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Differential Equations
About This Book
The first part of this book is mainly intended as a textbook for students at the Sophomore-Junior level, majoring in mathematics, engineering, or the sciences in general. The book includes the basic topics in Ordinary Differential Equations, normally taught at the undergraduate level, such as linear and nonlinear equations and systems, Bessel functions, Laplace transform, stability, etc. It is written with ample flexibility to make it appropriate either as a course stressing application, or a course stressing rigor and analytical thinking. It also offers sufficient material for a one-semester graduate course, covering topics such as phase plane analysis, oscillation, Sturm-Liouville equations, Euler-Lagrange equations in Calculus of Variations, first and second order linear PDE in 2D. There are substantial lists of exercises at the ends of the chapters. In this edition complete solutions to all even number problems are given in the back of the book.
The 2nd edition also includes some new problems and examples. An effort has been made to make the material more suitable and self-contained for undergraduate students with minimal knowledge of Calculus. For example, a detailed review of matrices and determinants has been added to the chapter on systems of equations. The second edition also contains corrections of some misprints and errors in the first edition.
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Table of contents
- Title Page
- Copyright
- Contents
- 1âA brief survey of some topics in calculus
- 2âFirst order linear differential equations
- 3âAnalytical study of first order differential equations
- 4âSolving and analyzing some nonlinear first order equations
- 5âExact differential equations
- 6âSecond order linear differential equations
- 7âHigher order linear equations
- 8âSystems of first order equations
- 9âPhase plane analysis
- 10âIntroduction to stability
- 11âSeries solutions for linear differential equations
- 12âLaplace transform
- 13âA primer on equations of SturmâLiouville type
- 14âA primer on linear PDE in 2D I: first order equations
- 15âA primer on linear PDE in 2D II: second order equations
- 16âThe EulerâLagrange equations in the Calculus of Variations: an introduction
- Solutions
- Subject Index