Differential Equations

A First Course on ODE and a Brief Introduction to PDE

Antonio Ambrosetti, Shair Ahmad

• Publisher: De Gruyter
• Year: 2023
• Print ISBN:
  9783111185248
• eBook ISBN:
  9783111185781
• Topic: Mathematics
• Subtopic: Mathematical Analysis
• Index: Mathematics

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.

Table of contents

• Title Page
• Copyright
• 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
• Solutions
• Subject Index