Introduction to Numerical Methods in Differential Equations by Mark H. Holmes (E

The Nile on eBay   Introduction to Numerical Methods in Differential Equations by Mark H. Holmes

This brings us to the next expression in the title: "numerical methods." This is a book about how to transform differential equations into problems that can be solved using a computer.The fact is that computers are only able to solve discrete problems and generally do this using ?nite-precision arithmetic.

FORMATPaperback LANGUAGEEnglish CONDITIONBrand New Publisher Description

The title gives a reasonable ?rst-order approximation to what this book is about. To explain why, let's start with the expression "di?erential equations." These are essential in science and engineering, because the laws of nature t- ically result in equations relating spatial and temporal changes in one or more variables.Todevelopanunderstandingofwhatisinvolvedin?ndingsolutions, the book begins with problems involving derivatives for only one independent variable, and these give rise to ordinary di?erential equations. Speci?cally, the ?rst chapter considers initial value problems (time derivatives), and the second concentrates on boundary value problems (space derivatives). In the succeeding four chapters problems involving both time and space derivatives, partial di?erential equations, are investigated. This brings us to the next expression in the title: "numerical methods." This is a book about how to transform differential equations into problems that can be solved using a computer.The fact is that computers are only able to solve discrete problems and generally do this using ?nite-precision arithmetic. What this means is that in deriving and then using a numerical algorithmthecorrectnessofthediscreteapproximationmustbeconsidered,as must the consequences of round-o? error in using ?oating-point arithmetic to calculatetheanswer.Oneoftheinterestingaspectsofthesubjectisthatwhat appears to be an obviously correct numerical method can result in complete failure. Consequently, although the book concentrates on the derivation and use of numerical methods, the theoretical underpinnings are also presented andusedinthedevelopment.

Notes

This book shows students how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. An essential component of this approach is the extensive collection of exercises, which develop both the analytical and computational aspects of the material. Numerical methods for differential equations are important in a variety of disciplines: most laws of physics involve differential equations, as do the modern theories of financial assets. Moreover many computer animation methods are now grounded in physics-based rules and are heavily invested in differential equations. In addition to more than 100 illustrations, the book includes a large collection of supplemental material: exercise sets, MATLAB computer codes for both student and instructor, lecture slides and movies.

Back Cover

This is a textbook for upper division undergraduates and beginning graduate students. Its objective is that students learn to derive, test and analyze numerical methods for solving differential equations, and this includes both ordinary and partial differential equations. In this sense the book is constructive rather than theoretical, with the intention that the students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. An essential component of this is the exercises, which develop both the analytical and computational aspects of the material. The importance of the subject of the book is that most laws of physics involve differential equations, as do the modern theories on financial assets. Moreover many computer animation methods are now based on physics based rules and are heavily invested in differential equations. Consequently numerical methods for differential equations are important for multiple areas. The author currently teaches at Rensselaer Polytechnic Institute and is an expert in his field. He has previously published a book with Springer, Introduction to Perturbation Methods.

Author Biography

Table of Contents

Initial Value Problems.- Two-Point Boundary Value Problems.- Diffusion Problems.- Advection Equation.- Numerical Wave Propagation.- Elliptic Problems.

Long Description

The title gives a reasonable ?rst-order approximation to what this book is about. To explain why, let's start with the expression "di'erential equations." These are essential in science and engineering, because the laws of nature t- ically result in equations relating spatial and temporal changes in one or more variables.Todevelopanunderstandingofwhatisinvolvedin'ndingsolutions, the book begins with problems involving derivatives for only one independent variable, and these give rise to ordinary di'erential equations. Speci'cally, the ?rst chapter considers initial value problems (time derivatives), and the second concentrates on boundary value problems (space derivatives). In the succeeding four chapters problems involving both time and space derivatives, partial di'erential equations, are investigated. This brings us to the next expression in the title: "numerical methods." This is a book about how to transform di'erential equations into problems that can be solved using a computer. The fact is that computers are only able to solve discrete problems and generally do this using ?nite-precision arithmetic. What this means is that in deriving and then using a numerical algorithmthecorrectnessofthediscreteapproximationmustbeconsidered,as must the consequences of round-o? error in using ?oating-point arithmetic to calculatetheanswer.Oneoftheinterestingaspectsofthesubjectisthatwhat appears to be an obviously correct numerical method can result in complete failure. Consequently, although the book concentrates on the derivation and use of numerical methods, the theoretical underpinnings are also presented andusedinthedevelopment.

Feature

Over 100 illustrations Numerous exercise sets, MATLAB computer codes (for both students and instructors), instructor overheads, and movies included

Description for Sales People

This book shows students how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. An essential component of this approach is the extensive collection of exercises, which develop both the analytical and computational aspects of the material. Numerical methods for differential equations are important in a variety of disciplines: most laws of physics involve differential equations, as do the modern theories of financial assets. Moreover many computer animation methods are now grounded in physics-based rules and are heavily invested in differential equations. In addition to more than 100 illustrations, the book includes a large collection of supplemental material: exercise sets, MATLAB computer codes for both student and instructor, lecture slides and movies.

Details ISBN144192163X Author Mark H. Holmes Publisher Springer-Verlag New York Inc. Series Texts in Applied Mathematics Year 2010 Edition 1st ISBN-10 144192163X ISBN-13 9781441921635 Format Paperback Imprint Springer-Verlag New York Inc. Place of Publication New York, NY Country of Publication United States DEWEY 515.35 Affiliation Rensselaer Polytechnic Institute, Troy, NY, USA Short Title INTRO TO NUMERICAL METHODS IN Language English Media Book Series Number 52 Publication Date 2010-11-29 Pages 239 AU Release Date 2010-11-29 NZ Release Date 2010-11-29 US Release Date 2010-11-29 UK Release Date 2010-11-29 Edition Description Softcover reprint of hardcover 1st ed. 2007 Alternative 9780387308913 Audience Professional & Vocational Illustrations XI, 239 p. We've got this

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