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Addison-Wesley / Prentice Hall

Mathematics

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Differential Equations and Boundary Value Problems: Computing and Modeling, 4/E
C. Henry Edwards
David E. Penney, University of Georgia, Athens

ISBN-10: 0131561073
ISBN-13:  9780131561076

Publisher:  Prentice Hall
Copyright:  2008
Format:  Cloth; 816 pp
Published:  07/26/2007
Status: Instock


Suggested retail price: $138.67
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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.

  • Chapter 3 now includes new explanations of signs and directions of internal forces in mass-spring systems; new introduction and illustration of polar exponential forms of complex numbers; and fuller explanation of method of undetermined coefficients.
  • Chapter 5 now includes new exposition to explain the connection between matrix variation of parameters and (scalar) variation of parameters for second-order equations previously discussed in Chapter 3.
  • Chapter 7 now includes new discussion clarifying functions of exponential order and existence of Laplace transforms and new much-expanded discussion of the proof of the Laplace-transform existence theorem and its extension to include the jump discontinuities that play an important role in many practical applications.
  • New problems have been added to most chapters to provide students with further practice of what they have learned.
  • New figures and images help increase student understanding of concepts.
  • Additional discussions appear at the beginning of select chapters to provide students with more clarity on difficult topics.

1. First Order Differential Equations.

Differential Equations and Mathematical Models. Integrals as General and Particular Solutions. Slope Fields and Solution Curves. Separable Equations and Applications. Linear First Order Equations. Substitution Methods and Exact Equations.



2. Mathematical Models and Numerical Methods.

Population Models. Equilibrium Solutions and Stability. Acceleration-Velocity Models. Numerical Approximation: Euler's Method. A Closer Look at the Euler Method, and Improvements. The Runge-Kutta Method.



3. Linear Equations of Higher Order.

Introduction: Second-Order Linear Equations. General Solutions of Linear Equations. Homogeneous Equations with Constant Coefficients. Mechanical Vibrations. Nonhomogeneous Equations and Undetermined Coefficients. Forced Oscillations and Resonance. Electrical Circuits. Endpoint Problems and Eigenvalues.



4. Introduction to Systems of Differential Equations.

First-Order Systems and Applications. The Method of Elimination. Numerical Methods for Systems.



5. Linear Systems of Differential Equations.

Linear Systems and Matrices. The Eigenvalue Method for Homogeneous Systems. Second Order Systems and Mechanical Applications. Multiple Eigenvalue Solutions. Matrix Exponentials and Linear Systems. Nonhomogenous Linear Systems.



6. Nonlinear Systems and Phenomena.

Stability and the Phase Plane. Linear and Almost Linear Systems. Ecological Models: Predators and Competitors. Nonlinear Mechanical Systems. Chaos in Dynamical Systems.



7. Laplace Transform Methods.

Laplace Transforms and Inverse Transforms. Transformation of Initial Value Problems. Translation and Partial Fractions. Derivatives, Integrals, and Products of Transforms. Periodic and Piecewise Continuous Forcing Functions. Impulses and Delta Functions.



8. Power Series Methods.

Introduction and Review of Power Series. Series Solutions Near Ordinary Points. Regular Singular Points. Method of Frobenius: The Exceptional Cases. Bessel's Equation. Applications of Bessel Functions.



9. Fourier Series Methods.

Periodic Functions and Trigonometric Series. General Fourier Series and Convergence. Even-Odd Functions and Termwise Differentiation. Applications of Fourier Series. Heat Conduction and Separation of Variables. Vibrating Strings and the One-Dimensional Wave Equation. Steady-State Temperature and Laplace's Equation.



10. Eigenvalues and Boundary Value Problems.

Sturm-Liouville Problems and Eigenfunction Expansions. Applications of Eigenfunction Series. Steady Periodic Solutions and Natural Frequencies. Applications of Bessel Functions. Higher-Dimensional Phenomena.



References.


Appendix: Existence and Uniqueness of Solutions.


Answers to Selected Problems.


Index.

Companion Website - Edwards, 4/E
Edwards & Penney
©2008 | Prentice Hall | On-line Supplement | Estimated Availability : 08/15/2007
ISBN-10: 0136006760 | ISBN-13: 9780136006763
URL:  http://www.prenhall.com/edwards


Sampling Edition, 4/E
Edwards & Penney
©2008 | Prentice Hall | Cloth; 816 pp | Instock
ISBN-10: 0132356589 | ISBN-13: 9780132356589


Companion Website - Edwards, 4/E
Edwards & Penney
©2008 | Prentice Hall | On-line Supplement | Estimated Availability : 08/15/2007
ISBN-10: 0136006760 | ISBN-13: 9780136006763
URL:  http://www.prenhall.com/edwards


Instructor Solution Manual, 4/E
Edwards
©2008 | Prentice Hall | On-line Supplement; 611 pp | Instock
ISBN-10: 013156109X | ISBN-13: 9780131561090
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Applications Manual, 4/E
Edwards & Penney
©2008 | Prentice Hall | Paper; 352 pp | Instock
ISBN-10: 0136006795 | ISBN-13: 9780136006794
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Companion Website - Edwards, 4/E
Edwards & Penney
©2008 | Prentice Hall | On-line Supplement | Estimated Availability : 08/15/2007
ISBN-10: 0136006760 | ISBN-13: 9780136006763
URL:  http://www.prenhall.com/edwards


Student Solutions Manual, 4/E
Edwards & Penney
©2008 | Prentice Hall | Paper; 342 pp | Instock
ISBN-10: 0131561103 | ISBN-13: 9780131561106
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Addison-Wesley's Basic Math Review
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ISBN-10: 0321247078 | ISBN-13: 9780321247070


Algebra Review Study Card, 2/E
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©2006 | Prentice Hall | Study Card; 6 pp | Instock
ISBN-10: 0321394739 | ISBN-13: 9780321394736
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ISBN-10: 0321394747 | ISBN-13: 9780321394743
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Basic Math Review Card, 2/E
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ISBN-10: 0321394763 | ISBN-13: 9780321394767
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Concept Videos: Algebra
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ISBN-10: 0321517199 | ISBN-13: 9780321517197


Concept Videos: Basic Math & Prealgebra
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©2008 | Prentice Hall | Multiple Media Package | Instock
ISBN-10: 032151758X | ISBN-13: 9780321517586


Discovering Algebra: Examples with Keystrokes on the TI-83/TI-82 and TI-85/TI-86, A Laboratory Approach
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ISBN-10: 0136492037 | ISBN-13: 9780136492030
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ISBN-10: 0321374398 | ISBN-13: 9780321374394
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©2004 | Prentice Hall | Paper | Instock
ISBN-10: 0321143094 | ISBN-13: 9780321143099
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©2006 | Prentice Hall | Study Card; 6 pp | Instock
ISBN-10: 0321394755 | ISBN-13: 9780321394750
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Graphing Calculator Tutorial CD
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©2006 | Prentice Hall | CD-ROM Only | Instock
ISBN-10: 0321357744 | ISBN-13: 9780321357748
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Interwrite Personal Response System
EduCue, Addison-Wesley & Benjamin Cummings
©2004 | Prentice Hall | Electronic Supplement | Instock
ISBN-10: 0321267354 | ISBN-13: 9780321267351


Math for Allied Health Study/Reference Card
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©2006 | Prentice Hall | Study Card; 0 pp | Out of Stock
ISBN-10: 0321336542 | ISBN-13: 9780321336545


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ISBN-10: 0201728966 | ISBN-13: 9780201728965
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ISBN-10: 0321566041 | ISBN-13: 9780321566041


Prealgebra Review Workbook
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ISBN-10: 0321473329 | ISBN-13: 9780321473325
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©2002 | Prentice Hall | Paper; 224 pp | Instock
ISBN-10: 0201773473 | ISBN-13: 9780201773477
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©2009 | Prentice Hall | Multiple Media Package | Estimated Availability : 09/01/2008
ISBN-10: 0321561880 | ISBN-13: 9780321561886


Spanish Basic Math Study Card
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©2007 | Prentice Hall | Study Card | Instock
ISBN-10: 0321438582 | ISBN-13: 9780321438584
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©2008 | Prentice Hall | Access Code Card | Instock
ISBN-10: 0201721708 | ISBN-13: 9780201721706
URL:  http://www.aw-bc.com/tutorcenter
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For Differential Equations

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©2003 | Prentice Hall | Paper; 200 pp | Instock
ISBN-10: 0130479748 | ISBN-13: 9780130479747
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Companion Website - Edwards, 4/E
Edwards & Penney
©2008 | Prentice Hall | On-line Supplement | Estimated Availability : 08/15/2007
ISBN-10: 0136006760 | ISBN-13: 9780136006763
URL:  http://www.prenhall.com/edwards


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Package ISBN-10: 032155602X | ISBN-13: 9780321556028
©2008 | Instock (Additional assembly time required) | Suggested retail price: $161.73 | Buy from myPearsonStore
This package contains:

Edwards & Penney | ©2008 | Prentice Hall | Cloth; 816 pp
Polking | ©2004 | Prentice Hall | Paper; 264 pp


Package ISBN-10: 0135143772 | ISBN-13: 9780135143773
©2008 | Instock | Suggested retail price: $142.00 | Buy from myPearsonStore
This package contains:

Edwards & Penney | ©2008 | Prentice Hall | Cloth; 816 pp
Edwards & Penney | ©2008 | Prentice Hall | Paper; 342 pp


Package ISBN-10: 013600122X | ISBN-13: 9780136001225
©2008 | Instock | Suggested retail price: $142.00 | Buy from myPearsonStore
This package contains:

Edwards & Penney | ©2008 | Prentice Hall | Cloth; 816 pp
Edwards & Penney | ©2008 | Prentice Hall | Paper; 352 pp


Package ISBN-10: 0132364425 | ISBN-13: 9780132364423
©2008 | Instock (Additional assembly time required) | Suggested retail price: $160.33 | Buy from myPearsonStore
This package contains:

Edwards & Penney | ©2008 | Prentice Hall | Cloth; 816 pp
Edwards & Penney | ©2008 | Prentice Hall | Paper; 352 pp
Edwards & Penney | ©2008 | Prentice Hall | Paper; 342 pp


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