Math 546-S10

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) 1.4-1.6; (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 Taylor’s Theorem in Rⁿ	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

Grading Policy

Course Policies (optional)

Important Departmental and University Policies

Prepared by Prof. Denis Blackmore, January 12, 2010