MATH& 153 - Calculus III

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