Laplace Transforms in Theory and Practice: A Computational Approach
Hrachya Khachatryan
Laplace transforms can seem difficult to understand, but this book makes them approachable. Hrachya Khachatryan introduces the subject in clear language alongside rigorous mathematics, supported by examples, illustrations and Wolfram Language visualizations. Readers move from the forward and inverse transforms of basic functions through advanced topics such as the complex inversion formula and Cauchy's residue theorem. Applications highlight how Laplace transforms simplify ordinary differential equations, partial differential equations, fractional systems and control problems—linking theory to practice across mathematics and engineering.
Readers can check their understanding with end-of-chapter exercises, detailed solutions and a sample final exam. Created with students and instructors in mind, the book also connects directly to the free online course from Wolfram U, Introduction to Laplace Transforms, which features videos that reinforce selected topics. Together, the text and course provide a thorough learning path that blends foundational concepts with worked examples and computational tools, making one of applied mathematics' central techniques both accessible and practical.
Notebooks can be opened in Mathematica or the free Wolfram Player.
Information & Media Inquiries
- Title: Laplace Transforms in Theory and Practice: A Computational Approach
- Author: Hrachya Khachatryan
- Technical Editor: Juan Ortiz
- Paperback: forthcoming
- Kindle: forthcoming
- Wolfram Notebooks: download free
- Publisher: Wolfram Media, Inc.
- Publication Date: March 12, 2026
- ISBN-13: 978-1-57955-104-9 (paperback)
- ISBN-13: 978-1-57955-106-3 (Kindle)
- ISBN-13: 978-1-57955-105-6 (Wolfram Notebooks)
Contents
- Introduction
- What Is a Laplace Transform?
- Formal Properties of the Laplace Transform: Part 1
- Formal Properties of the Laplace Transform: Part 2
- Special Functions
- Elementary Functions
- Piecewise and Generalized Functions
- Periodic Functions
- Numerical Evaluation
- Definition of the Inverse Laplace Transform
- Formal Properties of the Inverse Laplace Transform: Part 1
- Rational Functions
- Formal Properties of the Inverse Laplace Transform: Part 2
- Other Functions
- Complex Inversion
- Series and Asymptotic Expansions
- Multivariate Transforms
- Numerical Inverse Laplace Transform
- ODEs with Constant Coefficients
- ODEs: Applications in Physics and Engineering
- ODEs with Polynomial Coefficients
- Partial Differential Equations
- Integral Equations
- Fractional Differential Equations
- Evaluation of Integrals and Sums
- Control Systems
- Laplace Transforms in a Nutshell
- Sample Exam
- Table of Laplace Transforms
- References
Companion Online Course Introduction to Laplace Transforms
Wolfram U interactive courses are hosted on the Wolfram Cloud and allow you to interactively explore concepts using Wolfram Language functionality. This interactive course includes video lessons, practice problems, quizzes, a practice exam, a final exam and a chat-based Course Assistant (requires AI Access). Two shareable certificates are available: course completion and Wolfram Level 1 certification for proficiency in Laplace transforms. Work through the course content at your own pace and use the built-in progress tracker as you advance. Get started with our free courses by signing in to the Wolfram Cloud with your Wolfram ID—or create one; it's free!
See Course Details