MATH
402 – Advanced Calculus II
Spring 2010
Professor:
Dr. Janet Vassilev
Office: Humanities
Office
Hours: MWF 12 pm-1 pm and by appointment.
Telephone: 
(505)
277-2214
email: jvassil@math.unm.edu
webpage: http://www.math.unm.edu/~jvassil
Text
:
Advanced Calculus, by Gerald
Folland.
Course
Meetings: The course lectures will be held in Dane Smith Hall 324 on Mondays,
Wednesdays and Fridays at 11-11:50 am.
Topics: Generalization of 401/501 to several
variables and metric spaces: sequences, limits, compactness and continuity on
metric spaces; interchange of limit operations; series, power series; partial
derivatives; fixed point, implicit and inverse function theorems; multiple
integrals.
Homework
(200 points): Homework will be assigned weekly on Mondays and will be
collected the following Monday at the beginning of class. Homework will
not be graded unless it is written in order and labeled
appropriately. The definitions and theorems in the text and
given in class are your tools for the homework proofs. If the theorem has a name, use it. Otherwise, I would prefer that you fully
describe the theorem in words that you plan to use, than state “by Theorem
3”. Each week around 4 of the assigned problems will be graded. The
weekly assignments will each be worth 20 points. I will drop your lowest two homework scores
and the remaining homework will be averaged to get a score out of 200.
Exams (400
points): I will give two midterms (100 points) and a final (200
points). There are no make up exams. If a test is missed,
notify me as soon as possible on the day of the exam.
For the midterms only, if you have a legitimate and documented
excuse, your grade will be recalculated without that test. The Midterms
are tentatively scheduled for Friday, February 26 and Wednesday, April 7.
The Final is on Wednesay, May 12, from 10 am-12 noon.
Grades: General guidelines
for letter grades (subject to change; but they won't get any more strict):
90-100% - A; 80-89% - B; 70-79% - C; 60-69% - D; below 60% - F. In
assigning Final Grades for the course, I will compare your grade on all course
work (including the Final) and your grade on the Final Exam. You will
receive the better of the two grades.
Tentative
Schedule (for Dr. Vassilev’s Advanced Calculus):
Date
|
Chapter
|
Topic
|
Homework
|
1/20
|
1.1-1.2
|
Euclidean
n-space
|
|
1/22
|
1.3
|
Limits and
Continuity
|
|
1/25
|
1.4
|
Sequences
|
(p. 8) 2b, 4,
5, 7, 8
(p. 12) 5, 6, 8, 9
(p. 19) 8, 9
|
1/27
|
1.5
|
Completeness
|
|
1/29
|
1.6-1.7
|
Compactness and
Connectedness
|
Solutions HW 1
|
2/1
|
1.8
|
Uniform
Continuity
|
(p. 23) 5, 6
(p. 28-30) 3, 7, 8, 12
(p. 33) 4, 5, 6
|
2/3
|
2.2
|
Differentiability
|
|
2/5
|
2.2
|
Differentiability
continued
|
Solutions HW 2
|
2/8
|
2.3
|
Chain Rule
|
(p.37-38) 1(a,b), 2, 4, 7, 9
(p. 40-41) 1,
3, 4
|
2/10
|
2.3
|
More on Chain
Rule
|
|
2/12
|
2.4-2.5
|
Mean Value
Theorem and Implicit Functions
|
Solutions HW 3
|
2/15
|
2.6
|
Higher Order
Partials
|
(p. 61-62) 1b,
2a, 6, 7
(p. 69-70) 1, 4, 5
(p. 72-73) 1, 2
|
2/17
|
2.7
|
|
|
2/19
|
2.7
|
|
Solutions HW 4
|
2/22
|
2.8
|
Critical Points
|
|
2/24
|
|
Review
|
|
2/26
|
|
Midterm 1
|
|
3/1
|
2.9
|
Extreme Value
Problems
|
(p. 76-77) 2,
5, 6
(p. 84-85) 4, 5, 10
(p. 95) 10
|
3/3
|
2.10
|
Derivatives of
Vector-Valued Functions
|
Solutions HW 5
|
3/5
|
3.1
|
Implicit
Function Theorem
|
|
3/8
|
3.2
|
Curves in the
Plane
|
(p. 100) 2, 4
(p. 105-106) 1,
6, 9, 11, 16, 19
|
3/10
|
3.3
|
Surfaces and Curves
in Space
|
Solutions HW 6
|
3/12
|
3.4
|
Transformations
and Coordinate Systems
|
|
3/22
|
3.5
|
Functional
Dependence
|
(p. 111-112) 5,
6, 7, 9
(p. 119-120) 1,
5, 6, 8
|
3/24
|
4.2
|
Integration
|
Solutions HW 7
|
3/26
|
4.2
|
Integration
|
|
3/29
|
4.3
|
Multiple
Integrals
|
(p. 125) 2, 4
(p. 132-133) 3, 4
(p. 138-139) 2, 4, 6
(p. 146) 1
|
3/31
|
4.4
|
Change of
Variables
|
Solutions HW 8
|
4/2
|
4.4
|
Change of
Variables continued
|
|
4/5
|
|
Review
|
(p. 167) 2, 3,
4, 6
|
4/7
|
|
Midterm II
|
|
4/9
|
4.5
|
Functions
defined by Integrals
|
|
4/12
|
4.7
|
Improper
Integrals
|
|
4/14
|
5.1
|
Arclength and
Line Integrals
|
|
4/16
|
5.1
|
Arclength and
Line Integrals
|
|
4/19
|
5.2
|
Green’s Theorem
|
(p. 175-176) 4, 6, 7, 9
(p. 187-188) 6,
10, 11, 13
|
4/21
|
5.3
|
Surface
Integrals
|
|
4/23
|
5.4-5.5
|
Divergence
Theorem
|
|
4/26
|
5.6
|
Applications to
Physics
|
(p. 192-193) 2, 5, 6, 7
(p. 206-207) 2, 4
(p. 221) 2, 4,
5
|
4/28
|
5.7
|
Stoke’s Theorem
|
|
4/30
|
5.8
|
Integrating
Vector Derivatives
|
|
5/3
|
5.9
|
Differential
Forms
|
|
5/5
|
5.9
|
Differential
Forms continued
|
|
5/7
|
|
Review
|
|
5/12
|
|
Final exam
|
|