Mathematics

Material on Test 1

Test 1 is Tuesday, February 8. The test will be on Secs. 1.1 - 1.4, 2.2 - 2.4, pp. 34 - 36, 3.2, and 3.4.

Calculators may be used only to do arithmetic and evaluate the numerical value of expressions (for example, e^(.2) or sin(.7)). They may not be used for differentiation, integration, algebra, solving differential equations, graphing, etc.

You may use the table of integrals in the front of the text.

Things you should be able to do:

Sec. 1.1. 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 using isoclines; 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.

Pp. 34 - 36. Draw the phase line for an autonomous first-order differential equation. Find equilibria and tell their type (attractor, repeller, mixed).

Sec. 3.2. Set up and solve mixing problems and population problems.

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

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