Mathematics

Material on Test 2

Test 2 is Monday, March 21. The test will be on Secs. 4.4 - 4.6, 4.8 - 4.9, 7.1 - 7.6.

Calculators may be used for arithmetic only.

You may use the table of integrals in the front of the text, and the table of Laplace transforms in the back of the text. In addition, you may bring to the test one sheet of paper with whatever you find useful written on it.

Things you should be able to do:

Sec. 4.4. Use the method of undetermined coefficients to find a particular solution to a 2nd order equation.

Sec. 4.5. Use the method of undetermined coefficients and the superposition principle to find the general solution to a 2nd order equation, and use the general solution to solve initial value problems.

Sec. 4.6. Use the method of variation of parameters and the superposition principle to find the general solution to a 2nd order equation.

Secs. 4.8 - 4.9. Solve initial value problems for spring-mass systems, and interpret the answer. (ADDED 3/18/05: OMIT THIS MATERIAL.)

Sec. 7.2. Calculate Laplace transforms from the definition and from the table.

Sec. 7.3. Calculate Laplace transforms of e^(at) f(t), derivatives of f(t), and t^n f(t).

Sec. 7.4. Calculate inverse Laplace transforms using the table and partial fractions.

Sec. 7.5. Use Laplace transforms to solve initial value problems for 2nd order equations.

Sec. 7.6. Calculate Laplace transforms of discontinuous and periodic functions. Use Laplace transforms to solve initial value problems for 2nd order equations when the forcing function is discontinuous.

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