MA 532-001 Fall 2008
Ordinary Differential Equations I
Material on Test 1
Test 1 is Friday Oct. 3. In the Meiss text, it will cover what we have done in Chapters 1 and 2.
Things you should be able to do:
- x'=f(x), x in R: sketch the phase portrait (Homework 1).
- x''+f(x)=0, x in R: sketch the phase portrait (Homework 2, problem 1).
- x'=f(x,y), y'=g(x,y): sketch nullclines, vector field, some representative trajectories.
- For a differential equation with parameters, find a linear change of variables and time that reduces the number of parameters (Homework 3).
- Use the basic theory of linear differential equations (Homework 4, problems 1, 3).
- Calculate e^(tA) (Homework 4, problem 4; Homework 5, p. 69 problems).
- Sketch the phase portrait of x'=Ax, x in R^2, using eigenvalues and eigenvectors (Homework 5, p. 68 problems).
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