Differential Equations: Theory, Technique, and Practice

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This traditional text is intended for mainstream one- or two-semester differential equations courses taken by undergraduates majoring in engineering, mathematics, and the sciences. Written by two of the world's leading authorities on differential equations, SimmonsKrantz provides a cogent and accessible introduction to ordinary differential equations written in classical style. Its rich variety of modern applications in engineering, physics, and the applied sciences illuminate the concepts and techniques that students will use through practice to solve real-life problems in their careers. Features Award-winning Author Team- With Differential Equations: Theory, Technique and Practice, McGraw-Hill is proud to bring together the talents of two acclaimed authors and leading authorities in differential equations. George F. Simmons is renowned for his clear, direct, and engaging writing style over a 40-year career as author of highly-regarded textbooks for undergraduates in calculus and differential equations. Steven G. Krantz is one of the most visible and respected mathematicians in the community today, with over 45 books, 125 papers, and groundbreaking research in differential equations to his credit. Applications-SimmonsKrantz features a wealth of modern applications of differential equations to bring the subject to life and demonstrate its utility to students. These applications show how differential equations is the centerpiece of many areas of engineering, physics, the life sciences, and mathematical modeling, and prepare students for more concrete applied work in future courses. "Anatomy of an Application"- These sections, occurring at the end of each chapter, examine in detail a particular application of differential equations in engineering, physics, or the applied sciences. These applications apply topics learned in the chapter to practical problems students will face in these fields, and discuss in detail the differential equations used to solve those problems. Historical context-The text underscores the historical context and human element behind the development of key concepts in ordinary differential equations with biographical sketches students will find thought-provoking and fun. Short Math Nuggets appear within sections to illuminate the lives, accomplishments, and tribulations of important historical figures behind individual concepts. Longer Historical Notes appearing at the end of certain chapters go into greater detail about giants in the field such as Leonhard Euler, Carl Friedrich Gauss, and Pierre Simon de Laplace, and how they helped develop key areas students now study in modern differential equations. Exercises- Each chapter contains a variety of quality exercises, including Drill Exercises that test basic understanding, Challenge Problems that go into greater detail and feature a higher degree of complexity, and Problems for Discussion and Exploration that further develop students' critical thinking skills. Hints are given when appropriate to assist students with more difficult problems. Available for separate purchase, McGraw-Hill offers a Student's Solutions Manual containing worked solutions to all odd-numbered exercises. We also offer an Instructor's Solutions Manual containing solutions to all even-numbered exercises available free to instructors who adopt the text. Technology-Each chapter includes optional technology exercises designed to take advantage of computer algebra systems such as MAPLE or Mathematica for solving problems in differential equations Table Of Contents Preface Chapter 1 What is a Differential Equation? Chapter 2 Second-Order Linear Equations Chapter 3 Qualitative Properties and Theoretical Aspects Chapter 4 Power Series Solutions and Special Functions Chapter 5 Fourier Series: Basic Concepts Chapter 6 Partial Differential Equations and Boundary Value Problems Chapter 7 Laplace Transforms Chapter 8 The Calculus of Variations Chapter 9 Numerical Methods Chapter 10 Systems of First-Order Equations Chapter 11 The Nonlinear Theory Chapter 12 Dynamical Systems Bibliography