Analysis 2 - Spring 2003


Isaac Newton
December 25, 1642 - March 21, 1727
(old calender);
January 4, 1643 - March 31, 1727
(new calender)

Augustin-Louis Cauchy
August 21, 1789 - May 23, 1857

Karl Weierstrass
October 31, 1815 - February 19, 1897

Georg Friedrich Bernhard Riemann
September 17, 1826 - July 20, 1866
Images from Keith Lynn's "Pictures of Mathematicians" webpage and the The MacTutor History of Mathematics archive.

COURSE: MATH 4227/5227 Call # 14650/14655

TIME AND PLACE: 10:05-11:20 MW in Gilbreath 205

INSTRUCTOR: Dr. Robert Gardner OFFICE HOURS: TBA

OFFICE: Room 308G of Gilbreath Hall

PHONE: 439-6977 (308G Gilbreath), Math Department Office 439-4349

E-MAIL: gardnerr@etsu.edu
WEBPAGE: www.etsu.edu/math/gardner/gardner.htm (see my webpage for a copy of this course syllabus and updates for the course).

COURSE WEBPAGE: http://www.etsu.edu/math/gardner/4217/silspr03.htm

TEXT: An Introduction to Analysis, 2nd edition, by J. R. Kirkwood, Published by PWS Publishing Company and Waveland Press, Inc. 1995.

GRADING: Homework will be assigned and collected regularly. This will be the basis of your grade. Grades will be assigned based on a 10 point scale with ``plus'' and "minus" grades being assigned as appropriate.

NOTE. This term, we will study integration, and sequences and series of functions. We will prove the most difficult result in the book: the Riemann-Lebesgue Theorem. This theorem gives necessary and sufficient conditions for a function to be Riemann integrable. The topic of sequences of functions and their interaction with integration is one of the main topics of real analysis. Our main result along these lines is Corollary 8-10(b). This result is a real foreshadowing of what you would see in a graduate level real analysis course.

OUTLINE: We will cover the following chapters and topics:

If time permits, we will motivate the topics of Chapter 9 with applications. In particular, we will briefly explore partial differential equations and boundary conditions.

In commemoration of our proof of the so called Riemann-Lebesgue Theorem ("A bounded function f is Riemann integrable on ,a, b] if and only if it's set of discontinuities has measure zero") during the week of February 17, 2003, we present a photo of Henri Lebesgue from the The MacTutor History of Mathematics archive:


Henri Lebesgue, 1875-1941

HOMEWORK

ASSIGNMENT NUMBER
PROBLEMS
DUE DATE
POINTS
HW 1
5.1.1a, 5.1.1b, 5.1.2a
January 22
3+3+3=9
HW 2
5.1.5b, 5.1.5d, 5.1.5e, 5.1.8a, 5.1.8b, 5.1.8c, 5.1.9, 5.1.13
January 22
3+3+3+3+3+3+4+3=25
HW 3
5.2.2a, 5.2.2b, 5.2.4a(i), 5.2.7a, 5.2.7b, 5.2.13
February 3
3+3+3+3+2+3=17
HW 4
6.1.3, 6.1.4a, 6.1.4b, 6.1.6, Bonus 1
February 10
3+3+3+3+(3)=12+(3)
HW 5
6.1.10, 6.1.14, 6.1.15a, 6.1.5b
February 19
3+3+3+3=12
HW 6
6.2.1a, 6.2.1b, 6.2.1c, 6.2.2a, 6.2.2b, 6.2.4a, 6.2.4b, Bonus 2
March 5
3+3+3+3+4+3+3+(4)=22+(4)
HW 7
6.2.16, 6.2.17, 6.2.19a, 6.2.19b, 6.2.19c, Bonus 3
March 12
3+3+3+3+3+(4)=15+(3+3+1+3+3)
HW 8
6.3.1, 6.3.2a
March 24
4+3=7
HW 9
7.1.1c, 7.1.5, 7.1.13a, Bonus 4
March 28
3+3+3+(6)=9
HW 10
7.2.2a, 7.2.6a, 7.2.6c, 7.2.7, Bonus 5, Bonus 6
April 4
3+3+3+3+(4+3)=12
HW 11
8.1.2, 8.1.4, 8.1.6a, 8.1.6b, 8.1.15a, Bonus 7
April 14
3+3+2+3+3+(4)=14
HW 12
8.2.1d, 8.2.1e, 8.2.6, 8.2.7
April 21
3+3+3+3=12
HW 13
8.2.11, 8.2.12, Bonus 8
April 23
3+4+(9)=7+(9)
HW 14
8.3.2, 8.3.8, 8.3.10, Bonus 9
April 29, noon
3+3+4+(4)=10+(4)
TOTAL
-
-
183+(50)
NOTICE: The number of POINTS in the fourth column are for the graduate homework assignments, with bonus problems in parentheses.

BONUS PROBLEMS

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