Differential equations : modeling with MATLAB
著者
書誌事項
Differential equations : modeling with MATLAB
Prentice Hall, c1999
大学図書館所蔵 全6件
注記
Includes bibliographical references and index
内容説明・目次
内容説明
For undergraduate engineering and science courses in Differential Equations. This progressive text on differential equations utilizes MATLAB's state-of-the-art computational and graphical tools right from the start to help students probe a variety of mathematical models. Ideas are examined from four perspectives: geometric, analytic, numeric, and physical. Students are encouraged to develop problem-solving skills and independent judgment as they derive models, select approaches to their analysis, and find answers to the original, physical questions. Both qualitative and algebraic tools are stressed.
目次
1. Prologue.
Goals. A modeling example. Differential equations and solutions.
2. Models from Conservation Laws.
Simple population growth. Emigration and competition. Heat flow. Multiple species.
3. Numerical and Graphical Tools.
Numerical methods. Graphs, direction fields, and phase lines. Steady states, stability, and local linearization.
4. Analytic Tools for One Dimension.
Basic definitions. Separation of variables. Characteristic equations. Undetermined coefficients. Variation of parameters. Existence and uniqueness.
5. Two-Dimensional Models: Oscillating Systems.
Overview-populations, position, and velocity. Spring-mass systems. Pendulum. RLC circuits.
6. Analytic Tools for Two Dimensions:
Basic definitions. The Wronskian and linear independence. Characteristic equations: real roots. Characteristic equations: complex roots. Unforced spring-mass systems. Undetermined coefficients. Forced spring-mass systems. Linear vs. nonlinear.
7. Graphical Tools for Two Dimensions.
Back to the phase plane. More phase plane: nullclines, steady states, stability. Limit cycles.
8. Analytic Tools for Higher Dimensions: Systems.
Motivation and review. Basic definitions. Homogeneous systems. Connections with the phase plane. Nonhomogeneous systems: undetermined coefficients.
9. Diffusion Models and Boundary-Value Problems.
Diffusion models. Boundary-value problems. Buckling. Time-dependent diffusion. Fourier methods. Numerical tools: time-dependent diffusion. Finite difference approximations to steady states.
10. Laplace Transform.
The transform idea: jumps and filters. Inverse transforms. Other properties of Laplace transforms. Ramps and jumps. The unit impulse function. Control applications.
11. More Analytic Tools for Two Dimensions..
Variation of parameters for systems. Variation of parameters for second-order equations. Reduction of order. Cauchy-Euler equations. Power series methods. Regular singular points. Solution method summary.
Appendicies.
Bibliography
Solutions to Selected Exercises
Index
MATLAB tutorial. Calculus review.
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