MATH 250: Calculus III
March 3, 2025
Test # 1 Review Topics
1. Parametric equations of curves in the plane
2. Slope of a tangent line to a curve given in parametric form
3. Arc length of a curve given in parametric form
4. Speed along a parameterized path
5. Polar coordinates; conversions between polar and rectangular coordinates; graphing curves and regions in polar coordinates
6. Arc lengths and areas in polar coordinates
7. Conic sections; converting to standard forms
8. Vectors in two dimensions; magnitude of a vector; vector algebra; basic properties
9. Unit vectors, standard basis vectors
10. Vectors in three dimensions; distance formula
11. Parametric equations of a straight line in three dimensions; intersections of straight lines
12. Dot product; basic properties (with proofs); angle between vectors; projection of a vector along another vector
13. Determinants
14. Cross product; basic properties (with proofs)
15. Areas with the use of cross product
16. Planes in three dimensions; planes through three given points; intersection of a plane and a line; intersections of planes; traces of a plane
17. Cylindrical coordinates; conversions between cylindrical and rectangular coordinates; level surfaces; identifying surfaces and regions in cylindrical coordinates
18. Spherical coordinates; conversions between spherical and rectangular coordinates; level surfaces; identifying surfaces and regions in spherical coordinates
19. Basic quadric surfaces; traces of quadric surfaces
20. Vector-valued functions: parametric curves in three dimensions; projections of curves onto coordinate planes
21. Calculus of vector-valued functions
22. Tangent lines to parameterized curves
23. Arc length; speed
24. Arc length parameterization
25. Unit tangent vector; curvature
Note: Calculators will not be needed and are not allowed on the test.
Optional review problems:
Chapter 11 Review: 7, 11, 15, 21, 36, 43, 52
Chapter 12 Review: 9, 15, 27, 29, 39, 48, 49, 50, 51, 52, 60, 63, 64, 65, 68
Chapter 13 Review: 4, 23, 24, 29, 30