Fleisch D. A Student's Guide to Laplace Transforms

Cambridge: Cambridge University Press, 2022. — 222 p.The Laplace transform is a useful mathematical tool encountered by students of physics, engineering, and applied mathematics, within a wide variety of important applications in mechanics, electronics, thermodynamics and more. However, students often struggle with the rationale behind these transforms, and the physical meaning of the transform results. Using the same approach that has proven highly popular in his other Student's Guides, Professor Fleisch addresses the topics that his students have found most troublesome; providing a detailed and accessible description of Laplace transforms and how they relate to Fourier and Z-transforms. Written in plain language and including numerous, fully worked examples. The book is accompanied by a website containing a rich set of freely available supporting materials, including interactive solutions for every problem in the text, and a series of podcasts in which the author explains the important concepts, equations, and graphs of every section of the book.The Fourier and Laplace Transforms
Definition of the Laplace Transform
Phasors and Frequency Spectra
How These Transforms Work
Transforms as Inner Products
Relating Laplace F (s) to Fourier F (ω)
Inverse Transforms
Problems
Laplace-Transform Examples
Constant Functions
Exponential Functions
Sinusoidal Functions
tn Functions
Hyperbolic Functions
Problems
Properties of the Laplace Transform
Linearity
Time and Frequency Shifting
Scaling
Time-Domain Differentiation
Time-Domain Integration
Multiplication and Division of f (t) by t
Transform of Periodic Functions
Convolution
Initial- and Final-Value Theorems
Problems
Applications of the Laplace Transform
Differential Equations
Mechanical Oscillations
Electric-Circuit Oscillations
Heat Flow
Waves
Transmission Lines
Problems
The Z-Transform
Introduction to the Z-Transform
Examples of the Z-transform
Characteristics of the Z-transform
Problems
Further Reading