Mathematics

### Material on Test 2

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Test 2 is Thursday, March 22. The test will be on Secs. 4.1 - 4.6, 4.9 - 4.10, 7.1 - 7.6, 7.8. It will not cover Sec. 9.2; that material will be on Test 3.

Calculators may be used for arithmetic and evaluating functions only.

Bring your text to the test. 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. If your text does not have this material, or if you don't like to carry it around, click here to download a pdf file that you can print and bring to the test.

The properties of Laplace transforms that we use are all in the table in the back of the text:
• Theorem 3 in Sec. 7.3 is formula 2 in the table.
• Theorem 4 in Sec. 7.3 is formula 3 in the table.
• Theorem 5 in Sec. 7.3 is formula 4 in the table.
• Theorem 6 in Sec. 7.3 is formula 5 in the table.
• Theorem 8 in Sec. 7.6 is formula 10 in the table.
• Formulas (11) in Sec. 7.6 is formulas 11 in the table.

A brief description of the method of undetermined coefficients is on the inside back cover of the text; you are welcome to refer to it, but it is very brief!

Variation of parameters is also described on the inside back cover of the text.

Things you should be able to do:

Secs. 4.2 - 4.3. Find the general solution of ay''+by'+cy=0. Determine the values of the arbitrary constants needed to solve an initial value problem.

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 variation of parameters formula and the superposition principle to find the general solution to a 2nd order equation.

Secs. 4.9 - 4.10. Solve initial value problems for spring-mass systems, and interpret the answer.

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 functions. (Omit periodic functions.) Use Laplace transforms to solve initial value problems for 2nd order equations when the forcing function is discontinuous.

Sec. 7.8. Use Laplace transforms to solve initial value problems for 2nd order equations when the forcing function is a delta function.