
Differential Equations and Boundary Value Problems: Computing and Modeling, 2/e
C. Henry Edwards Published April, 1999 by Prentice Hall Engineering/Science/Mathematics
 
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NEW—Increased emphasis on and flexible treatment of linear systems of differential equations—With coverage in Chapters 4 and 5 (along with the necessary linear algebra) followed by a substantial treatment of nonlinear systems and phenomena in Chapter 6 (including chaos in dynamical systems). Chapter 4 offers an early, intuitive introduction to firstorder systems, models, and numerical approximation techniques. Chapter 5 begins with a selfcontained treatment of the linear algebra required, then presents the eigenvalue approach to linear systems. Section 5.5 now includes a more extensive treatment of matrix exponentials. A new section (5.6) on nonhomogeneous linear systems was added to this edition.
Coverage begins and ends with discussions and examples of the mathematical modeling of realworld phenomena.
The projects are expanded considerably in the Computing Projects Manual that accompanies the text. Provided are parallel subsections entitled Using Maple, Using Mathematica, and Using MATLAB that detail the applicable methods and techniques of each system. This manual is free when wrapped with text. Project notebooks and worksheets can be downloaded from the supporting web site: www.prenhall.com/edwards
Supported by a fully dedicated DE Website. —A superb direction field and phase portrait plotter is provided. Written as Java applets, all you need is a computer with a browser—no other software. —Includes expanded versions of the intext projects. Each project is supported by a Maple V worksheet, a Mathematica (version 3) notebook, and a MATLAB (version 5) script that illustrates the computing techniques used in the project. Students can download these technologyspecific versions of the individual projects directly from the site: www.prenhall.com/edwards for FREE. —An Internet Tutor—available on Sunday nights to answer student questions concerning the problem sets. Free to adopters. —Selected text examples are animated to provide better visual understanding of DEs. —Quizzes, verbal in nature, are provided for each section to help ensure that the students will actually read the core text.
Differential Equations and Mathematical Models. Integrals as General and Particular Solutions. Direction Fields and Solutions Curves. Separable Equations and Applications. Linear FirstOrder Equations. Substitution Methods and Exact Equations. 2. Mathematical Models and Numerical Methods. Population Models. Equilibrium Solutions and Stability. AccelerationVelocity Models. Numerical Approximation: Euler's Method. A Closer Look at the Euler Method. The RungeKutta Method. 3. Linear Equations of Higher Order. Introduction: SecondOrder Linear Equations. General Solutions of Linear Equations. Homogeneous Equations with Constant Coefficients. Mechanical Vibrations. Nonhomogeneous Equations and the Method of Undetermined Coefficients. Forced Oscillations and Resonance. Electrical Circuits. Endpoint Problems and Eigenvalues. 4. Introduction to Systems of Differential Equations. FirstOrder 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 Eignvalue Solutions. Matrix Exponentials and Linear Systems. Nonhomogeneous 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. Fourier Sine and Cosine Series. Applications of Fourier Series. Heat Conduction and Separation of Variables. Vibrating Strings and the OneDimensional Wave Equation. SteadyState Temperature and Laplace's Equation. 10. Eigenvalues and Boundary Value Problems. StrumLiouville Problems and Eigenfunction Expansions. Applications of Eigenfunction Series. Steady Periodic Solutions and Natural Frequencies. Cylindrical Coordinate Problems. HigherDimensional Phenomena.
