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Department
of Mathematics
Mathematics 107. Vector Calculus
Fall 2007
Course Outline
T=
ime
and Place: =
MWF
11:00 am - 11:50 am
Millikan 207
Instructor: =
&=
nbsp; Dr.
Adolfo J. Rumbos
Office:<=
span
style=3D'mso-spacerun:yes'> =
=
Andrew
259
Phone / e-mail: =
ext. 18713 /
Office Hours: =
&=
nbsp; MWF
9:15 am-9:50 am, Tu 9:15 am-10:50 am, 2:30 pm- 3:30 pm
or by appointment
Text:<=
span
style=3D'mso-tab-count:3'> &=
nbsp; &nbs=
p; Second
Year Calculus by David M. Bressoud
Undergraduate
Texts in Mathematics, Springer 2000
Prerequisites:<=
span
style=3D'mso-spacerun:yes'> Math
60 (Linear Algebra) or equivalent course.
=
The main goal of this course is th=
e development
of differential and integral calculus ideas, which students learned in a
single-variable calculus courses, in dimensions higher than 1. The main objects of study are func=
tions
from n-dimensional Euclidean sp=
ace to
m-dimensional Euclidean space (=
also
known as Vector Fields) and th=
eir
differentiation and integration properties. We will also be concerned with the=
study
of subsets of Euclidean space on which those functions act. The culmination of the course will=
be
the multivariable version of the F=
undamental
Theorem of Calculus (also known as the generalized Stokes’ Theorem).
In the process leading to Stokes’ Theorem, the machinery of differentiable manifolds and differential forms will be introd=
uced
and developed.
=
The
specific topics to be covered are listed in the attached Tentative Schedule of Lectures and Examinations.
Grades will be based on the homewo=
rk, two
50-minute examinations, plus a comprehensive final examination. The grades will be computed as fol=
lows:
=
homework
&=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; 20%
=
Two
50-minute exams &nbs=
p; &=
nbsp; &=
nbsp; 50%
=
final
examination &n=
bsp;  =
; &n=
bsp;  =
; 30%
Time: =
Tuesday,
December 18 &=
nbsp;
9:00 am
Place: Millikan
207
Math 107=
&=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; &=
nbsp; =
&nb=
sp; =
Fall 2007
Tentative Schedule of Lecture=
s and
Examinations
Date &=
nbsp; &nbs=
p; Topic
W Sep.<=
span
style=3D'mso-spacerun:yes'> 5 n-Dimensional Euclidean Space
F &=
nbsp; Sep. 7 &=
nbsp; n-Dimensional Euclidean Space
(continued)
M &n=
bsp; Sep. 10 Continu=
ous
Functions on Euclidean Space
W Sep. 12&=
nbsp; Differentiable
Functions on Euclidean Space
F &=
nbsp; Sep. 14 Differe=
ntiability
M &n=
bsp; Sep. 17 The
Chain Rule
W Sep. 19 Partial
derivatives, the gradient and directional derivatives
F &=
nbsp; Sep. 21 Problems
and examples
M &n=
bsp; Sep. 24 Differe=
ntial
forms
W Sep. 26 Differe=
ntial
forms (continued)
F &=
nbsp; Sep. 28 Differe=
ntiable
manifolds
M &n=
bsp; Oct. 1 Different=
iable
manifolds (continued)
W Oct. 3 Line
integrals
F &=
nbsp; Oct. 5 Line
integrals (continued)
M &n=
bsp; Oct. 8 &=
nbsp; Double
integrals
W Oct. 10&=
nbsp; Integrals
over surfaces
F &=
nbsp; Oct. 12 Integra=
ls
over surfaces (continued)
M &n=
bsp; Oct. 15&=
nbsp; Review
W Oct. 17 Exam
1
F &=
nbsp; Oct. 19 Problems
and Examples
M &n=
bsp; Oct. 22 Fall
recess: No Classes
W Oct. 24 Triple
integrals
F &=
nbsp; Oct. 26 Change of variab=
les
M &n=
bsp; Oct. 29 Change
of variables (continued)
W Oct. 31 Orienta=
tion
of manifolds
F &=
nbsp; Nov. 2 In=
tegration
on manifolds
M &n=
bsp; Nov. 5 &=
nbsp; Integration
on manifolds (continued)
W Nov. 7 The
fundamental Theorem of Calculus
F &=
nbsp; Nov. 9 StokesR=
17;
Theorem
M &n=
bsp; Nov. 12=
The
Divergence Theorem
W Nov. 14=
Green’s
Theorem
F &=
nbsp; Nov. 16=
Problems
and examples
M &n=
bsp; Nov. 19=
Quadratic
functions
W Nov. 21=
Quadratic
functions (continued)
F &=
nbsp; Nov. 23=
Thanksgivi=
ng
recess
M &n=
bsp; Nov. 26=
Locating
extrema.
W Nov. 28&=
nbsp;
F &=
nbsp; Nov. 30=
Lagrange
multipliers
M &n=
bsp; Dec. 3 Prob=
lems
and examples
W Dec. 5 Revi=
ew
F &=
nbsp; Dec. 7 E=
xam
2
M &n= bsp; Dec. 10= Review<= o:p>
W Dec. 12= Review<= o:p>
Tu Dec. 18=
Final
Examination