Math 4121 Home Page, Spring 2018

SYLLABUS AND COURSE INFORMATION

Instructor: Steven G. Krantz

Course Title: The Lebesgue Integral

Textbook: Elementary Introduction to the Lebesgue Integral by Steven G. Krantz

In fact the book is right here---yours for free download:


Elementary Introduction to the Lebesgue Integral by Steven G. Krantz


Office: 103, Cupples I

Office Hour: MWF 11:00am-noon.

Phone: (314) 935-6712

e-mail: sk@math.wustl.edu

Personal Web Address: http://www.math.wustl.edu/~sk

Class Web Page: The class Web page is:

http://www.math.wustl.edu/~sk/math4121.html

You can also just go to my personal Web page (above) and click on the button

for Math 4121.

Dept. Office: 100, Cupples I

Dept. Phone: (314) 935-6760

 

Course Description:

The purpose of this course is to learn about the theory of Lebesgue measure and the Lebesgue integral. This integration theory is quite different from the Riemann integral which you already know. The course will be challenging but also quite interesting.


Prerequisites for the Course:

You should be familiar with the basic topology of the real line (open and closed sets), you should be familiar with Cantor's theory of cardinality (countable and uncountable sets), and you should be comfortable with proofs. Everything in this course will be proved.


Work Required in the Course:

There will be regular homework assignments. These will be handgraded in the usual manner. There will also be a midterm exam and a final exam.


The relative weights of the course components are as follows:

Homework: 25%

Midterm: 35%

Final: 40%


First Homework Assignment:

Due Wednesday, January 31 in class.


pages 17-19: #1, 3, 5, 6, 8, 9, 11

Solutions to Math 4121 Homework 1




Second Homework Assignment:

Due Monday, February 12 in class.


pages 25-26: #1, 2, 4, 5, 6, 8, 9, 11

Solutions to Math 4121 Homework 2




Third Homework Assignment:

Due Monday, February 26 in class.


pages 30-31: #1, 2, 4, 5, 7, 8, 10, 11, 12

Solutions to Math 4121 Homework 3





Fourth Homework Assignment:

Due Monday, March 19 in class.


pages 40-42: #1, 2, 3, 5, 7, 8, 9, 10, 12


Solutions to Math 4121 Homework 4





Math 4121 Midterm





Solutions to Math 4121 Midterm





Fifth Homework Assignment:

Due Monday, April 16 in class.


pages 52-53 (Chapter 5): #1, 3, 6, 9, 13

pages 59-60 (Chapter 6): #2, 6, 9

page 68 (Chapter 7): #1, 4, 6, 8

Solutions to Homework 5





Sixth and Last Homework Assignment:

Due Friday, April 27 in class.


pages 79-80, Chapter 8: #2, 3, 6, 7

pages 92-93, Chapter 9: #1, 3, 6, 10

pages 99, Chapter 10: #2, 5, 7

Solutions to Homework 6




Final Exam





Solutions to Final Exam