Overview 459 5.2 Part Organization 460 Applied Numerical Methods with MATLAB fo

P ART S IX Ordinary Differential Equations 547

6.1 Overview 547 6.2 Part Organization 551

CHAPTER 22 Initial-Value Problems 553 22.1 Overview 555 22.2 Euler’s Method 555 22.3 Improvements of Euler’s Method 561 22.4 Runge-Kutta Methods 567 22.5 Systems of Equations 572 22.6 Case Study: Predator-Prey Models and Chaos 578 Problems 583 CHAPTER 23 Adaptive Methods and Stiff Systems 588 23.1 Adaptive Runge-Kutta Methods 588 23.2 Multistep Methods 597 23.3 Stiffness 601 23.4 MATLAB Application: Bungee Jumper with Cord 607 23.5 Case Study: Pliny’s Intermittent Fountain 608 Problems 613 CHAPTER 24 Boundary-Value Problems 616 24.1 Introduction and Background 617 24.2 The Shooting Method 621 24.3 Finite-Difference Methods 628 Problems 635 APPENDIX A: MATLAB BUILT-IN FUNCTIONS 641 APPENDIX B: MATLAB M-FILE FUNCTIONS 643 BIBLIOGRAPHY 644 INDEX 646 CONTENTS xi McGraw-Hill Digital Offerings Include: McGraw-Hill Create™ Craft your teaching resources to match the way you teach With McGraw-Hill Create™, www.mcgrawhillcreate.com, you can easily rearrange chapters, combine material from other content sources, and quickly upload content you have written like your course syllabus or teaching notes. Find the content you need in Create by searching through thou- sands of leading McGraw-Hill textbooks. Arrange your book to fit your teaching style. Create even allows you to personalize your book’s appearance by selecting the cover and adding your name, school, and course information. Order a Create book and you’ll receive a complimentary print review copy in 3–5 business days or a complimentary electronic review copy eComp via email in minutes. Go to www.mcgrawhillcreate.com today and register to experience how McGraw-Hill Create™ empowers you to teach your students your way. McGraw-Hill Higher Education and Blackboard Have Teamed Up Blackboard, the Web-based course-management system, has partnered with McGraw-Hill to better allow students and faculty to use online materials and activities to complement face-to-face teaching. Blackboard features exciting social learning and teaching tools that foster more logical, visually impactful and active learning opportunities for students. You’ll transform your closed-door classrooms into communities where students remain connected to their educational experience 24 hours a day. This partnership allows you and your students access to McGraw-Hill’s Create™ right from within your Blackboard course—all with one single sign-on. McGraw-Hill and Blackboard can now offer you easy access to industry leading technology and content, whether your campus hosts it, or we do. Be sure to ask your local McGraw-Hill represen- tative for details. Electronic Textbook Options This text is offered through CourseSmart for both instructors and students. CourseSmart is an online resource where students can purchase the complete text online at almost half the cost of a traditional text. Purchasing the eTextbook allows students to take advantage of CourseSmart’s web tools for learning, which include full text search, notes and highlight- ing, and email tools for sharing notes between classmates. To learn more about CourseSmart options, contact your sales representative or visit www.CourseSmart.com.