| Description |
1 online resource (244 p.) |
| Series |
Textbooks in Mathematics Ser |
|
Textbooks in Mathematics Ser
|
| Contents |
Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Contents -- 1. Introduction to the Maple DEtools -- 1.1. Analytical Solutions and Their Plotting -- 1.2. Direction Fields and Integral Curves -- 1.3. Computer Lab -- 1.4. Supplementary Maple Programs -- 1.4.1. Implicit and Explicit Solutions -- 1.4.2. Numerical Solutions -- 2. First-Order Differential Equations -- 2.1. Linear Differential Equations -- 2.2. Project: Mixing Problems -- 2.2.1. Project1: One Tank -- 2.2.2. Project2: Two Tanks -- 2.3. Separable Differential Equations -- 2.4. Exact Equations |
|
3. Numerical Methods for First-Order Equations -- 3.1. Picard's Iteration Method and Semi-Batch Reactor -- 3.2. An Existence and Uniqueness Theorem -- 3.3 Picard Iteration Method -- 3.4. Computer Lab -- 3.5. Numerical Procedures and Fermentation Kinetics -- 3.6. The Euler Method -- 3.7. Higher-Order Methods -- 3.8. Maple Procedures -- 3.9. Computer Lab -- 3.10. Supplementary Maple Programs -- 3.10.1. The Order of Convergence -- 4. Differential Equations with Constant Coefficients -- 4.1. Second-Order Equations with Constant Coefficients -- 4.2. Variation of Parameters -- 4.2.1. The Wronskian |
|
4.3. The Method of Undetermined Coefficients -- 4.4. Higher-Order, Homogeneous Equations -- 4.4.1. Polynomial Solutions -- 4.5. Nonhomogeneous Linear Equations -- 4.5.1. Undetermined Coefficients -- 4.5.2. Variation of Parameters -- 4.5.3. Further Remarks on the Variation of Parameters Method -- 5. Applications of Second-Order Linear Equations -- 5.1. Simple Harmonic Motion -- 5.2. General Solutions -- 5.3. Method of Undetermined Coefficients -- 5.4. Additional Useful Commands -- 5.5. Computer Lab -- 5.6. Supplementary Maple Programs -- 5.6.1. The Phenomenon of Beats |
|
5.6.2. The Phenomenon of Resonance -- 5.7. Particular Solutions -- 5.8. Computer Lab -- 5.9. Supplementary Maple Programs -- 5.9.1. Resonance Curves -- 5.9.2. An Example -- 6. Two-Point Boundary Value Problems, Catalytic Reactors and Boundary-Layer Phenomena -- 6.1. Analytical Solutions -- 6.2. Finite-Difference Methods -- 6.2.1. Finite-Difference Procedure for the Two-Point BVP: -- 6.3. Computer Lab -- 6.4. Supplementary Maple Programs -- 6.4.1. An Exact Asymptotic Expansion -- 7. Eigenvalue Problems -- 7.1. Sturm-Liouville Problems -- 7.2. Numerical Approximations |
|
7.3. The Newton-Raphson Method -- 7.4. Computer Lab -- 7.5. Supplementary Mapple Programs -- 7.5.1. An Eigenvalue Equation -- 8. Power Series Methods for Solving Differential Equations -- 8.1. Nonlinear Differential Equations -- 8.2. Regular-Singular Points -- 8.3. Programs for Finding Solutions -- 8.4. Projects -- 9. Nonlinear Autonomous Systems -- 9.1. The Taylor Series Method -- 9.2. The Phase Plane -- 9.3. Linear Systems -- 9.4. Useful Maple Commands -- 9.5. Computer Lab -- 9.6. Supplementary Maple Programs -- 9.6.1. Taylor Series Expansion -- 9.6.2. The Damped Pendulum |
| Notes |
Description based upon print version of record |
|
10. Integral Transforms |
| Form |
Electronic book
|
| Author |
Hsiao, George C
|
|
Ronkese, Robert J
|
| ISBN |
9781000402575 |
|
1000402576 |
|
