MATH 250: Calculus III
April 13, 2024
Test # 2 Review Topics
1.
Arc length; speed
2.
Arc length parameterization
3.
Unit tangent
vector; curvature; unit normal vector
4.
Motion in
three-dimensional space; velocity and acceleration; finding velocity and path
from acceleration
5. Tangential and normal components of acceleration
6. Functions of two variables; traces; level curves and
contour maps
7. Functions
of three variables; level surfaces and contour maps
8. Limits
and continuity of functions of several variables
9. Partial
derivatives; higher-order partial derivatives; Clairaut’s theorem
10. Linearizations; linear approximations; finding tangent
planes to surfaces z=f(x,y)
without using gradient
11. Gradient
12. Chain rule
for paths
13. Directional
derivatives
14. Significance
of gradient: direction and value of maximum rate of increase; normal vector to
level surface; finding tangent planes to level surfaces
15. Chain rule
for functions of several variables
16. Critical
points; local extrema
17. Global
extrema theorem
18. Finding
local and global extrema for functions of two variables, including applications
19. Integration
in two variables; double Riemann sum
20. Iterated
integrals; Fubini’s theorem for double integrals
21. Double
integrals over general regions; vertically and horizontally simple regions
22. Changing
the order of double integration
23. Average
value of a function of two variables
24. Integration
in three variables; triple Riemann sum
25. Iterated
integrals; Fubini’s theorem for triple integrals
26. Triple
integrals over general regions
27. Triple integrals
over regions between surfaces
28. Various
orders in triple integration
29. Computing
volumes with double and triple integration
30. Double
integrals in polar coordinates
31. Triple
integrals in cylindrical and spherical coordinates
32. Average
value of function in a 3D region
33. Using double and triple integrals to find mass
(charge, etc.) of an object
34. Change of variables; Jacobian
Note: Calculators
will not be needed and are not allowed
on the test.
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