Infinite Series:WRITING UP HOMEWORK SOLUTIONS: You are expected to show all essential steps in solving a problem. Draw appropriate figures. If in doubt, PUT IT IN! Make your solution flow. Ask yourself the question: "If I were the reader, how would I score this problem?'' Numerical answers alone, single words "yes" or "no", etc., are NEVER, EVER acceptable as complete answers. One of the skills you are expected to learn in this class is that of communicating mathematics clearly and completely in writing. Writing up homework exercises is your opportunity to hone these skills. Your grade depends on it! Weekly HandWritten HomeWork (WHW) Sets:
Definitions: sequences, series, and convergence. Tests
for convergence: The geometric series test, n-th term test, Integral test,
p-series test, comparison tests, Alternating Series test, the Ratio and
Root tests. Power series, representing functions with series, Taylor
and Maclaurin series.
Parametric Equations, Polar Coordinates, and Conic Sections:
Parametric equations, arc length and speed, polar coordinates, area and
arc length in polar coordinates, conic sections, Kepler's Laws.
Vectors and the Geometry of Space:
Vectors in the plane and space, lines in space, dot and cross products,
planes in 3-space, quadric surfaces in space. Cylindrical and spherical
coordinates.
Calculus of Vector-Valued Functions:
Definitions, differentiation and integration, arc length and speed,
curvature, motion in 3-space, planetary motion vis-a-vis Kepler and
Newton.
1. _________________________________________________
2. _________________________________________________
3. _________________________________________________
4. _________________________________________________
5. _________________________________________________
6. _________________________________________________
7. _________________________________________________
8. _________________________________________________
9. _________________________________________________
10. _________________________________________________