Introduction to Numerical Methods and MATLAB: Implementations and Applications

Book Description

From the Back Cover: The outstanding pedagogical features of this book are: o use of numerical experiments as a means of learning

why numerical methods work and how they fail; o a separate chapter reviewing the basics of applied

linear algebra, and how computations involving

matrices and vectors are naturally expressed in MATLAB; o use of a range of examples from those that provide a

succinct illustration of a basic algorithm, to those

that develop solutions to substantial problems in

engineering; o consistent use of well-documented and structured code

written in the MATLAB idiom; o a library of general purpose routines—-the NMM

Toolbox-—that are readily applied to new problems; o a progressive approach to algorithm development

leading the reader to an understanding of the more

sophisticated routines in the built-in MATLAB toolbox.

Customer Reviews:

Okay for a text.......2006-03-18

This book is okay for a text book, however there arent many examples, and the examples that are there are very simple. There are solutions for some problems online, though most of them are very basic and don't help very much.

Useful Book.......2004-08-28

This is a nice book for scientists and engineers. There are MATLAB programs already written that you can download from the webpage very easily, and modify for your specific use. I am no programmer, so having programs I can easily modify is a plus. This is meant to only be a review of linear algebra, so if you are trying to learn that subject, you will probably need to supplement this text with another book. This is not terribly in-depth on the MATLAB either. But it is a very useful handbook of plotting and interpolation methods, and how to choose the best methods for your particular set of data.

Scientific Computing and Differential Equations : An Introduction to Numerical Methods

Average customer rating:

Does the job well

Scientific Computing and Differential Equations : An Introduction to Numerical Methods
Gene H. Golub , and James M. Ortega
Manufacturer: Academic Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0122892550

Book Description

Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places the subject in a larger context.
This book is appropriate for upper undergraduate courses in mathematics, electrical engineering, and computer science; it is also well-suited to serve as a textbook for numerical differential equations courses at the graduate level.

* An introductory chapter gives an overview of scientific computing, indicating its important role in solving differential equations, and placing the subject in the larger environment
* Contains an introduction to numerical methods for both ordinary and partial differential equations
* Concentrates on ordinary differential equations, especially boundary-value problems
* Contains most of the main topics for a first course in numerical methods, and can serve as a text for this course
* Uses material for junior/senior level undergraduate courses in math and computer science plus material for numerical differential equations courses for engineering/science students at the graduate level

Customer Reviews:

Does the job well.......2001-06-30

This book is an excellent introduction to the field of scientific computing and serves well as a textbook, given the many exercises included in it. Although the software packages quoted in the book have been considerably revised since the time of publication of the book, one can still use it effectively as a guide to the construction of algorithms and software for scientific applications. The level of the book makes it suitable for a course in numerical analysis at the advanced undergraduate level. After a brief review of the concepts and strategies employed in mathematical modeling in chapter 1, the author begins in chapter 2 with the study of initial value problems for ordinary differential equations. He motivates the discussion with the predator-prey problem from mathematical biology and the ballistic trajectory problem with air resistance from physics. The initial-value problem for the general case of systems of ordinary differential equations is then solved using finite difference methods. The author treats thoroughly Euler's method along with its discretization error. Recognizing that first-order methods have very slow rates of convergence, Runge-Kutta methods are discussed next to alleviate this problem. The Heun method, fourth-order method, and more general one-step methods are discussed in detail. The sample initial value problems are then treated using some of these techniques. The technique of polynomial interpolation, so popular as a solution technique in high-level symbolic programming languages such as Mathematica, is discussed in this chapter also. Multistep methods, such as the Adams-Bashforth, Adams-Moulton, and predictor-corrector methods are treated also. The author also discusses the important concept of stability in this chapter. Although he does not give a rigorous definition of stability, due to the mathematical formalism needed for such a definition, he does give several examples of differential equations that are not stable, and also examples of instabilities in the actual numerical methods employed.

Boundary value problems for ordinary differential equations are treated in the next chapter. The author motivates the problem via a two-point boundary value problem, but only concentrates on linear boundary value problems in this chapter, with the nonlinear case treated in chapter 5. The author carefully distinguishes between Dirichlet and Neumann boundary conditions. The solution of the discretized problem is solved appropriately with Gaussian elimination, and the author gives a numerical example. The case of periodic boundary conditions is also treated, and the author chooses to solve the resulting linear system using the Sherman-Morrison technique, instead of Gaussian elimination, arguing (correctly) that this method only needs code for solving tridiagonal matrices.

The study of the solution of linear systems of equations is taken up in more detail in the next chapter, with emphasis on solution techniques for banded or full matrices. The class of least square problems is treated first, with least square polynomials and their calculation using orthogonal polynomials. The author then treats Gaussian elimination in more detail in this chapter, with treatments of LU factorization and banded matrices being treated. The author gives the reader more details on the performance issues involved in the different solution techniques. Ill-conditioning and error analysis are first discussed here in the context of solution of systems of linear equations, along with definitions and calculations of condition numbers. The author also gives good overviews of alternative factorization techniques, such as Cholesky and QR factorization.

The most important application of numerical methods is in the class of nonlinear problems, since these usually do not have analytical solutions. Even if analytical solutions are found in terms of special functions, the calculation of these special functions typically must be done using techniques from numerical analysis. Nonlinear problems are discussed in chapter 5 of this book, wherein the author again uses the projectile problem to introduce shooting methods. This is followed by a very detailed discussion of the solution of a nonlinear equation using bisection, secant, and Newton's methods. Systems of nonlinear equations are then discussed, with the infamous Picard iteration technique leading the discussion, followed again by a treatment using Newton's method.

Then in the next chapter, the author switches gears somewhat by moving away from techniques based on finite differences and discussing ones such as finite element, Galerkin's and Rayleigh-Ritz methods. The mathematical considerations employed in this chapter are a little more involved than the other chapters, but the author explains the ideas well, and the assigned exercises shed more light on the issues involved. Spine approximations are also discussed, along with the numerical evaluation of the integrals that naturally arise in Galerkin methods.

Eigenvalue problems, so ubiquitous in all areas of science and engineering, are the subject of the next chapter. Interestingly, the author discusses Gerschgorin's theorem, which usually does not appear in a book at this level. Most of the popular techniques for solving eigenvalue problems, such as QR and iterative methods, are discussed thoroughly.

Book Description

Assuming no prior MATLAB experience, this clear, easy-to-read book walks readers through the ins and outs of this powerful software for technical computing
Generously illustrated through computer screen shots and step-by-step tutorials that are applied in the areas of mathematics, science, and engineering
Clearly shows how MATLAB is used in science and engineering

Customer Reviews:

Great for learning the basics of MATLAB........2007-08-18

I purchased this title because I am starting a numerical analysis sequence next year using Matlab and I knew only how to plot in 2D and do simple calculations at the command line. After studying from Gilat's text for the past month or so I feel very comfortable using Matlab for all the basics and I am ready to learn how to exploit the full power of the program.

Each chapter gives just enough mathematical background to provide anyone with at least college algebra/trig enough to understand what is going on.
Although this book does not cover any topic too deeply, it does cover the fundamentals of many aspects of Matlab in a way that allows the reader to move fairly quickly through the whole book without getting bogged down in any one area.

In the end you will know the basics about how Matlab operates: how to work with vectors and matrices, how to write simple programs and function files, how to plot and format data, how to fit data to a curve, and how to differentiate and integrate both numerically and symbolically, and a bunch of other great tools for solving problems.

Also, as the other reviewers mentioned, the book makes very good use of graphics to show how input and output should look, as well as what exactly each line means.

I would recommend this text to anyone wanting to learn the basics of Matlab.

Reader.......2007-04-23

If you plan to start with Matlab with no prior experience, this book beats most of the other available titles.Since an inside view of the book is not available on Amazon, I will for the benefit of others list out the chapters here.Ch1 begins with the necessary introduction,developing familiarity with the command window,display formats and precedence of operators.It moves on to Ch2 and Ch3 where arrays are introduced and the mathematical operations on them explained.Ch4 is about script files,Ch5 on elementary plotting techniques using in-built functions like plot and fplot.Ch6 introduces functions and Ch7 extends the previous material to formal programming techniques like loops and control structures.Ch8 explains curve fitting and interpolation,Ch9 is about three dimensional plots and special graphics.Ch10, the last one of the book uses Matlab to do symbolic math which cover elementary algebraic equations.The examples contained in the book are from elementary physics and engineering,so if you are looking for more advanced material that has been treated using Matlab,this might be a little less helpful.The numerical techniques again cover simple problems like projectile trajectory,flow of water from a vessel with a small hole punched in its sidewall,RC circuits, viscosity and so on.Relatively advanced topics like Fourier transforms and applications to signal processing are also left out.If you are done with this book or feel that the material isnt of much help, I will suggest that you might try "Numerical Computing with Matlab" by Moler(he is perhaps one of the architects of Matlab).This book(electronic version) is available for free from the mathworks website [...].Overall this book does a good job in explaining details and is also generously sprinkled with figures and screenshots.Please try it if you are first timer to Matlab.

Very good introduction.......2006-05-04

I had never used matlab when I started reading this book and I found it very easy to follow. I now have a good working understanding of the matlab basics and I recommend that anyone who's looking to get started with matlab pick up a copy.

The perfect introductory text for MATLAB.......2005-12-08

If you are completely new to MATLAB then you will find no better book to guide you through the basics. It is perfectly suited for teaching yourself several basic but still very interesting and useful programming techniques. Topics are presented to the reader in an order carefully determined to produce maximum benefit and knowledge. The book is short and very readable, with many example programs.

In short: if you want a FIRST introductory textbook for MATLAB, you can't beat this book. And it covers the latest version (Release 14).

A truly excellent text!.......2005-11-21

This book was written for teaching Matlab to freshmen in an introductory engineering course, so most of the examples are from first year physics and engineering. Nevertheless, after looking at all competing texts, I chose it to teach Matlab to sophomore geology majors, most of whom had not yet taken calculus or physics. I was very happy with the results; by the end of the semester the students were well on their way to being competent programmers, and I think they will find calculus and physics much easier because of their experience with this book.

I chose this text because it is very well written--you can tell the author has had long experience teaching the subject--and because of its many excellent examples. Most people learn faster by example than by theory, and the examples in this book are easier to follow than those of other texts. Each example shows the command window with a gray background and white insets, or call-outs, containing explanations. The pages are attractive.

In the main text, Matlab commands are set in Courier to clearly distinguish them from the discussion itself. Sections are fairly short and easy to follow, and at the end of each chapter there are many problems of gradually increasing difficulty. The solutions to some problems are given at the back of the book. The abundance of complete examples makes it easy to skip around in the book as soon as students are familiar with Matlab syntax. There are astonishingly few typos and none were serious. Cell arrays and structures are used only where needed for particular commands, a wise pedagogical decision. I particularly enjoyed the second edition's new chapter on symbolic math, as I had never used this part of Matlab in my own research.

The book is 7.5"x9.25" in size with 343 pages, and so is easy to carry around. It's inexpensive, as textbooks go nowadays.

An Introduction to Recent Developments in Theory and Numerics for Conservation Laws: Proceedings of the International School on Theory and Numerics for ... in Computational Science and Engineering)

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An Introduction to Recent Developments in Theory and Numerics for Conservation Laws: Proceedings of the International School on Theory and Numerics for ... in Computational Science and Engineering)

Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 3540650814

Book Description

The book concerns theoretical and numerical aspects of systems of conservation laws, which can be considered as a mathematical model for the flows of inviscid compressible fluids.Five leading specialists in this area give an overview of the recent results, which include: kinetic methods, non-classical shock waves, viscosity and relaxation methods, a-posteriori error estimates, numerical schemes of higher order on unstructured grids in 3-D, preconditioning and symmetrization of the Euler and Navier-Stokes equations.This book will prove to be very useful for scientists working in mathematics, computational fluid mechanics, aerodynamics and astrophysics, as well as for graduate students, who want to learn about new developments in this area.

Introduction to the Numerical Solution of Markov Chains

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Introduction to the Numerical Solution of Markov Chains
William J. Stewart
Manufacturer: Princeton University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0691036993

Book Description

A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse--and applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, however, it is necessary to understand how Markov chains can be solved numerically. In this book, the first to offer a systematic and detailed treatment of the numerical solution of Markov chains, William Stewart provides scientists on many levels with the power to put this theory to use in the actual world, where it has applications in areas as diverse as engineering, economics, and education. His efforts make for essential reading in a rapidly growing field.

Here Stewart explores all aspects of numerically computing solutions of Markov chains, especially when the state is huge. He provides extensive background to both discrete-time and continuous-time Markov chains and examines many different numerical computing methods--direct, single-and multi-vector iterative, and projection methods. More specifically, he considers recursive methods often used when the structure of the Markov chain is upper Hessenberg, iterative aggregation/disaggregation methods that are particularly appropriate when it is NCD (nearly completely decomposable), and reduced schemes for cases in which the chain is periodic. There are chapters on methods for computing transient solutions, on stochastic automata networks, and, finally, on currently available software. Throughout Stewart draws on numerous examples and comparisons among the methods he so thoroughly explains.

Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction

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Here's hoping for a third edition of this great text!
Post Graduate Compressible flow
Outstanding text or reference for graduate level CFD!

Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction
Eleuterio F. Toro
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Accessories:

ASIN: 3540659668

Book Description

High resolution upwind and centered methods are today a mature generation of computational techniques applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. The book is designed to provide readers with an understanding of the basic concepts, some of the underlying theory, the ability to critically use the current research papers on the subject, and, above all, with the required information for the practical implementation of the methods. Applications include: compressible, steady, unsteady, reactive, viscous, non-viscous and free surface flows.

Customer Reviews:

Here's hoping for a third edition of this great text!.......2001-06-30

This is the book you want if you need to solve real compressible flow problems. It covers all the basics plus there's tons of advanced materials. I especially like the fact that there are numerous detailed examples and coding templates. In addition, the book contains a very extensive reference, allowing the reader to go back to the orginal papers.

Post Graduate Compressible flow.......2000-12-18

Have to agree with Mark, this book is quite superb. Professor Toro does a superb job - it took me from knowing nothing about shock capture to being able to write my own high resolution code in about six months. Coupled with the Numerica software it is an invaluable tool for learning about compressible flow.

Outstanding text or reference for graduate level CFD!.......1998-12-01

By far the best computational fluid dynamics text I have come across during my thesis research! The author presents modern shock-capturing numerical methods for solving the time-dependent hyperbolic conservation laws in multiple dimensions with exceptional clarity. Most of the text focuses on Godunov methods and is littered with practical applications and discussions for those with a limited background in CFD. In addition, Toro presents a simpler interpretation of his WAF method. In terms of readability, I found this book to be far superior. It will undoubtedly become as indispensible in the CFD field as those by Fletcher, Hirsch and LeVeque!

Applied CFD Techniques: An Introduction Based on Finite Element Methods

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Applied CFD Techniques: An Introduction Based on Finite Element Methods
Rainald Löhner
Manufacturer: Wiley
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471498432

Book Description

Computational fluid dynamics (CFD) is concerned with the efficient numerical solution of the partial differential equations that describe fluid dynamics, and CFD techniques are commonly used in many areas of engineering where fluid behavior is a factor. This book covers the range of topics required for a thorough study and understanding of CFD.

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Professors Should Choose Another Book
Another excellent Real Analysis Text

Introduction to Real Analysis
Manfred Stoll
Manufacturer: Addison Wesley Publishing Company
ProductGroup: Book
Binding: Hardcover

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ASIN: 0673995895

Customer Reviews:

Professors Should Choose Another Book.......2006-06-01

This was my undergraduate textbook for Advanced Calculus I and II (as they were called at my school). I am returning to school to start my master's degree this next term and am going through the book to refresh my memory.

Wow, it is just the way I remember it. Frankly, I can't believe the other reviewers ratings. So, I thought I'd balance the average rating a bit with a review of my own.

When I was in college, this was my most dreaded reading material. It is a difficult subject to master, sure, but the author does not help matters by using failing to use a clear structure with emphasis on key points. Instead, there is barely any structure at all. Headings consist of unenlightening phrases such as "Theorem." Pragraphs are downplayed by the typesetting style as well, making each section almost an undifferentiated block of information. (The author has not even used an end-of-proof symbol!)

And not only is this book unfriendly, it is dry. The author tends to use strictly symbolic language when explaining in words would be so much clearer. In fact, he frequently skips the explanatory material altogether and moves straight to the examples. What is the context or object for these examples? The reader is mystified.

If you are a professor, please do not choose this book for your analysis class. I have a feeling it is only comprehensible to those who already thouroughly understand the material.

If you are a student who has come here to buy this book, you have my sympathy.

Another excellent Real Analysis Text.......2002-03-10

The style of this book is a bit like Robert Bartle's Introduction to Real Analysis. It is detailed and rigorous. It is an excellent book for those who want to learn Real Analysis.

An Introduction to Unconstrained Optimisation (Computer Illustrated Text)

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An Introduction to Unconstrained Optimisation (Computer Illustrated Text)
J McKeown , D Meegan , and D Sprevak
Manufacturer: Taylor & Francis
ProductGroup: Book
Binding: Paperback

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ASIN: 0750300256

Book Description

Integrating computer graphics and computer-based exercises with the text, An Introduction to Unconstrained Optimisation illustrates key methods with many examples and exercises using the computer. The book takes an elementary approach to this advanced topic, allowing readers to concentrate on learning and understanding the concepts of numerical optimization without unnecessary involvement in the intricacies of the subject. In addition, the modular approach of the software provides the opportunity to explore the algorithms used and to develop them further or try alternative approaches. Most of the algorithms are based upon a "hill-climbing" concept which, in two dimensions, is illustrated dynamically on the computer screen in the form of contour plots and search directions. The text is not specific to any particular microcomputer. Software is available for the BBC series of machines (40/80 track disc formats) and PC-compatible machines. The software is not available from your local bookstore, but is easily obtainable using the order form in the book. Keeping proofs and lists of methods to a minimum, the book is at a level suitable for a first course in numerical analysis, with a basic knowledge of calculus and vector algebra assumed. This book/software package will be of interest to professionals, teachers, and undergraduate students in mathematics, operational research, science, and engineering as well as economics and management courses that deal with quantitative methods.

Applied Numerical Methods for Partial Differential Equations: An Introduction with Spreadsheet Programs

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Applied Numerical Methods for Partial Differential Equations: An Introduction with Spreadsheet Programs
Lam Chung Yau
Manufacturer: Prentice Hall Southeast Asia Pte Ltd (a Pearson Education Asia Company)
ProductGroup: Book
Binding: Paperback

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