Differential Equations : : A first course on ODE and a brief introduction to PDE / / Shair Ahmad, Antonio Ambrosetti.

• Superior document: Title is part of eBook package: De Gruyter DG Plus eBook-Package 2019
• VerfasserIn: Ahmad, Shair,; Ambrosetti, Antonio,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2019]; ©2019
• Year of Publication: 2019
• Language: English
• Series: De Gruyter Textbook
• Physical Description: 1 online resource (XV, 293 p.)

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.

Table of Contents

Frontmatter -- 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