عنوان

Elementary differential equations with boundary value problems /

0321288351

0321303482

0321398505

9780321288356

9780321303486

9780321398505

Elementary differential equations with boundary value problems /

[Book]

Werner Kohler and Lee Johnson.

2nd ed.

Boston :

Pearson Addison-Wesley,

©2006.

xiii, 717 pages :

illustrations (some color) ;

26 cm +

1 computer optical disc (4 3/4 in.)

Includes index.

Includes index.

Machine generated contents note: 1.1. Introduction -- 1.2. Examples of Differential Equations -- 1.3. Direction Fields -- 2.1. Introduction -- 2.2. First Order Linear Differential Equations -- 2.3. Introduction to Mathematical Models -- 2.4. Population Dynamics and Radioactive Decay -- 2.5. First Order Nonlinear Differential Equations -- 2.6. Separable First Order Equations -- 2.7. Exact Differential Equations -- 2.8. The Logistic Population Model -- 2.9. Applications to Mechanics -- 2.10. Euler's Method -- Review Exercises -- Projects -- 3.1. Introduction -- 3.2. The General Solution of Homogeneous Equations -- 3.3. Constant Coefficient Homogeneous Equations -- 3.4. Real Repeated Roots; Reduction of Order -- 3.5.Complex Roots -- 3.6. Unforced Mechanical Vibrations -- 3.7. The General Solution of a Linear Nonhomogeneous Equation -- 3.8. The Method of Undetermined Coefficients -- 3.9. The Method of Variation of Parameters -- 3.10. Forced Mechanical Vibrations, Electrical Networks, and Resonance.

Note continued: 3.11. Higher Order Linear Homogeneous Differential Equations -- 3.12. Higher Order Homogeneous Constant Coefficient Differential Equations -- 3.13. Higher Order Linear Nonhomogeneous Differential Equations -- Review Exercises -- Projects -- 4.1. Introduction -- 4.2. Existence and Uniqueness -- 4.3. Homogeneous Linear Systems -- 4.4. Constant Coefficient Homogeneous Systems; the Eigenvalue Problem -- 4.5. Real Eigenvalues and the Phase Plane -- 4.6.Complex Eigenvalues -- 4.7. Repeated Eigenvalues -- 4.8. Nonhomogeneous Linear Systems -- 4.9. Numerical Methods for Systems of Linear Differential Equations -- 4.10. The Exponential Matrix and Diagonalization -- Review Exercises -- Projects -- 5.1. Introduction -- 5.2. Laplace Transform Pairs -- 5.3. The Method of Partial Fractions -- 5.4. Laplace Transforms of Periodic Functions and System Transfer Functions -- 5.5. Solving Systems of Differential Equations -- 5.6. Convolution -- 5.7. The Delta Function and Impulse Response.

Note continued: 9.8. Higher-Dimensional Problems; Nonhomogeneous Equations -- Project -- 10.1. Introduction -- 10.2. The Cauchy Problem -- 10.3. Existence and Uniqueness -- 10.4. The Method of Characteristics -- Projects -- 11.1. Introduction -- 11.2. Existence and Uniqueness -- 11.3. Two-Point Boundary Value Problems for Linear Systems -- 11.4. Sturm-Liouville Boundary Value Problems -- Project.

Note continued: Projects -- 6.1. Introduction -- 6.2. Equilibrium Solutions and Direction Fields -- 6.3. Conservative Systems -- 6.4. Stability -- 6.5. Linearization and the Local Picture -- 6.6. Two-Dimensional Linear Systems -- 6.7. Predator-Prey Population Models -- Projects -- 7.1. Introduction -- 7.2. Euler's Method, Heun's Method, and the Modified Euler's Method -- 7.3. Taylor Series Methods -- 7.4. Runge-Kutta Methods -- Appendix 1: Convergence of One-Step Methods -- Appendix 2: Stability of One-Step Methods -- Projects -- 8.1. Introduction -- 8.2. Series Solutions Near an Ordinary Point -- 8.3. The Euler Equation -- 8.4. Solutions Near a Regular Singular Point and the Method of Frobenius -- 8.5. The Method of Frobenius Continued: Special Cases and a Summary -- Projects -- 9.1. Introduction -- 9.2. Heat Flow in a Thin Bar; Separation of Variables -- 9.3. Series Solutions -- 9.4. Calculating the Solution -- 9.5. Fourier Series -- 9.6. The Wave Equation -- 9.7. Laplace's Equation.

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Systems requirements for accompanying CD-ROM. Windows. 366 MHz CPU; Windows 98, 2000, NT, XP; 64 MB RAM; 800 x 600 screen resolution; Browser: Internet Explorer 5.0 or higher; Netscape 7.0; Plug-Ins: Flash Player 6, Java 1.5, Adobe Reader; Internet Connection: 56k modem minimum for Website.

Boundary value problems, Textbooks.

Differential equations, Textbooks.

Boundary value problems.

Differential equations.

Kohler, W. E., (Werner E.),1939-

Johnson, Lee W.

20200822100041.0

[Book]

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