Learning Goals
Math 20D Spring 2015
Lecture A



By the end of the course you will be able to:
  1. Model a simple (physical) system to obtain an ODE or system of ODEs. (1.1, 1.3, 2.5, 7.1)

  2. Use graphical methods (sketched by hand) to predict the long-term behavior of a physical system described by a first order ODE or 2-dimensional system of first order linear equations. (1.1, 2.3, 2.5, 3.3, 7.5, 7.6, 7.8)

  3. Determine the qualitative behavior of an autonomous equation by means of an analysis of behavior near critical points. Sketch typical solutions by hand. (2.5)

  4. Use MATLAB to visualize solutions to first order ODE or 2-dimensional system using direction fields and approximate them using Euler's method. (MATLAB 1-4)

  5. Calculate with complex numbers and exponentials. (3.3, 7.6)

  6. Identify and solve various types of differential equations (and initial value problems) via the appropriate method. The types include: separable ODEs, homogeneous equations, linear first order ODEs, exact equations, homogeneous second order linear equations with constant coefficients, nonhomogeneous second order linear equations with constant coefficients. (1.2, 2.1, 2.2, 2.6, 3.1, 3.3, 3.4, 3.5, 3.6)

  7. Calculate eigenvalues, eigenvectors, and use them to solve first order linear systems. Relate first order systems with higher-order ODEs. Sketch the phase portrait of a two-dimensional linear system with constant coefficients. (7.2, 7.3, 7.4, 7.5, 7.6, 7.8)

  8. Use the Wronskian to determine a fundamental set of solutions (and in which interval they work) for homogeneous second order ODEs or homogeneous linear systems. (3.2, 3.6, 7.4, 7.5, 7.6, 7.8)

  9. Solve nonhomogeneous first order linear systems via undetermined coefficients. (7.9)

  10. Solve ODEs (including higher order equations) using Taylor series expansions. (5.1, 5.2, 5.3)

  11. Utilize step functions to model abrupt phenomena. (6.3, 6.4)

  12. Solve constant coefficient linear initial value problems using the Laplace transform together with tables of standard values, both for continuous and discontinuous inputs. (6.1, 6.2, 6.3, 6.4)

  13. Determine the domain of definition for the solution to an initial value problem. (2.2, 2.4, 3.2, 5.3)


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