Differential Equations: From Calculus to Dynamical Systems: Second Edition (AMS/MAA Textbooks)

Description

A thoroughly modern textbook for the sophomore-level differential equations course. The examples and exercises emphasize modeling not only in engineering and physics but also in applied mathematics and biology. There is an early introduction to numerical methods and, throughout, a strong emphasis on the qualitative viewpoint of dynamical systems. Bifurcations and analysis of parameter variation is a persistent theme. Presuming previous exposure to only two semesters of calculus, necessary linear algebra is developed as needed. The exposition is very clear and inviting. The book would serve well for use in a flipped-classroom pedagogical approach or for self-study for an advanced undergraduate or beginning graduate student. This second edition of Noonburg's best-selling textbook includes two new chapters on partial differential equations, making the book usable for a two-semester sequence in differential equations. It includes exercises, examples, and extensive student projects taken from the current mathematical and scientific literature. An instructor's manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to [email protected] for more information. Contents Preface 1 Introduction to Differential Equations 2 First-order Differential Equations 3 Second-order Differential Equations 4 Linear Systems of First-order Differential Equations 5 Geometry of Autonomous Systems 6 Laplace Transforms 7 Introduction to Partial Differential Equations 8 Solving Second-order Partial Differential Equations A Answers to Odd-numbered Exercises B Derivative and Integral Formulas C Cofactor Method for Determinants D Cramer’s Rule for Solving Systems of Linear Equations E The Wronskian F Table of Laplace Transforms G Review of Partial Derivatives Index