Differential Equations: Modeling with MATLAB
Utilizing MATLAB's computational and graphical tools right from the start, this analysis of differential equations helps users probe a variety of mathematical models, encouraging them to develop problem-solving skills and independent judgment as they derive mathematical models, select approaches to their analysis, and find answers to the original physical questions. Providing immediate graphic and numeric support, it demonstrates how physical problems motivate the central ideas and techniques of differential equations, showing how they model physical phenomena by examining ideas from four perspectives: geometric, analytic, numeric, and physical.Introduces qualitative analysis and numerical methods for scalar equations and systems early on, without sacrificing coverage of the most important traditional analytical methods. Fully integrates MATLAB into the text and exercises, and uses mathematical models of physical problems throughout to emphasize the interplay between the physical problem and the analytic, graphical, and numeric information available from the differential equation model. Seamlessly integrates over 1,400 exercises, open-ended chapter projects, and motivational 'Thought Questions'.For scientists and
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NUMERICAL AND GRAPHICAL TOOLS
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amplitude analysis analytic approximation arbitrary constant behavior boundary conditions Cauchy-Euler equation characteristic equation characteristic roots constant-coefficient corresponding curve damped decay defined derivative determine differential equation eigenvalues eigenvectors emigration equa equilibrium point Euler method exact solution example EXERCISE GUIDE exponential first-order equations forcing term frequency function global error graph heat-loss Hence Heun method homogeneous equation homogeneous solution initial conditions initial-value problem integral Laplace transform linear equation linear system linearly independent logistic equation mass Matlab nonhomogeneous equation nullcline numerical obtain oscillations particular solution pendulum pendulum equation pendulum system perturbation phase plane phase plane diagram polynomial population model position RLC circuit satisfies second-order equation separation of variables Show shown in figure slope solve spring spring-mass system stability steady Stop and Think Substitute temperature theorem tion trajectory trial solution Try exercises undamped spring-mass underdamped undetermined coefficients vector velocity Verify Write Wronskian zero