Final Exam Review Math 308-503 (Spring
2011)
General Information
The final exam will be given on Tuesday, 5/10/2011, from 8 to 10 am, in our usual classroom (BLOC 128). I will have these extra office hours: Thursday, 9-11; Friday, 10-1; Monday, 1:30-3:30.
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Calculators. You may use scientific calculators to do numerical
calculations logs, exponentials, and so on. You
may not use any calculator that has the capability of doing
algebra or calculus, or of storing course material.
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Other devices. You may not use cell phones, computers, or any
other device capable of storing, sending, or receiving information.
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Structure and Coverage There will be 8 to 10 questions, some
with multiple parts. The problems will be similar to homework
problems, examples done in class and worked out in the text. The exam is comprehensive; it covers all of the material listed on previous review sheets, and, in addition, sections A.3, A.4, 6.3 and 6.4. The percentages for each of the three general topics below will be roughly 20%, 40%, 40%.
Topics covered
First Order Equations
Second Order Equations
- See Test 2 Review. Be sure to go over the material on forced vibrations and variation of parameters. Note: the text's notation concerning phase is inconsistent. In section 4.5, he uses δ for the phase. But in section 4.7, 2δ is the damping coefficient and φ(ω) is the phase. In any problem involving these, I'll be sure to specify in words what I want you to find. As always, know the concept and be careful about tying yourself to specific notation in formulas.
- Laplace transforms. See Test 3 Review. You will be given a table of Laplace transforms.
Systems of Differential Equations
- 2×2 systems and applications. See Test 1 Review and Test 2 Review.
- General n×n systems of differential equations. See sections 6.3 and 6.4. The material on matrices in sections A.1-A.4 solving systems of algebraic equations, determinants, and eigenvalue problems was needed to deal with systems of differential equations, and it will be covered on the test only in connection with the material from 6.3 and 6.4.
Updated 5/4/2011.