MAT265: DIFFERENTIAL EQUATIONS
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Course outline
- Slope field and Euler method. Uniqueness of solutions, dependence on initial conditions.
- Analytical resolution of separable, linear and exact E.D.s. Variable change method.
- Physical applications: rectilinear motion, RL and RC circuits, exponential growth, etc. Use of I.T.
- Higher-order linear differential equations. Homogeneous equations with constant coefficients.
- Algebra of complex numbers. Methods of indeterminate coefficients, method of varying parameters. Use of I.T.
- Laplace transforms. Use of tables. Applications. Inverse transforms, various techniques, convolution, piecewise-defined functions, pulses and periodic functions. Systems of differential equations. Use of I.T.
- Applications: study of harmonic motion, RLC circuits, transfer function, etc. Use of I.T.
- Use I.T. for: Runge-Kutta method, numerical solution of differential equations of order 2 (or higher) using a system of differential equations of order 1, "Suite" graphics mode, create and use a recursive function to generate the coefficients of a power series...
- Solving with power series. Periodic functions and Fourier series. Definition and properties, even and odd extensions, use of tables. Application. Use of I.T.
Course content
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