Lab Report Grading Scheme
(2 points) Your name (1 point) and your group partner names (1 point for the
whole group; 0 points if dont know the names of all of their group members!)
(3 points) Title: has to be informative. Provide a short title that tells u
13
VECTOR FUNCTIONS
VECTOR FUNCTIONS
Later in this chapter, we are going to use
vector functions to describe the motion of
planets and other objects through space.
Here, we prepare the way by developing
the calculus of vector functions.
VECTOR FUNCTIONS
10
PARAMETRIC EQUATIONS
AND POLAR COORDINATES
PARAMETRIC EQUATIONS & POLAR COORDINATES
A coordinate system represents
a point in the plane by an ordered
pair of numbers called coordinates.
PARAMETRIC EQUATIONS & POLAR COORDINATES
Usually, we use Cartesian
10
PARAMETRIC EQUATIONS
AND POLAR COORDINATES
PARAMETRIC EQUATIONS & POLAR COORDINATES
So far, we have described plane curves
by giving:
y as a function of x [y = f(x)] or x as a function of y
[x = g(y)]
A relation between x and y that defines y implici
10
PARAMETRIC EQUATIONS
AND POLAR COORDINATES
PARAMETRIC EQUATIONS & POLAR COORDINATES
We have seen how to represent curves by
parametric equations.
Now, we apply the methods of calculus to
these parametric curves.
PARAMETRIC EQUATIONS & POLAR COORDINATES
Math 203 Homework #2. Due in class Wednesday, September 16th.
Problem 1: Find equation of line through (1, 1, 2) and (2, 1, 3).
Problem 2: Find intersection point between
x3
2
=
y1
1
=
z4
1
and
x+2
3
=
y3
1
=
z2
.
1
Problem 3: Find equation of plane conta
Math 203 Homework #3. Due in class Wednesday, September 30th.
Problem 1: Consider the helix (cos t, sin t, t) where 0 t 2 over one full revolution. Use the formula
for lengths of curves to calculate the length of this helix.
Problem 2: Consider the inters
Math 203 Homework #1. Due in class Wednesday, September 9th.
Problem 1: (i) Find the two unit vectors orthogonal to v = 2i + k and w = i j k.
(ii) Find projv w, the projection of w onto v.
(iii) Find the angle between the vectors v and w.
Problem 2: Find
EXAM 2 PRACTICE PROBLEMS
Math 203
Spring 2017
I
Find the following limits if they exist:
a)
Ans: 2
x2 y2
lim
( x ,y ) (0, 0)
x2 y2 1 1
b)
x 2 xy 2
lim
( x , y ) (0, 0) x 2 y 2
Ans: DNE
II
a) Use implicit differentiation to find
xze
z
x
and
z
y
for the fol
SYLLABUS
Math 203
Summer 2017
Text: Stewart, Essential Calculus, 2nd Edition
Instructor: Cheikh A. T. MBOUP
Office Hours: M, Tu., W, Th. 2:00 2:50 PM or by Appointment
Office: NAC 6/272
Email: [email protected]
There will be three (3) or four (4) in-class
EXAM 2 PRACTICE PROBLEMS
Math 203
Summer 2017
I
Find the following limits if they exist:
a)
Ans: 2
x2 y2
lim
( x ,y ) (0, 0)
x2 y2 1 1
b)
x 2 xy 2
lim
( x , y ) (0, 0) x 2 y 2
Ans: DNE
II
a) Use implicit differentiation to find
xze
z
x
and
z
y
for the fol
I t
_. 5 . _, _.
Let :7 = 2? + 3 k and )1: 2i 4- j + 3]: Compute:
a) Let it = z? 217 . Compute "it" .
b) Find the angle between the vectors 17 and it.
c) The vector projection of f4 onto 17 .
d) Find two unit vectors orthogonal to the vector projection of
10
PARAMETRIC EQUATIONS
AND POLAR COORDINATES
PARAMETRIC EQUATIONS & POLAR COORDINATES
10.4
Areas and Lengths
in Polar Coordinates
In this section, we will:
Develop the formula for the area of a region
whose boundary is given by a polar equation.
AREAS IN