311 INTRODUCTION TO ANALYSIS II (3+0) 3 credits
Instructor Course Section Time ------------------------------------------------------------------------ Eric Olson 001 Math 311 INTRO TO ANALYSIS II MWF 12:00-12:50pm PE101
Continuation of MATH 310. Emphasizes proving theorems about series, uniform convergence, functions of several variables: limits, continuity, differentiation, extrema, integration, implicit and inverse function theorems. Prereq(s): MATH 283; MATH 310. Coreq(s): MATH 330.
Spring 2008
The textbooks will be
Title: Advanced Calculus
Author: Gerald B. Folland
Publisher: Prentice-Hall, Inc., 2002
ISBN: 0130652652
Author: Frank Dangello, Michael Syfried,
Title: Introductory Real Analysis
Publisher: Houghton Mifflin Company.
ISBN: 0395959330
with an optional supplementary book
Author: Robert C. Wrede, Murray Spiegel,
Title: Schaum's Outline of Advanced Calculus, Second Edition,
Publisher: McGraw-Hill.
ISBN: 0071375678
6 Quizzes 10 points each (drop 1)
6 Homework Assignments 10 points each (drop 1)
1 Midterm 100 points each
1 Final Exam 150 points
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350 points total
# Date Chapter Topic
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1 Jan 23 6.1 Existence of the Riemann Integral
2 Jan 25 6.2 Riemann Sums
3 Jan 28 6.3 Property of the Riemann Integral
4 Jan 30 6.4 Continuous Functions
5 Feb 1 6.4 Monotone Functions
6 Feb 4 6.5 Fundamental Theorem of Calculus
7 Feb 6 6.5 Fundamental Theorem continued...
8 Feb 8 6.6 Improper Integrals
9 Feb 11 7.1 Convergence and Divergence
10 Feb 13 7.2 Absolute and Conditional Convergence
11 Feb 15 7.3 Regrouping and Rearranging Series
Feb 18 Holiday--President's Day
12 Feb 20 7.4 Multiplication of Series
13 Feb 22 8.1 Sequences and Series of Functions
14 Feb 25 8.2 Preservation Theorems
15 Feb 27 8.2 Preservation Theorems continued...
16 Feb 29 8.3 Series of Functions
17 Mar 3 8.3 Series of Functions continued...
18 Mar 5 Review
19 Mar 7 Midterm Exam
Switch books to Folland.
20 Mar 10 Partial derivatives and the Chain Rule
21 Mar 12 3.1 The Implicit Function Theorem
22 Mar 14 3.1 The Implicit Function Theorem continued...
23 Mar 17 3.2 Curves in the Plane
24 Mar 19 3.3 Surfaces and Curves in Space
25 Mar 21 3.4 Transformations of Coordinate Systems
Mar 2 Holiday--Spring Break
Mar 26 Review 4.1 Integration on the Line
Mar 28 over the Spring Break
26 Mar 31 4.2 Integration in Higher Dimensions
27 Apr 2 4.2 Integration in Higher Dimensions continued...
28 Apr 4 4.3 Multiple Integrals and Iterated Integrals
29 Apr 7 4.4 Change of Variables for Multiple Integrals
30 Apr 9 4.4 Change of Variables continued...
31 Apr 11 5.1 Arc Length and Line Integrals
32 Apr 14 5.2 Green's Theorem
33 Apr 16 5.2 Green's Theorem continued.
34 Apr 18 5.3 Surface Area and Surface Integrals
35 Apr 21 5.4 Vector Derivatives
36 Apr 23 5.5 The Divergence Theorem
37 Apr 25 5.5 The Divergence Theorem continued...
38 Apr 28 5.7 Stoke's Theorem
39 Apr 30 5.7 Stoke's Theorem continued...
40 May 2 5.8 Integrating Vector Derivatives
41 May 5 Review
42 May 7 Preparation Day
43 May 9 Final Exam at 12 noon.
Final exam will be held on on Friday, May 9 at 12:00-2:00pm in PE101.