Department
of Mathematics
Math 67. Vector Calculus
Fall 2018
Course Outline
Time
and Place: MWF
9:00 am - 9:50 am Millikan 2393
Instructor:
Dr. Adolfo J. Rumbos
Office: Andrew 2287
Phone / e-mail: ext. 18713
/ arumbos@pomona.edu
Course Website: http://pages.pomona.edu/~ajr04747/
Office Hours:
TuTh 9:00 am - 10:15 am, or by
appointment
Text: Vector Calculus by Peter
Baxandall and Hans Liebeck
Dover
Publications, Inc., 2008 printing
Prerequisites: Math
60 (Linear Algebra) or equivalent course.
Course
Description. The main goal of this course is the 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 functions from n-dimensional Euclidean space to m-dimensional Euclidean space (also
known as Vector Fields) and their
differentiability and integrability 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 Fundamental 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 introduced.
The
specific topics to be covered are listed in the attached Tentative Schedule of Lectures and Examinations.
Assigned
Grading
Policy. Grades will be based on the homework, two 50-minute
examinations, plus a comprehensive final examination. The grades will be computed as follows:
homework
20%
Two 50-minute
exams 50%
final examination 30%
Final
Examination.
Time: Tuesday,
December 18, 2018 9:00 am
Place: Millikan
2393
Math 67-Rumbos Fall
2018
Tentative Schedule of Lectures and
Examinations
Date Topic
W Sep.
5 n-Dimensional Euclidean Space
F Sep.
7 Spans, lines and
planes
M Sep.
10 Dot product and Euclidean
norm
W Sep. 12 Orthogonality
and projections
F Sep. 14 The cross product
M Sep.
17 Functions on Euclidean space
W Sep. 19 Open
subsets of Euclidean space
F Sep. 21 Continuous functions
M Sep.
24 Continuous functions
(continued)
W Sep. 26 Limits
and continuity
F Sep. 28 Differentiability
M Oct. 1 The derivative map
W Oct.
3 The derivative map (continued)
F Oct.
5 Sufficient conditions for
differentiability
M Oct. 8 Sufficient
conditions for differentiability (continued)
W Oct. 10 Derivatives of compositions
F Oct. 12 Derivatives of
compositions (continued)
M Oct.
15 Review
W Oct. 17 Exam 1
F Oct. 19 Path integrals
M Oct.
22 Fall Recess
W Oct. 24 Path
integrals (continued)
F Oct. 26 Line integrals
M Oct.
29 Gradient
fields
W Oct. 31 Flux across plane curves
F Nov.
2 Differential
forms
M Nov. 5 Calculus of differential forms
W Nov.
7 Calculus
of differential forms (continued)
F Nov.
9 Evaluating
2-forms: Double integrals
M Nov.
12 Green’s Theorem
W Nov. 14 Fundamental
Theorem of Calculus in two dimensions
F Nov. 16 Change of variables Theorem
M Nov.
19 Change of variables Theorem
(continued)
W Nov. 21 Thanksgiving Recess
F Nov. 23 Thanksgiving Recess
Math
67-Rumbos Fall
2018
Date Topic
M Nov.
26 Triple integrals
W Nov. 28 Surface
integrals
F Nov. 30 Surface integrals (continued)
M Dec. 3 Stokes’
Theorem
W Dec.
5 Review
F Dec. 7 Exam
2
M Dec.
10 Review
W Dec. 12 Review
Tu Dec.
18 Final Examination