Analysis 2 - Spring 2006


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

TIME AND PLACE: 9:45-11:05 TR in Gilbreath 314

INSTRUCTOR: Dr. Robert Gardner OFFICE HOURS: TBA

OFFICE: Room 308F of Gilbreath Hall

PHONE: 439-6979 (308F 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/silspr06.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.

HOMEWORK

ASSIGNMENT NUMBER
PROBLEMS
DUE DATE
POINTS
HW 1
5.1.1a, 5.1.2a, 5.1.10
Tuesday, January 31
3+3+3=9
HW 2
5.2.3, 5.2.7, 5.2.9
Tuesday, February 7
3+3+3=9
HW 3
6.1.3, 6.1.4, 6.1.6
Tuesday, February 14
3+3+3=9
HW 4
6.1.10, 6.1.12, 6.1.14
Tuesday, February 21
3+3+3=9
HW 5
6.2.1c, 6.1.4a, 6.2.4b, BONUS: 6.2.5
Thursday, March 16
3+3+3+(3)=9+(3)
HW 6
6.3.1, 6.3.2c, 6.3.3a, BONUS: 6.3.3b (find counterexample)
Thursday, March 28
3+3+3+(3)=9+(3)
HW 7
7.1.4, 7.1.8, 7.1.13a
Thursday, April 6
3+3+3=9
HW 8
7.2.6c, 7.2.7, Bonus 1, Bonus 2
Thursday, April 13
3+3+(3+3)=6+(6)
HW 9
8.1.2, 8.1.4, 8.1.15a, Bonus 8.1.11
Thursday, April 20
3+2+3+(14)=8+(14)
HW 10
8.2.1d, 8.2.2, 8.2.6
Thursday, April 27
3+3+3=9
HW 11
8.2.11, 8.3.2, 8.3.10, BONUS 8.2.15
Thursday, May 4
3+3+3=9
TOTAL
-
-
95+(26)
NOTICE: The number of POINTS in the fourth column are for the graduate homework assignments, with bonus problems in parentheses.

BONUS PROBLEMS

Solutions to the bonus problems in PDF are here.

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 14, 2006, we present photos of Bernard Reimann and Henri Lebesgue from the The MacTutor History of Mathematics archive:


Georg Friedrich Bernhard Riemann
September 17, 1826 - July 20, 1866

Henri Lebesgue
1875-1941

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