Differential Equations and Boundary Value Problems

For introductory courses in Differential Equations.This best-selling text by these well-known authors blends the traditional algebra problem solving skills with the conceptual development and geometric visualization of a modern differential equations course that is essential to science and engineering students. It reflects the new qualitative approach that is altering the learning of elementary differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB. Its focus balances the traditional manual methods with the new computer-based methods that illuminate qualitative phenomena and make accessible a wider range of more realistic applications. Seldom-used topics have been trimmed and new topics added: it starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the text.Approximately 2000 problems-These problems span the range from computational problems to applied and conceptual problems. There are over 300 new qualitative problems in this edition. Provides students with problem sets that are carefully graded so that the opening problems can be easily solved by most students, giving them encouragement to continue through the set.NEW - Emphasis on the intersection of technology and ODEs-Recognizes the need to instruct students in the new methods of computing differential equations. Shows students the software systems tailored specifically to differential equations as well as the widely used Maple, Mathematica, and MATLAB. NEW - 300 new computer-generated graphics-Show vivid pictures of slope fields, solution curves, and phase plane portraits. Brings to life the symbolic solutions of differential equations through the visualizing of qualitative features.NEW - Extensive expansion of qualitative solutions to the problem sets. Scan the Answer section to see the new geometric flavor.NEW - Fresh numerical methods emphasis-Made possible by the early introduction of numerical solution techniques, mathematical modeling, stability and qualitative properties of differential equations. The text includes generic numerical algorithms that can be implemented in various technologies. Gives students and instructors a choice when implementing which type of technology they can utilize, as well as provides an innovative combination of topics usually dispersed later in other texts.NEW - Application Modules-Follow key sections throughout the text; while many involve computational investigations, they are written in a technology-neutral manner. Technology-specific systems modules are available in the accompanying Applications Manual. Actively engages students, providing facility and experience in the geometric visualization and qualitative interpretation that play a prominent role in contemporary differential equations.NEW - Leaner and more streamlined coverage-Shaped by the availability of computational aids. Allows students to learn traditional manual topics (like exact equations and variation of parameters) more easily.Unusually flexible treatment of linear systems-Covers in Chapters 4 and 5 the necessary linear algebra followed by a substantial treatment of nonlinear systems and phenomena in Chapter 6. The use of matrix exponential methods plays an enhanced role in this edition. Reflects the current trends in science and engineering education and practice.Accompanying 350-page Applications Manual-Provides detailed coverage of Maple, Mathematica, and MATLAB and is free when shrink-wrapped with text. Expands and enhances for students the text's applications material.Very Robust DE Website-Presents text projects in the form of interactive Maple, Mathematica, and MATLAB notebooks and worksheets. Provides students with the opportunity to download technology-specific versions of individual projects. Also, Polkings DField and PPlane, are available here in Java applets.Accompanying Instructor's Solutions Manual and Student's Solutions Manual. Gives both students and instructors valuable detailed text support.