A Course in Ordinary Differential Equations, Second Edition

Praise for the First Edition:""A Course in Ordinary Differential Equations deserves to be on the MAA's Basic Library List ... the book with its layout, is very student friendly-it is easy to read and understand; every chapter and explanations flow smoothly and coherently ... the reviewer would recommend this book highly for undergraduate introductory differential equation courses."" -Srabasti Dutta, College of Saint Elizabeth, MAA Online, July 2008""An important feature is that the exposition is richly accompanied by computer algebra code (equally distributed between MATLAB, Mathematica, and Maple. Read more... Abstract: Praise for the First Edition:""A Course in Ordinary Differential Equations deserves to be on the MAA's Basic Library List ... the book with its layout, is very student friendly-it is easy to read and understand; every chapter and explanations flow smoothly and coherently ... the reviewer would recommend this book highly for undergraduate introductory differential equation courses."" -Srabasti Dutta, College of Saint Elizabeth, MAA Online, July 2008""An important feature is that the exposition is richly accompanied by computer algebra code (equally distributed between MATLAB, Mathematica, and Maple A Course in Ordinary Differential Equations deserves to be on the MAA's Basic Library List ... the book with its layout, is very student friendly--it is easy to read and understand; every chapter and explanations flow smoothly and coherently ... the reviewer would recommend this book highly for undergraduate introductory differential equation courses."--Srabasti Dutta, College of Saint Elizabeth, MAA Online, July 2008 "An important feature is that the exposition is richly accompanied by computer algebra code (equally distributed between MATLAB, Mathematica, and Maple). The major part of the book is devoted to classical theory (both for systems and higher order equations). The necessary material from linear algebra is also covered. More advanced topics include numerical methods, stability of equilibria, bifurcations, Laplace transforms, and the power series method." --EMS Newsletter, June 2007 "This is a delightful textbook for a standard one-semester undergraduate course in ordinary differential equations designed for students who had one year of calculus and continue their studies in engineering and mathematics. The main idea is to focus on the applications and methods of solutions, both analytical and numerical, with special attention paid to applications to real-world problems in engineering, physics, population dynamics, epidemiology, etc. A winning feature of the book is the extensive use of computer algebra codes throughout the text. Assuming that the students have no previous experience with Maple, MATLAB, or Mathematica, the authors present the relevant syntax and theory for all three programs. This helps students to understand better the theoretical material, use computer support more sensibly, and interpret results of computer simulation properly. Some background material from linear algebra is also provided throughout the text whenever necessary. ... The book is nicely written, generously illustrated, and well structured. There are plenty of exercises ranging from drilling to challenging. Additional problems for revision and projects are collected at the end of each chapter. ... An excellent blend of analytical and technical tools for studying ordinary differential equations, this text is a welcome addition to existing literature and is warmly recommended as essential reading for a first undergraduate course in differential equations." A Course in Ordinary Differential Equations, Second Edition teaches students how to use analytical and numerical solution methods in typical engineering, physics, and mathematics applications. Lauded for its extensive computer code and student-friendly approach, the first edition of this popular textbook was the first on ordinary differential equations (ODEs) to include instructions on using MATLAB(r), "Mathematica"(r), and Maple . This second edition reflects the feedback of students and professors who used the first edition in the classroom. New to the Second Edition Moves the computer codes to Computer Labs at the end of each chapter, which gives professors flexibility in using the technology Covers linear systems in their entirety before addressing applications to nonlinear systems Incorporates the latest versions of MATLAB, Maple, and "Mathematica" Includes new sections on complex variables, the exponential response formula for solving nonhomogeneous equations, forced vibrations, and nondimensionalization Highlights new applications and modeling in many fields Presents exercise sets that progress in difficulty Contains color graphs to help students better understand crucial concepts in ODEs Provides updated and expanded projects in each chapter Suitable for a first undergraduate course, the book includes all the basics necessary to prepare students for their future studies in mathematics, engineering, and the sciences. It presents the syntax from MATLAB, Maple, and "Mathematica" to give students a better grasp of the theory and gain more insight into real-world problems. Along with covering traditional topics, the text describes a number of modern topics, such as direction fields, phase lines, the Runge-Kutta method, and epidemiological and ecological models. It also explains concepts from linear algebra so that students acquire a thorough understanding of differential equations." Front Cover 1 Dedication 4 Contents 6 About the Authors 10 Preface 12 Chapter 1: Traditional First-Order Differential Equations 18 Chapter 2: Geometrical and Numerical Methods for First-Order Equations 98 Chapter 3: Elements of Higher-Order Linear Equations 172 Chapter 4: Techniques of Nonhomogeneous Higher-Order Linear Equations 258 Chapter 5: Fundamentals of Systems of Differential Equations 340 Chapter 6: Geometric Approaches and Applications of Systems of Differential Equations 440 Chapter 7: Laplace Transforms 520 Chapter 8: Series Methods 600 Appendix A: An Introduction to MATLAB, Maple, and Mathematica 676 Appendix B: Selected Topics from Linear Algebra 700 Answers to Odd Problems 754 References 796 Content: Front Cover Dedication Contents About the Authors Preface Chapter 1: Traditional First-Order Differential Equations Chapter 2: Geometrical and Numerical Methods for First-Order Equations Chapter 3: Elements of Higher-Order Linear Equations Chapter 4: Techniques of Nonhomogeneous Higher-Order Linear Equations Chapter 5: Fundamentals of Systems of Differential Equations Chapter 6: Geometric Approaches and Applications of Systems of Differential Equations Chapter 7: Laplace Transforms Chapter 8: Series Methods Appendix A: An Introduction to MATLAB, Maple, and Mathematica Appendix B: Selected Topics from Linear AlgebraAnswers to Odd Problems References