The Laplace Transform: Theory and Applications (Undergraduate Texts in Mathematics) [Hardcover]

Joel L. Schiff (Author)

Book Description

Publication Date: October 14, 1999 | ISBN-10: 0387986987 | ISBN-13: 978-0387986982 | Edition: 1

The Laplace transform is an extremely versatile technique for solving differential equations, both ordinary and partial. It can also be used to solve difference equations. The present text, while mathematically rigorous, is readily accessible to students of either mathematics or engineering. Even the Dirac delta function, which is normally covered in a heuristic fashion, is given a completely justifiable treatment in the context of the Riemann-Stieltjes integral, yet at a level an undergraduate student can appreciate. When it comes to the deepest part of the theory, the Complex Inversion Formula, a knowledge of poles, residues, and contour integration of meromorphic functions is required. To this end, an entire chapter is devoted to the fundamentals of complex analysis. In addition to all the theoretical considerations, there are numerous worked examples drawn from engineering and physics. When applying the Laplace transform, it is important to have a good understanding of the theory underlying it, rather than just a cursory knowledge of its application. This text provides that understanding.

Editorial Reviews

Review

"The book contains plenty of examples, exercises (with answers at the end) and a table of transforms. The book is certainly a handsome introduction to the Laplae transform, by its clear representation well-suited for self-study." Nieuw Archief voor Wiskunde, March 2001 "This clearly written undergraduate textbook can be recommended to students and teachers of this subject, both in a mathematial and engineering context." Newsletter of the EMS, issue 42, December 2001

Product Details

• Hardcover: 247 pages
• Publisher: Springer; 1 edition (October 14, 1999)
• Language: English
• ISBN-10: 0387986987
• ISBN-13: 978-0387986982
• Product Dimensions: 9.3 x 6.3 x 0.8 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #1,738,697 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

15 of 16 people found the following review helpful:

4.0 out of 5 stars I like this book, July 6, 2000

By 

Pedro Tomas Hasdeu (capital federal Argentina) - See all my reviews
(REAL NAME)   

This review is from: The Laplace Transform: Theory and Applications (Undergraduate Texts in Mathematics) (Hardcover)

This book is written in a very clear style, suitable for self-study. The exercises have been well chosen and correctly placed. It might be most effective if read concurrently or immediately after an elementary course on Differential Equations at the level of Zill's book. Teachers should take a look at this book, it shows how to deal with the subject rigorously without being boring. No measure theory is required.

3 of 3 people found the following review helpful:

5.0 out of 5 stars The Laplace Transform, October 9, 2007

By 

Nicholas D. Ward (Philadelphia, Pennsylvania United States) - See all my reviews
(REAL NAME)   

This review is from: The Laplace Transform: Theory and Applications (Undergraduate Texts in Mathematics) (Hardcover)

The Laplace Transform: Theory and Applications (Undergraduate Texts in Mathematics)

Joel Schiff has demonstrated on a number of occasions that he is a master expositor of Mathematics and the current volume has to be among Dr Schiff's finest. 'The Laplace Transform' is an excellent starting point for those who want to master the application of transform techniques to boundary value problems and thus provides a backdrop to Davies' Integral Transforms and Duffy's Transform Methods.

Dr Schiff is to be particularly commended for his treatment of the inverse Laplace transform, which often receives scant attention in engineering texts.

Dr Schiff's book can be read at several levels; readers less interested in mastering the proofs may be interested to note that most of the standard transforms one meets in practice are covered either in the text or in exercises.

In sum, 'The Laplace Transform' is for those who want to get beyond the 'operational technique' status of the method, and is strongly recommended to readers who have covered a first course in complex variables. It should appeal to Mathematicians and Engineers alike.

5 of 6 people found the following review helpful:

5.0 out of 5 stars Well Written and Presented, July 10, 2006

By 

Allan Vandyke (New Zealand) - See all my reviews

This review is from: The Laplace Transform: Theory and Applications (Undergraduate Texts in Mathematics) (Hardcover)

I thought this book was really well written and presented. It has really helped with my understanding of Laplace Transforms. I would highly recommend this book to engineers who want a deeper understanding of transforms. It is worth while reading up on Residue Theory and Cauchys Theorem before reading this book. I am sure that I will constantly reference back to this book for my work.