MATH 401/501 Advanced Calculus
Fall 2009
Professor:
Dr.
Janet Vassilev
Office:
Humanities
467
Office Hours: TWTh 11-12
Telephone:
(505) 277-2214
Email: jvassil@math.unm.edu
webpage: http://www.math.unm.edu/~jvassil
Text : Analysis
With and Introduction to Proof, 4th Edition by Steven Lay
Course
Meetings: The course lectures will be held 132 Dane
Smith Hall on Tuesday and Thursday from 12:30-1:45 p.m. There is
also a Discussion Session on Wednesday from 12-12:50 p.m.
Topics: Definition
and topology of real numbers, sequences, limits, functions, continuity,
differentiation and integration with an emphasis on rigorous proofs.
Homework
(200 points): Homework will be assigned weekly on
Thursdays and will be collected the following Thursday. Late homework
will be penalized 20% off per each day that it is late. 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 I will select about 4 or 5 of the assigned problems to
grade. 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 Tuesday, September 29 and Tuesday,
November 10. The Final is on Thursday, December 17, 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
|
Section
|
Topic
|
Homework
|
8/25
|
3 and 4
|
Proof
Techniques
|
|
8/27
|
5 and 6
|
Sets and Relations
|
3.1,
3.6(a,b,d,g,i), 3.7(a,b,c), 3.9, 4.4, 4.8, 4.11, 4.17, 4.19, 5.7, 5.14, 5.18,
5.25(a,b), 6.10(a,d), 6.12(a,b,c), 6.14, 6.21, 6.25, 6.27(b,d,e)
|
9/1
|
7
|
Functions
|
Homework 1 Solutions
|
9/3
|
8 and 10
|
Cardinality
and Natural numbers
|
7.4(b,c),
7.6(a,b), 7.7(b,g), 7.8, 7.13, 7.14, 7.17, 7.26, 7.27, 7.32, 8.3(a,c,d),
8.13, 8.18, 8.20, 8.22
|
9/8
|
10 and 11
|
Induction and
Ordered Fields
|
Homework 2 Solutions
|
9/10
|
12
|
Completeness
|
10.3,
10.4, 10.6, 10.7, 10.14, 10.20, 10.21b, 11.4, 11.6, 11.8, 11.9
|
9/15
|
13
|
Topology of
Reals
|
Homework
3 Solutions Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7
|
9/17
|
14
|
Compact Sets
|
12.3(b,h,l),
12.4(b,h,l), 12.6, 12.8, 12.12(a,b), 13,3(a,b), 13.4(a,b), 13.5(c,d),
13.7(a,b,f), 13.12, 13.20,(a,c), 13.21(b,d)
|
9/22
|
15
|
Metric Spaces
|
Homework 4 Solutions
|
9/24
|
16
|
Convergence
|
|
9/29
|
|
Midterm 1
|
|
10/1
|
17
|
Limit Theorems
|
14.3(a,c),
14.4, 14.5a, 14.8, 14.9, 14.11, 14.12
|
10/6
|
18
|
Monotone and
Cauchy Sequences
|
Homework 5 Solutions
|
10/8
|
19
|
Subsequences
|
16.6(b,c),
16.8b, 16.9a, 16.13, 16.15, 17.5(d,f), 17.6(a,b), 17.7, 17.8, 17.18, 18.3b,
18.4, 18.14
|
10/13
|
20
|
Limits of
Functions
|
Homework 6 Solutions
|
10/15
|
21 and 22
|
Continuous
Functions
|
|
10/20
|
23
|
Uniform
Continuity
|
|
10/22
|
25
|
The Derivative
|
19.3(a,d),
19.4(a,b), 19.8, 19.9, 19.17, 19.19, 20.13, 20.14, 20.20, 21.8, 21.13, 21.16,
22.3(a,e,g,h), 22.4, 22.7, 22.9
|
10/27
|
26
|
The Mean Value
Theorem
|
Homework 7 Solutions
|
10/29
|
27
|
L’Hopital’s
Rule
|
23.3(a,e),
23.5, 23.6, 23.10, 23.15, 25.6, 25.8, 25.11, 25.12, 26.6, 26.9, 26.11, 26.13,
26.23
|
11/3
|
28
|
|
Homework 8 Solutions
|
11/5
|
29
|
The Riemann
Integral
|
|
11/10
|
|
Midterm 2
|
|
11/12
|
30
|
Properties of
the Riemann Integral
|
|
11/17
|
31
|
Fundamental
Theorem of Calculus
|
|
11/19
|
32
|
Convergence of
Series
|
26.6,
26.8, 26.18, 26.23, 27.6, 28.9, 28.12, 29.8, 29.9, 29.11a, 29.13, 29.15,
20.5, 30.10, 30.11, 30.21
|
11/24
|
33
|
Convergence
Tests
|
Homework 9 Solutions
|
11/26
|
34
|
Power Series
|
|
12/1
|
35
|
Pointwise and
Uniform Convergence
|
|
12/3
|
36
|
Applications
of Uniform Convergence
|
32.3,
32.5 (e,k), 33.6, 33.9, 33.11, 33.13, . 34.9, 34.10, 35.3, 35.7, 35.10,
35.14, 35.15
|
12/8
|
37
|
Uniform
Convergence of Power Series
|
Homework 10 Solutions
|
12/10
|
|
Review
|
|
12/17
|
|
Final Exam
|
|