
Differential Equations: Modeling with MATLAB, 1/e
Paul Davis Published April, 1999 by Prentice Hall Engineering/Science/Mathematics
 
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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. TwoDimensional Models: Oscillating Systems. Overview—populations, position, and velocity. Springmass 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 springmass systems. Undetermined coefficients. Forced springmass 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 BoundaryValue Problems. Diffusion models. Boundaryvalue problems. Buckling. Timedependent diffusion. Fourier methods. Numerical tools: timedependent 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 secondorder equations. Reduction of order. CauchyEuler equations. Power series methods. Regular singular points. Solution method summary. Appendicies. Bibliography Solutions to Selected Exercises Index MATLAB tutorial. Calculus review.
