MATH& 153 - Calculus III

1. Identify the different types of sequences and series.
2. Determine when a sequence or series is convergent or divergent.
3. Perform basic convergence tests (including the ratio test, comparison test, and integral test).
4. Compute the radius and interval of convergence for a power series.
5. Compute the Taylor Series expansion of a function.
6. Perform vector arithmetic computations.
7. Compute using vector components.
8. Perform vector operations (including dot product, cross product, and projections).
9. Find an equation of a line and plane using vector notation.
10. Differentiate and integrate vector-valued functions.
11. Find tangent and unit tangent vectors to a smooth curve at a point.
12. Compute curvature.
13. Find the unit normal and binormal vectors of a smooth curve defined by a vector-valued function.
14. Determine the tangential and normal components of the acceleration vector.
15. Convert points and equations between rectangular coordinates and polar coordinates.
16. Recognize and sketch graphs of equations in polar coordinates.
17. Construct graphs, find domains and ranges, and analyze continuity and differentiability of functions with two or more independent variables.
18. Write expressions for partial derivatives using limits.
19. Calculate partial derivatives using formulas.