Spring 2010 Course
Syllabus: Math
546
Course
Title: |
Advanced Calculus II |
Textbook: |
(H) J. Hubbard & B. Hubbard, Vector Calculus, Linear Algebra
and Differential Forms, 3rd Ed., Matrix, 2007 (T) W. Trench, Real Analysis (free download) |
Prerequisites: |
Math 545 or permission |
Course Outline |
||||
Date |
Lecture |
Sections |
Topic |
Assignment |
1/19 |
1 |
(T) 4.5 |
Power Series |
Selected Problems |
1/26 |
2 |
(H) 1.4-1.6; (T) 5.1-5.3 |
Geometry, Limits and
Continuity in Rn |
Selected Problems |
2/2 |
3 |
(H) 1.8, 1.9; (T) 5.3, 5.4
|
Derivatives of
Multivariable Functions |
Selected Problems |
2/9 |
4 |
(H) 2.9, (T) 6.3, 6.4 |
Inverse and Implicit
Functions, Review for Exam I |
Selected Problems |
2/16 |
5 |
(H) 2.9, (T) 6.3, 6.4 |
EXAM I, Inverse and Implicit Functions |
Selected Problems |
3/2 |
6 |
(H) 3.1-3.3; (T) 5.4 |
Manifolds, Tangents and |
Selected Problems |
3/9 |
7 |
(H) 3.4-3.6 |
Critical Points and Extrema, Review for Exam II |
Selected Problems |
3/16 |
8 |
--------- |
SPRING RECESS |
------------------------ |
3/23 |
9 |
(H) 3.7 |
EXAM II, Extrema |
Selected Problems |
3/30 |
10 |
(H) 3.8, 4.1; (T) 7.1 |
Curves and Surfaces,
Multiple Integrals |
Selected Problems |
4/6 |
11 |
(H) 4.2, 4.3-4.5, 4.10; (T) 7.2, 7.3 |
Multiple Integrals,
Iterated Integrals, Fubini’s Theorem and the Change
of Variables Formula |
Selected Problems |
4/13 |
12 |
(H) 6.1-6.5 |
Forms, Integration on
Manifolds and Integral Theorems of Vector Calculus |
Selected Problems |
4/20 |
13 |
(H) 6.6-6.9 |
Integral Theorems of
Vector Calculus and Their Applications |
Selected Problems |
4/27 |
15 |
(H) 6.10, 6.11 |
Generalized Stokes’ Theorem,
Review for Final Exam |
Study for Exam |
IMPORTANT DATES |
|
FIRST |
January 19, 2010 |
Exam I |
February 16, 2010 |
Exam II |
March 23, 2010 |
LAST |
March 29, 2010 |
LAST |
May 4, 2010 |
FINAL EXAM PERIOD |
May 6 – 12, 2010 |
Grading Policy
Assignment Weighting |
|
Tentative Grading Scale |
||
Homework |
15 % |
|
A |
90 -- 100 |
|
|
|
B+ |
85 -- 89 |
Exam I |
25% |
|
B |
75 -- 84 |
Exam II |
25 % |
|
C+ |
70 – 74 |
|
|
|
C |
60 -- 69 |
|
|
|
D |
50 -- 59 |
Final Exam |
35 % |
|
F |
0 -- 49 |
Course Policies (optional)
Important
Departmental and University Policies
Prepared by Prof. Denis Blackmore,
January 12, 2010