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Fourier Analysis and Boundary Value Problems
 
 
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Fourier Analysis and Boundary Value Problems [Hardcover]

Enrique A. Gonzalez-Velasco (Author)
4.4 out of 5 stars  See all reviews (5 customer reviews)

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Book Description

0122896408 978-0122896408 December 2, 1996 1
Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.
A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.

Key Features
* Topics are covered from a historical perspective with biographical information on key contributors to the field
* The text contains more than 500 exercises
* Includes practical applications of the equations to problems in both engineering and physics

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Editorial Reviews

Review

"This is a lovely book. I would want to have it on my shelf as a serious Fourier Analyst...For history and mathematics this book rates very high both in scholarship and exposition...I would insist on my library getting it. It starts carefully and moves ahead to advanced material including Lebesgue integration."
--John Gilbert, University of Texas
"Gonzalez-Velasco makes historical development of the subject a major theme. For me this makes the book very interesting...this interweaving of history, integration, and PDE/BVP reads very nicely...Plenty of good exercises...very well written."
--Keith Phillips, University of Colorado, Colorado Springs

From the Back Cover

Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solution. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.

A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.

Product Details

  • Hardcover: 551 pages
  • Publisher: Academic Press; 1 edition (December 2, 1996)
  • Language: English
  • ISBN-10: 0122896408
  • ISBN-13: 978-0122896408
  • Product Dimensions: 9.4 x 6.3 x 1.2 inches
  • Shipping Weight: 2.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #1,600,536 in Books (See Top 100 in Books)

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Average Customer Review
4.4 out of 5 stars (5 customer reviews)
 
 
 
 
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4 of 4 people found the following review helpful:
5.0 out of 5 stars One of "THE" Books on Fourier and Boundary Value Problems, July 5, 2001
By A Customer
This review is from: Fourier Analysis and Boundary Value Problems (Hardcover)
This book is very complete and comprehensive. It is meant for the advanced undergraduate (and even graduate) student. The book states it assumes you know the 1st year of calculus and how to solve some ordinary differential equations. It would help if you took one more upper division math class, as to be familiar with the proofs.

In a nutshell, this book is great! I used it to study for my PhD Quals in physics. It has a nice portion on Green's functions. The book is 'mathematical' but the backdrop on the topics are based on physical problems. The historical notes are great, and act as a complement to the physical problems (I'm not a big fan of history in textbooks, but this book does a nice job of integrating it).

Lots of problems are given, though no solutions are given for any of them. It would be a nice compliment to at least show the start, a tid bit in the middle, and then the solution. The solution at the very least. There are other books that do provide solutions to the types of problems listed here, but it would be nice just to carry around this one when learning boundary value problems.

A must for anyone that works on any problems that have ODEs, PDEs, Fourier and Laplace transforms, Boundary Value Problems and Green's Functions. You won't be disappointed!

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2 of 2 people found the following review helpful:
5.0 out of 5 stars Fourier Analysis and Boundary Value Problems, July 30, 2002
By A Customer
This review is from: Fourier Analysis and Boundary Value Problems (Hardcover)
This is an excellent introduction to Fourier series and its
applications to boundary value problems. It has a very good combination of history, theory,and exercises. In particular,
the book is an ideal text for math students who are taking
their first PDE course and do not have enough backgound in physics. The only problem with this book is its high price.
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1 of 1 people found the following review helpful:
2.0 out of 5 stars Having a professor who writes his own text not always good., May 24, 2005
This review is from: Fourier Analysis and Boundary Value Problems (Hardcover)
I had Professor Gonzalez for my applied math class and we used this book. while is a unique take, including history and background, the subject matter remained unclear at times. It is hard to grasp as a sophmore in college and it goes to fast in a classroom setting. While I agree that other professor's should use this book as a reference tool, I have experienced it first-hand in the classroom and it caused more confusion than anything else.
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Inside This Book (learn more)
First Sentence:
Napoleon Bonaparte's expedition to Egypt took place in the summer of 1798, the expeditionary forces arriving on July 1 and capturing Alexandria the following day. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
usual trigonometric system, regular distribution corresponding, boundary value prohlem, endpoint conditions, piecewise continuous derivative, charged box, complete orthogonal system, second linearly independent solution, heated bar, heat propagation, bounded subinterval, hounded solution, telegraph equation, distribution sense, piecewise continuously differentiable, arbitrarily small interval, odd extension, initial temperature distribution, sine series, boundary value problem, hounded interval, nth partial sum, circular membrane
Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Repeat Exercise, Weierstrass M-test, Columbia University, Daniel Bernoulli, Lord Armstrong, University of Berlin, Académie des Sciences, Cambridge University Press, David Eugene Smith Collection, Ecole Polvtechnique, Sir William Thomson, The Analytical Theory of Heat, Academic Press, Type of Parabolic Boundary Value Problem, Use the Rodrigues
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