Spring 2010 Course
Syllabus: Math
546
Course
Title: 
Advanced Calculus II 
Textbook: 
(H) J. Hubbard & B. Hubbard, Vector Calculus, Linear Algebra
and Differential Forms, 3^{rd} 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) 1.41.6; (T) 5.15.3 
Geometry, Limits and Continuity in R^{n}^{} 
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) 3.13.3; (T) 5.4 
Manifolds, Tangents and 
Selected Problems 
3/9 
7 
(H) 3.43.6 
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, 4.34.5, 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) 6.16.5 
Forms, Integration on
Manifolds and Integral Theorems of Vector Calculus 
Selected Problems 
4/20 
13 
(H) 6.66.9 
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