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Differential Equations : Computing and Modeling - 3rd edition

Differential Equations : Computing and Modeling (ISBN10: 0130673374; ISBN13: 9780130673374)
ISBN13: 978-0130673374
ISBN10: 0130673374

Summary: For introductory courses in Differential Equations.

This text provides the conceptual development and geometric visualization of a modern differential equations course that is still essential to science and engineering students. It reflects the new emphases that permeate the learning of elementary differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB; its focus has shifted from the
traditional manual methods to 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.

Features
  • NEW--Emphasis on new technology--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 for students the symbolic solutions of differential equations by visualizing their qualitative features.
  • NEW--Added figures to the Answers Section.
    • Emphasizes for students the qualitative features of problem solutions.
  • NEW--Application modules--Follow key sections throughout the text; many involve computational investigations, but 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--Fresh numerical emphasis--Afforded 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--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 for students the current trends in science and engineering education and practice.
  • Accompanying 350-page Applications Manual--Provides detailed coverage of Maple, Mathematica, and MATLAB.
    • Expands and enhances for students the text's applications material.
  • Approximately 1500 problems--Includes 300 new or revised in this edition; these span the range from computational problems to applied and conceptual problems.
    • 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.
  • DE Website--Presents 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.
  • Accompanying Instructor's Solutions Manual and Student's Solutions Manual.
    • Gives both students and instructors valuable text support.
...show more
Summary: For introductory courses in Differential Equations.

This text provides the conceptual development and geometric visualization of a modern differential equations course that is still essential to science and engineering students. It reflects the new emphases that permeate the learning of elementary differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB; its focus has shifted from the traditional manual methods to 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.

Features
  • NEW--Emphasis on new technology--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 for students the symbolic solutions of differential equations by visualizing their qualitative features.
  • NEW--Added figures to the Answers Section.
    • Emphasizes for students the qualitative features of problem solutions.
  • NEW--Application modules--Follow key sections throughout the text; many involve computational investigations, but 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--Fresh numerical emphasis--Afforded 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--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 for students the current trends in science and engineering education and practice.
  • Accompanying 350-page Applications Manual--Provides detailed coverage of Maple, Mathematica, and MATLAB.
    • Expands and enhances for students the text's applications material.
  • Approximately 1500 problems--Includes 300 new or revised in this edition; these span the range from computational problems to applied and conceptual problems.
    • 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.
  • DE Website--Presents 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.
  • Accompanying Instructor's Solutions Manual and Student's Solutions Manual.
    • Gives both students and instructors valuable text support.
...show less

Edition/Copyright: 3RD 04
Cover: Hardcover
Publisher: Prentice Hall, Inc.
Published: 06/19/2003
International: No

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