Introduction to Analysis II

311 INTRODUCTION TO ANALYSIS II (3+0) 3 credits

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 2006

Course Information

Instructor:

Eric Olson

email:

ejolson at unr.edu

Office:

MWF 12am Ansari Business Building AB 614 and by appointment.

Homepage:

http://fractal.math.unr.edu/~ejolson/311/

Texts:

Frank Dangello, Michael Syfried, Introductory Real Analysis, Houghton Mifflin Company, 2004.

Harold M. Edwards, Advanced Calculus: A Differential Forms Approach, Birkhauser, 1994.

Supplementary Text:

Robert C. Wrede, Murray Spiegel, Schaum's Outline of Advanced Calculus, Second Edition, McGraw-Hill.

Section:

001 Math 310 Introduction To Analysis I

MWF 10:00-10:50am AB 209

Grading

    6 Quizzes                      10 points each (drop 1)
    6 Homework Assignments         10 points each (drop 1)
    2 Exams                        50 points each
    1 Midterm                      100 points each
    1 Final Exam                   140 points
    -------------------------------------------------------
                                   440 points total

Calendar

#   Date     Chapter     Topic
------------------------------------------------------------------------
1   Jan 23  6.1-6.3      Review of Definitions
2   Jan 25    6.3        Property of the Riemann Integral
3   Jan 27    6.4        Continuous Functions
4   Jan 30    6.4        Monotone Functions
5   Feb 1     6.5        Fundamental Theorem of Calculus
6   Feb 3     6.5            Fundamental Theorem continued...
7   Feb 6     6.6        Improper Integrals
8   Feb 8                Exam I
9   Feb 10    7.1        Convergence and Divergence
10  Feb 13    7.2        Absolute and Conditional Convergence
11  Feb 15    7.2            Convergence continued...
12  Feb 17    7.3        Regrouping and Rearranging Series
13  Feb 20    7.3        Regrouping and Rearranging Series continued...
14  Feb 22    7.4        Multiplication of Series
15  Feb 24    7.4        Multiplication of Series continued...
16  Feb 27    8.1        Sequences and Series of Functions
17  Mar 1     8.2        Preservation Theorems
18  Mar 3     8.2        Preservation Theorems continued...
19  Mar 6     8.3        Series of Functions
20  Mar 8                Review
21  Mar 10               Midterm
22  Mar 13    8.3        Series of Functions
23  Mar 15    8.4        Weierstrass Approximation Theorem
24  Mar 17    8.4            Weierstrass continued...
                         Final date for dropping class no refund
    Mar 20               Holiday
26  Mar 27    1.1-1.3    Constant 1- and 2-forms and pullbacks
27  Mar 29    4.2        Constant k-forms and pullbacks
28  Mar 31    4.3        Exterior Powers and Jacobians
29  Apr 3     2.1-2.3    Non-constant forms and Integration
30  Apr 5     2.4        Integrals and Pullbacks 
31  Apr 7     3.1        The Fundamental Theorem of Calculus
32  Apr 10    9.4        Compactness
33  Apr 12    3.2        The Fundamental Theorem in Two Dimensions
34  Apr 14    3.3        The Fundamental Theorem in Three Dimensions
35  Apr 17               Exam II
36  Apr 19    8.6        The Poincare Lemma
37  Apr 21    6.3        Definition of a Manifold/Charts and Atlas
38  Apr 24    6.3        Independence of Parameterization
39  Apr 26    
40  Apr 28    
41  May 1     
42  May 3     
43  May 5                Review
44  May 8                Review

Final Exam

• Section 001 on Friday, May 12 at 9:45am-11:45am in AB205.

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