MATH 250: Calculus III
February 23, 2024
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
Note: Calculators
will not be needed and are not allowed
on the test.
Optional review problems:
Chapter 11 Review: 7, 11, 15,
21, 33, 43, 52
Chapter 12 Review: 9, 15, 29,
39, 48, 49, 50, 51, 52, 60, 63, 64
Chapter 13 Review: 3, 4, 9,
17
Most likely, I will be
available for an additional hour on Thursday, 2/29, from 2 to 3 (from 3 to 4
are my usual Thursday’s office hours). Nolan will be available for help after classes
on Wed and Thu.
Please begin reviewing
over the weekend!!!