Study Guide 3 (For week of 9/5/00-9/12/00)
(Math 2422, Calculus III, Section 002, Fall 2000)
Homework:
Read Sections 10.7, 11.1 and 11.2, and work the following problems:
(You do not need to hand these problems in, but any of them
may appear on the quiz.) (problems with and asterisk (*)
will be turned in on Tues. Sept. 19)
Section 10.7:
5, 8, 15, 16, 22, 27, 35, 37*, 69-74, 76*, 83, 88
Section 11.1: 1, 2, 3, 13, 17-20, 33, 35*,
50*, 51, 57, 59, 63 (for number 35: We do
not need to see the vectors, we just want the curve. So
enter the expression as a parametric curve: x=sin(t),
y=....)
Section 11.2: 3, 9, 13, 14, 15, 19a,b,e; 39, 42*, 45, 48*, 54, 63, 64 (For problem 3, may use computer; for remaining problems, must do by hand)
Overview: The goals for this week are
to understand cylindrical and spherical coordinates, to introduce
vector-valued functions, and to learn to differentiate and integrate
vector-valued functions.
Things to learn this week:
Terminology: cylindrical
coordinates, spherical coordinates, space curves, vector-valued function,
derivatives and integrals for vector-valued
functions.
Essential Material :
(The quiz will emphasize these skills)
- Convert a point
from cylindrical to rectangular coordinates,
from rectangular to cylindrical, from rectangular to spherical,
or from spherical to rectangular coorinates.
- Convert an equation from cylindrical to rectangular coordinates,
from rectangular to cylindrical, from rectangular to spherical,
or from spherical to rectangular coordinates.
- Evaluate a vector-valued function at a given value.
- Match a vector valued function with its graph.
- Sketch a plane curve defined by a vector-valued function.
- Sketch a simple space curve defined by a vector-valued function.
- Represent a 2-D graph by a vector-valued function.
- Calculate the derivative of a vector-valued function.
- Apply properties of derivatives (Thm 11.2) to determine
derivatives of expressions involving vector valued functions.
- Calculate indefinite integrals of vector valued function
(be careful to include a constant of integration for each
component of the vector).
- Calculate the antiderivative of a vector-valued function
(given initial conditions).
- Calculate a definite integral of a vector-valued function.
Lesser Priority :
- Find the domain of a vector-valued function.
- Evaluate the limit of a vector-valued function.
- Determine intervals on which a vector-valued function is continuous.