A Student's Guide to Laplace Transforms

Well written, very descriptive of the LaPlace transform and how it works. The solved problems are well-documented and afford the reader a great opportunity for study

Very accessible easy to read book. Great for self-studying or for someone willing to invest time in the topic at their own pace. It doesn't sacrifice readability, having a large amount of figures that provide the much necessary conceptual insights on the topic. In fact, the entire rationale of the book seems precisely to provide the reader with a very solid grounding on the meaning of the Laplace transform, rather than just being a dry, boring, mechanical book on the topic. This alone makes it stand out above the rest - it bothers explain the why, the how, and specially, what does it really mean.

This book certainly is NOT the first place to learn about Laplace Transformations...that is probably best done in an introductory text to differential equations, such as the one by Dennis Zill. Here the transform is rigorously introduced in enormous detail, both mathematically and geometrically, and it is not until much later on are the applications introduced-the raison d'etre. It is however nice to be able to have a good understanding of the similarities and the differences between the Laplace and the Fourier transforms, and the concept that the real part of 's' acts as a frequency was quite illuminating, as before I had just thought of it as the growth/decay factor. I must admit, I have never heard of or used the Z-transformation discussed towards the end of the book. In summary, if you use the Laplace transforms simply as a tool in conjunction with tables of foward and reverse transforms, and are not interested in the machinery behind the transformation, this book is way beyond your needs. But how could you NOT want to know more??

Really Great! I was trying to understand the transient response of RC circuits in a Kicad/spice simulation and this book really explains the mathematical details of the solution nicely. I used a lot of Fourier transforms in school, but sadly never realized how useful Laplace transforms are for so many real world problems. The author did a great job - I have found the book really accessible and easy to follow. Figure to look at some of his other work as well now.

I am still reviewing this book, having just gotten it recently - however, a full quick overview shows it to be about right for those wishingto refresh or re-learn Laplacian transforms. I always strggled with this as it was not covered well in the courses I took in University, so this will re-jog my brain and allow more use moving forward when needed. A great book, so far, and well written, with "student" exercises to practice - just what the "math doctor" ordered! Thanks - recommended for students and adults re-training.

This book is excellent and has answered many questions he answered like why -0 vs 0. He shows how the transforms work. Then applications. I have studied Laplace Transforms in other textbooks. I’m an applied mathematics as a tool and don’t care about proofs or theorems however I got interested in operational calculus. I also studied the inverse transform and how residues fit in. The author also has other books that I will check on in due time. I highly recommend this book and will try to give further updates.

Good book to refresh my memory about Laplace transforms as Engineer who learned that 30 years ago! I like the explanation about the interest and the use of such mathematical transforms a stools to help to solve complex Engineering tasks. it will be easier if the problem solutions where part of the book instead of online but I can understand why.

The purpose of this work is clearly stated on the backcover of the book and stated by the author on page 40 of the book. It is best not only to have a background in multivariable calculus but also some basic knowledge of LaPlace, Fourier, and z-transforms. You should be familiar with Heaviside step-functions, Dirac delta functions, and gamma functions prior to reading this text. Professor Fleisch does a incredible job of explaining how these transforms are related, the time and frequency domains, and what integration of angular frequencies are required for the best approximation of the inverse transforms. The first two chapters meticulously derive the transforms for constant, sin, cos, and t^n power, and hyperbolic functions using Euler's equation and limits. The problems sets have ten problems for each chapter. You can either use hints and try to solve on your own or look at the full solution. The pdf of the solutions was easy to download from the publisher. Chapter 3 properties of LaPlace transform including integration, differentiation, and convolution. Chapter 4 covers applications. Chapter 5 z-transforms. At least for me this work is written at a more difficult level than previous books by Fleisch in the Student's Guide Series. Fortunately the end of the chapter problems are written at an easier level. I was primarily interested in the first three chapters, which I have read through twice. I am a self learner and the solved solution sets are critical. Professor Flesich has given us another wonderful text, I would love to see a similar work in this series on complex variables and differential geometry. The solutions sets should be in a similar formats hints and complete solutions.

制御工学では，初期値はゼロと信じて無視し，ラプラス変換表を機械的に使うだけでした．実用的にはそれで十分でしたが，本書には，積分の上限と下限の意味，収束性，フーリエ変換がラプラス変換の特殊な場合であることなどが丁寧に説明されています． 実部と虚部の２つのパラメータを使うラプラス変換により，減衰と振動がまとめて扱えることの便利さを味わうことができます．変換表を丸暗記すれば十分と信じていた工学部生にとって，大変示唆に富む教科書です．演算子法にも繋がります．この著者のテキストは，どれをとっても良書です．

Ho trovato questo libro estremamente utile per lo studio delle trasformate di Laplace. È scritto in modo chiaro e accessibile, con spiegazioni passo passo e numerosi esempi pratici che aiutano a comprendere concetti complessi. Ideale sia per studenti universitari che per chiunque voglia approfondire questo argomento matematico. 📌 Pro ✅: Spiegazioni semplici e dettagliate Esempi pratici e applicazioni reali Ottimo per studenti di ingegneria, fisica e matematica Organizzazione chiara dei contenuti 📌 Contro ❌: Alcune sezioni possono risultare troppo tecniche per principianti assoluti Mancanza di esercizi con soluzioni dettagliate 📌 Conclusione 💡: Nel complesso, un libro eccellente per chi vuole padroneggiare le trasformate di Laplace con un approccio graduale e concreto.

I had been wanting to learn the Laplace transform for years, and when I saw this book i had to order it. It is a page-turner. Very methodical and clear. Unfortunately, I waited too many years, and I'm rusty on calculus, so I've had problems concentrating, but too curious about what's next to be able to slow down and try to understand some detail that wasn't clear. What I really like about it is the effort the author put into helping the reader connect to Laplace from intuition, not just algebra. Lots of graphs, lots of questions and answers. For example, the fact that both real and imaginary axes in the s domain are "frequency" was a revelation. The imaginary axis is certainly frequency, but the real axis determines decay, so how is that a frequency? It is, in the sense that it expresses how often the envelope grows or falls by e.

An important topic well explained.

A Wonderful book! Definitely not the first book to read on this subject. Before reading this book, you have to be familiar with this transformation, you have to had performed some transformations with the given formulas in the text books during your student life. If you wonder what is “actually” going on with the Laplace Transformations, this book is written for you. This book is a very useful tool for understanding the meaning of the Laplace and Fourier transformations. It makes you enter the “engine-room” of the famous Laplace Transformation Formula, understand the working principle and the philosophy of the mechanism at the background. Beside video tutorials, there are also supplementary material available in the specified web-link inside the book. The book is great! Enjoy the book!