Mathematics

Material on Test 1

Test 1 is Wednesday, February 9. The test will be on Secs. 1.1 - 1.4, 2.2 - 2.4, 3.2, 3.4, 4.2 - 4.3.

Calculators may be used for arithmetic only.

You may use the table of integrals in the front 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. 1.1. Tell whether an ordinary differential equation is linear or nonlinear. Translate a physical description into an ordinary differential equation.

Sec. 1.2. Check whether a function is a solution of a differential equation. Check whether an equation implicitly defines a solution of a differential equation. Tell whether the Existence-Uniqueness Theorem applies.

Sec. 1.3. Sketch direction fields; given the direction field, sketch the solution of an initial value problem; interpret what the direction field is telling you.

Sec. 1.4. Use Euler's method to approximate the solution of a differential equation.

Secs. 2.2 - 2.4. Recognize and solve separable, linear, and exact differential equations. Determine the value of the arbitrary constant needed to solve an initial value problem.

Sec. 3.2. Set up and solve mixing problems.

Sec. 3.4. Set up and solve simple mechanics problems that lead to first-order differential equations.

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.

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