Infinite Interval Problems for Differential, Difference and Integral Equations

Book Description

This monograph is a cumulation mainly of the author's research over a period of more than ten years and offers easily verifiable existence criteria for differential, difference and integral equations over the infinite interval. An important feature of this monograph is the illustration of almost all results with examples. This book should turn out to be a stimulus to the further development of the theory. Audience: This work will be of interest to mathematicians and graduate students in the disciplines of theoretical and applied mathematics.

Average customer rating:

Laplace Transforms
Not for us
Learning
Laplace Transforms Explained in Plain English
It helped me through control systems

Schaum's Outline of Laplace Transforms
Murray R Spiegel
Manufacturer: McGraw-Hill
ProductGroup: Book
Binding: Paperback

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Study Guides | Reference | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Reference | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

ASIN: 007060231X

Book Description

This book proveds a clear, concise explanation of Laplace transforms, or operational calculus--now necessary knowledge for engineers, physicists, mathematicians and other scientists. Definitions, principles and theorems are illustrated and reinforced by hundreds of fully worked out problems. Also included are chapters on complex variable theory and Fourier series and integrals, so important to discussions of the complex inversion formula.

Customer Reviews:

Laplace Transforms.......2007-05-12

I have several books on Laplace Transforms; but the Schaum's Outline by Murray Spiegel is particularly well done. The book is logically organized with many worked out examples. This is a classic overview of the Laplace Transform.

Not for us.......2007-05-01

Not for people who need a book on Laplace Transforms. Yes, lots of practice problems with answers. If you get lost and don't know how to go about a problem well page reference would have been nice.

Learning.......2007-01-06

Good overall coverage. nice explanations, and worked examples. id recommend it to anyone wanting to brush up on their transforms before an exam.

Laplace Transforms Explained in Plain English.......2005-09-23

This is a valuable reference to keep handy as a reminder about which transform methods best apply to various problems that you need to solve around the office.

It helped me through control systems.......2003-12-29

This book taught me both the basics and some of the finer points of LaPlace Transforms to get me past that hurdle so that I could begin focussing on the actual material presented in my BioControl Systems course. Many people got so caught up on the mathematics of LaPlace Transforms that they did not even get to the point where they could begin understanding control systems. I bought this book from Amazon at the beginning of the semester and it turned out to be a life-saver for me. I think that had I not sat down with this book for a weekend and taught myself LaPlace Transforms, I would have not passed that class.

Granted, this is a single case for a single class of a single bioengineering student; nevertheless, for my part I strongly recommend this book. I was put in a class where the teacher expected the students to have an understanding of the mathematics from the start. The majority of us didn't have that background, and this book clearly, simply, and without too much complication prepared me for my class which was exactly what I wanted it to do. It has been one of the best investments (as far as school books go) of my college career.

Book Description

This book presents most of the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics. Both the standard C8 pseudodifferential calculus and the analytic microlocal analysis is developed, in a context which remains intentionally global so that only the relevant difficulties of the theory are encountered. The originality lies in the fact that the main features of analytic microlocal analysis are derived from a single and elementary a priori estimate. Various exercises illustrate the chief results of each chapter while introducing the reader to further developments of the theory. This book is aimed at non-specialists of the subject and the only required prerequisite is a basic knowledge of the theory of distributions.

Fourier Series and Boundary Value Problems

Average customer rating:

Excellent
Great text for an intro to pde's course!
Try Another Text
An excellent book on Fourier Series

Fourier Series and Boundary Value Problems
James Ward Brown , and Ruel V. Churchill
Manufacturer: McGraw-Hill Science/Engineering/Math
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Infinity | Mathematics | Science | Subjects | Books

Mathematical Analysis | Mathematics | Science | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

Accessories:

ASIN: 0072325704

Book Description

Published by McGraw-Hill since its first edition in 1941, this classic text is an introduction to Fourier series and their applications to boundary value problems in partial differential equations of engineering and physics. It will primarily be used by students with a background in ordinary differential equations and advanced calculus. There are two main objectives of this text. The first is to introduce the concept of orthogonal sets of functions and representations of arbitrary functions in series of functions from such sets. The second is a clear presentation of the classical method of separation of variables used in solving boundary value problems with the aid of those representations.

Customer Reviews:

Excellent.......2003-11-08

This book is quite thorough, but remains easy to follow (considering the material). It starts out with partial differential equations (no previous PDE experience needed) and shows where Fourier series comes from, which I found motivating since the purpose of Fourier Analysis was evident from the beginning. It then goes into making solutions of arbitrary functions out of sine and cosine functions as well as touching on other orthogonal sets.

The book's main focus is on starting with PDEs and ending with a solution of a Fourier series.

The first chapter was the hardest since the approaches to problems were much different than in calculus, but after adjusting to the material and the approaches to the problems, it gets easier!

Great text for an intro to pde's course!.......2003-04-30

My first encounter with partial differential equations was out of this book. Since then, I've had another course on pde's, and used this book as a reference quite often. Fourier Series adn Boundary Value Problems is very much like Complex Variables and Applicatoins, also by Churchill and Brown. It's accessible to a large audience. Though it would help to have had an advanced calculus course, it isn't necessary to understand the mechanics of solving pde's (namely the variables seperable cases, which is mostly what's in this book). If you're an undergraduate math, engineering or physics student, you'll probably be using this book.

Try Another Text.......2000-08-23

I found Dr. Brown, in conjunction with Dr. Churchill, to have written a very dry and non-useful text. It fails to provide the undergraduate student with the resources and background information that more highly touted books offer. There are a few examples that are somewhat helpful, but overall I found myself having to use reference texts to supplement this one. I am not a math major, but am continually searching for good math texts to help me grasp the fundamentals of more difficult topics. I did not find that help here. Too much 'math prose' and not enough to-the-point definitions and examples, which is the cry of every non-math major. Their treatment of the Laplacian is not even worth the bother of placing it in the book. The physical size of the book is small, (9 1/2 by 6") with 335 pages. Not nearly enough for the treatment of its titled subject.

An excellent book on Fourier Series.......2000-02-12

This is a great book that gives precise examples which are easy to comprehend. Dr. Brown proves to be an excellent author once again.

Average customer rating:

Good, concise treatment
Excellent book
Little more than class notes...POOR class notes.

Fourier Series and Integral Transforms
Allan Pinkus , and Samy Zafrany
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Mathematical Analysis | Mathematics | Science | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 0521597714

Book Description

This volume provides a basic understanding of Fourier series, Fourier transforms, and Laplace transforms. It is an expanded and polished version of the authors' notes for a one-semester course intended for students of mathematics, electrical engineering, physics and computer science. Prerequisites for readers of this book are a basic course in both calculus and linear algebra. The material is self contained with numerous exercises and various examples of applications.

Customer Reviews:

Good, concise treatment.......2007-05-02

One reviewer characterized this book as little more than class notes. It is much better than that. It is, however, concise; the authors cover a lot of ground in few pages. As usual for graduate courses, a lot is required of the student. A good foundation in real analysis is assumed. For example, the authors say that Lebesgue's Dominated Convergence Theorem is beyond the scope of the book. This suggests that it is a more advanced topic, while really it is a less advanced topic that ought to have been covered in a prior course. In general, the book could be amplified to two or three times its length without taking up additional topics. I would not say that there are too few exercises, but it is true that a complete working out of the exercises in the back of the book would have been good.

Excellent book.......2004-03-07

I think this is an excellent book on Fourier series and Fourier transforms. I think their style is clear, concise and informative.

For example their treatment of pointwise conergence is explained in far simpler way then in other text.

The book is well done.

Little more than class notes...POOR class notes........2002-02-04

It appears that well-written advanced mathematics texts are few and far in between. "Fourier Series and Integral Transforms" is no exception. The authors belie their goal in the preface, stating that the "aim of this book is to provide ... important examples of useful series of functions." They admit that this text was a bundling of class notes from a course of the same name, but do not specify who actually gave the course. After reading the first few chapters, I'm forced to conclude that either the authors have little experience in writing comprehensive texts or they do not know the material.

I'll say one nice thing before I rip into this: the price. When all of my other science books cost a minimum of $100 each, it is nice to only have to fork out $... for a book.

One axiom that holds true in all mathematics courses is that the way to quickly master the material is to work problems. It goes without saying that rote problem working without feedback serves no purpose but to burn trees and waste time. This is the crux of the problem that I have with this book: inadequate number of problems, no problem key and no examples in the book.

The number of problems in the book is sparse at best, and most aspects of the ideas in the text seem underrepresented in the problems.

The lack of a problem key means that when the student is working the problems she has no idea if she got it correct. Doing a problem wrong serves no purpose whatsoever, except to demoralize the student. Providing a key does not allow students to "cheat" as it were, since one needs to demonstrate the steps toward getting the answer.

Finally, there are "examples" in the book, but the majority of them end abruptly with the sentence "it is not difficult to show~" or "it is easy to verify~."
This is fine and dandy if there were enough complete examples to get you going. Unfortunately, there are not. I would expect this sort of thing from someone who slept through the actual class, then-faced with a publishing deadline-was forced to "finish" his book quickly.

Book Description

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.

Customer Reviews:

The Laplace Transform.......2007-10-10

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.

Well Written and Presented.......2006-07-11

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.

I like this book.......2000-07-06

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.

Periodic Integral & Pseudodifferential Equations with Numerical Approximation

Average customer rating:

Periodic Integral & Pseudodifferential Equations with Numerical Approximation
Jukka Saranen , Gennadi Vainikko , and J. Saranen
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Mathematical Analysis | Mathematics | Science | Subjects | Books

All Amazon Upgrade | Amazon Upgrade | Stores | Books

Professional & Technical | Amazon Upgrade | Stores | Books

Science | Amazon Upgrade | Stores | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 3540418784

Book Description

Classical boundary integral equations arising from the potential theory and acoustics (Laplace and Helmholtz equations) are derived. Using the parametrization of the boundary these equations take a form of periodic pseudodifferential equations. A general theory of periodic pseudodifferential equations and methods of solving are developed, including trigonometric Galerkin and collocation methods, their fully discrete versions with fast solvers, quadrature and spline based methods. The theory of periodic pseudodifferential operators is presented in details, with preliminaries (Fredholm operators, periodic distributions, periodic Sobolev spaces) and full proofs. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.

Partial Differential Equations: Vol. 1 Foundations and Integral Representations (Universitext)

Average customer rating:

Partial Differential Equations: Vol. 1 Foundations and Integral Representations (Universitext)
Friedrich Sauvigny
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Mathematical Analysis | Mathematics | Science | Subjects | Books

Mathematical Physics | Physics | Science | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

Partial Differential Equations 2: Functional Analytic Methods (Universitext)

ASIN: 3540344578

Book Description

This comprehensive two-volume textbook presents the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Special emphasis is put on the connection of PDEs and complex variable methods.

In this first volume the following topics are treated: Integration and differentiation on manifolds, Functional analytic foundations, Brouwer's degree of mapping, Generalized analytic functions, Potential theory and spherical harmonics, Linear partial differential equations. While we solve the partial differential equations via integral representations in this volume, we shall present functional analytic solution methods in the second volume.

This textbook can be chosen for a course over several semesters on a medium level. Advanced readers may study each chapter independently from the others.

Real Analysis: Theory of Measure And Integration

Average customer rating:

Real Analysis: Theory of Measure And Integration
J. Yeh
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

Measurement | Experiments, Instruments & Measurement | Science | Subjects | Books

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Mathematical Analysis | Mathematics | Science | Subjects | Books

Mensuration | Mathematics | Science | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

ASIN: 9812566538

Boundary Value Problems and Integral Equations in Nonsmooth Domains (Lecture Notes in Pure and Applied Mathematics)

Average customer rating:

Boundary Value Problems and Integral Equations in Nonsmooth Domains (Lecture Notes in Pure and Applied Mathematics)

Manufacturer: CRC
ProductGroup: Book
Binding: Paperback

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Mathematical Analysis | Mathematics | Science | Subjects | Books

Book Description

Based on the International Conference on Boundary Value Problems and lntegral Equations In Nonsmooth Domains held recently in Luminy, France, this work contains strongly interrelated, refereed papers that detail the latest findings in the fields of nonsmooth domains and corner singularities. Two-dimensional polygonal or Lipschitz domains, three-dimensional polyhedral corners and edges, and conical points in any dimension are examined.

Books:

Books Index

Books Home

Recommended Books