MATH 250: Calculus III. Section 2
November 11, 2024
Test # 2 Review Topics
1.
Motion in
three-dimensional space; velocity and acceleration; finding velocity and path
from acceleration
2. Tangential and normal components of acceleration
3. Functions of two variables; traces; level curves and contour maps
4. Functions of three variables; level surfaces and contour maps
5. Limits and continuity of functions of several variables
6. Partial derivatives; higher-order partial derivatives; Clairaut’s theorem
7. Linearizations; linear approximations; finding tangent planes to surfaces z=f(x,y) without using gradient
8. Gradient
9. Chain rule for paths
10. Directional derivatives
11. Significance of gradient: direction and value of maximum rate of increase; normal vector to level surface; finding tangent planes to level surfaces
12. Chain rule for functions of several variables
13. Critical points; local extrema
14. Global extrema theorem
15. Finding local and global extrema for functions of two variables, including applications
16. Integration in two variables; double Riemann sum
17. Iterated integrals; Fubini’s theorem for double integrals
18. Double integrals over general regions; vertically and horizontally simple regions
19. Changing the order of double integration
20. Average value of a function of two variables
21. Integration in three variables; triple Riemann sum
22. Iterated integrals; Fubini’s theorem for triple integrals
23. Triple integrals over general regions
24. Triple integrals over regions between surfaces
25. Various orders in triple integration
26. Computing volumes with double and triple integration
27. Double integrals in polar coordinates
28. Triple integrals in cylindrical and spherical coordinates
29. Average value of function in a 3D region
Optional review problems:
Chapter 13 Review:
25, 28
Chapter 14 Review: 5,
6, 7, 11, 21, 23, 25, 31, 35, 37, 41, 43, 45
Chapter 15 Review:
15, 17, 19, 22, 23, 31, 33, 35, 36, 37, 38