and laplace transform

## What are Laplace and Fourier transforms?

Laplace and Fourier transforms are mathematical operations that are used to transform a function from the time or space domain to the frequency domain, and vice versa. These transforms are commonly used in engineering and science to analyze and solve differential equations and signal processing problems.

## Why are Laplace and Fourier transforms important?

Laplace and Fourier transforms are important because they allow us to simplify complex mathematical operations and solve problems in the frequency domain, which is often easier and more intuitive than the time or space domain. These transforms also have a wide range of applications in various fields such as electrical engineering, physics, and mathematics.

## How do Laplace and Fourier transforms work?

Laplace and Fourier transforms work by decomposing a function into its constituent frequencies. The Laplace transform uses complex numbers to represent the frequency components, while the Fourier transform uses sine and cosine functions. The transformed function can then be analyzed and manipulated with mathematical operations before being transformed back to the original domain.

## What are some common applications of Laplace and Fourier transforms?

Laplace and Fourier transforms have many practical applications, including signal processing, image analysis, control systems, and circuit analysis. They are also used in fields such as physics, biology, and economics to model and analyze complex systems.

## Are there any limitations to Laplace and Fourier transforms?

While Laplace and Fourier transforms are powerful tools, they do have some limitations. For example, they are only applicable to linear systems and are not suitable for non-linear systems. In addition, the transforms may not converge for some functions, making them unsuitable for certain applications.

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