Differential Equations: A first course on ODE and a brief introduction to PDE
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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 in an undergraduate class, as linear and nonlinear equations and systems, Bessel functions, Laplace transform, stability, etc. It is written with ample exibility to make it appropriate either as a course stressing applications, or a course stressing rigor and analytical thinking. This book 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 chapters. A solutions manual, containing complete and detailed solutions to all the exercises in the book, is available to instructors who adopt the book for teaching their classes. Solving linear and nonlinear equations and systems Theoretical aspects and qualitative analysis discussed Substantial list of exercises at the ends of chapters Appropriate for undergraduate and graduate students Preface Acknowledgment Contents 1. A brief survey of some topics in calculus 2. First order linear differential equations 3. Analytical study of first order differential equations 4. Solving and analyzing some nonlinear first order equations 5. Exact differential equations 6. Second order linear differential equations 7. Higher order linear equations 8. Systems of first order equations 9. Phase plane analysis 10. Introduction to stability 11. Series solutions for linear differential equations 12. Laplace transform 13. A primer on equations of Sturm–Liouville type 14. A primer on linear PDE in 2D I: first order equations 15. A primer on linear PDE in 2D II: second order equations 16. The Euler–Lagrange equations in the Calculus of Variations: an introduction Bibliography Index
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