Final Exam Survival Tips
- The exam will be comprehensive, covering all material that we
went over in class, with the exception of the following sections:
3.8, 5.5, 5.6, and 8.4.
- I will certainly ask a question about existence and uniqueness
theorems for ODE's--something from one of the sections 2.2, 2.4,
or 7.1.
- There will certainly be some questions involving direction
fields or phase portraits.
- A good strategy for practicing computation is to go back through
the homework problems and work problems similar to those assigned.
The major computational skills you should have acquired are
- Solving first order linear ODE's and initial value
problems (integrating factors).
- Finding and classifying critical points of autonomous
first order ODE's.
- Using Euler's method to numerically approximate the
solution of a first order ODE.
- Estimating local truncation error in Euler's method.
- Solving higher order, constant coefficient, linear,
homogeneous ODE's.
- Using the method of undetermined coefficients to solve
higher order, constant coefficient, linear,
inhomogeneous ODE's.
- Finding power series solutions of initial value problems.
- Solving first order, constant coefficient, linear, homogeneous
systems of ODE's.
- Using variation of parameters to solve first order, linear
inhomogeneous systems.
- Finding and classifying critical points of a non-linear
autonomous 2x2 system of ODE's.