9789382993797
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Partial Differential Equations: Methods, Applications and TheoriesTRANSCRIPT
Partial Differential EquationsMethods, Applications and TheoriesHarumi HattoriHarumi Hattori, West Virginia University, USA
Price ` 495.00 only
Size : 150mm x 230mm
Pages : xvi+376pp
Year : 2014
Binding : Paperback
ISBN : 9789382993797
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This volume is an introductory level textbook forpartial differential equations (PDE’s) and suitablefor a one-semester undergraduate level or two-semester graduate level course in PDE’s or appliedmathematics. Chapters One to Five are organizedaccording to the equations and the basic PDE’sare introduced in an easy to understand manner.They include the first-order equations and the threefundamentals second-order equations, i.e. theheat, wave and Laplace equations. Through theseequations we learn the types of problems, how wepose the problems, and the methods of solutionssuch as the separation of variables and themethods of characteristics. The modeling aspectsare explained as well. The methods introduced inearlier chapters are developed further in Chapters
Partial DifferentialEquationsMethods, Applicationsand TheoriesHarumi Hattori
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Six to Twelve. They include the Fourier series, theFourier and the Laplace transforms, and theGreen’s functions. The equations in higherdimensions are also discussed in detail.
This volume is application-oriented and rich inexamples. Going through these examples, thereader is able to easily grasp the basics of PDE’s.
CONTENTS
Preface
1. First and Second Order Linear Equations -Preparation; 2. Heat Equation;3. Wave Equation;4. Laplace Equation; 5. First Order EquationsRevisited; 6. Fourier Series and EigenvalueProblems; 7. Separation of Variables in HigherDimensions; 8. More Separation of Variables;9. Fourier Transform;10. Laplace Transform;11. Higher Dimensional Problem - OtherApproaches; 12. Green’s Functions
Appendices
Hints and Solutions to Selected Exercises
Bibliography
Index