MAT 271 Test 1 Review

MAC CALIII Chap9 -- Review

1 Understand how parametric curves are defined. Know how to graph them by hand if you need to and also be able to use your calculator effectively. Don't forget to set the domain for the parameter according to the interval given in the problem and always indicate which direction the parameter is increasing. You should be able to match equations with graphs. Be able to write down any rectangular ( y = f(x) ) function in parametric form.

2 Be able to find the derivative dy/dx of a parametric curve using the idea of the chain rule. Be able to write up the equation of a tangent line to a parametric curve. Know how to calculate arc length for functions in parametric form. Area calculation makes sense between two constant values of the parameter or for closed loops. Know what system of equations to solve to find parameter values for which the curve intersects itself. Also be able to follow the orientation of the curve to be able to find positive area (should be clockwise as the prameter increases).

3 Understand how polar coordinates are defined. Be able to convert rectengular coordinates to polar and vice versa. Know how to convert rectengular equations to polar and vice versa. Know how to graph polar curves by hand if you need to and also be able to use your calculator effectively. Don't forget to set the domain for the parameter according to the interval given in the problem. You should be able to match equations with graphs. Also know how to find the derivative dy/dx of a polar curve using the idea of the chain rule. Be able to write up the equation of a tangent line to a polar curve.

4 Know how to calculate arc length for functions in polar form. We covered three different types of area calculations: (1) for closed loops, (2) for regions that are overlapping parts of two given curves (3) for regions that are between two given curves. Review trigonometry to know well how to find the angles for which two polar curves intersects or a polar curve loops around.

Remember that a very good formula sheet is available. See link on my webpage.