18.03 Differential Equations, Spring 2004
Author(s)Miller, Haynes R., 1948-; Mattuck, Arthur
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Study of ordinary differential equations, including modeling of physical problems and interpretation of their solutions. Standard solution methods for single first-order equations, including graphical and numerical methods. Higher-order forced linear equations with constant coefficients. Complex numbers and exponentials. Matrix methods for first-order linear systems with constant coefficients. Non-linear autonomous systems; phase plane analysis. Fourier series; Laplace transforms.
Ordinary Differential Equations, ODE, modeling physical systems, first-order ODE's, Linear ODE's, second order ODE's, Undetermined coefficients, variation of parameters, Sinusoidal signals, exponential signals, oscillations, damping, resonance, Fourier series, periodic solutions, Delta functions, convolution, Laplace transform methods, Matrix systems, first order linear systems, Non-linear autonomous systems, critical point analysis, phase plane diagrams, constant coefficients, complex numbers, exponentials, eigenvalues, eigenvectors