MATH S4062

Welcome to Math S4062 – more fun with epsilon!

In this course, we will delve deeper in the fascinating world of analysis by learning some further analytical tools, such as Fourier series, multivariable analysis, and measure theory. This course will be especially useful if you’re planning on going to math grad school. My hope is that you will finally learn to appreciate the importance and beauty of this powerful subject that mathematicians use in their real lives.

Syllabus

Math S4062 Syllabus

#	Chapter	Title
1	7	Sequences of Functions
2	7	Uniform Convergence
3	7	Equicontinuity
4	7	Fixed Points and ODE
5	7	Weierstrass Approximation
6	8	Power Series
7	8	Fourier Series
8	8	Convolution
9	8	Orthogonality
10	8	Fourier Transform
11	9	Multivariable Analysis
12	9	Derivatives
13	9	Directional Derivatives + Review
14		Midterm
15	9	Inverse Function Theorem
16	9	Implicit Function Theorem
17	9	Second-Order Derivatives
18	11	Lebesgue Measure
19	11	Measurable Functions
20	11	Lebesgue Integral (I)
21	11	Lebesgue Integral (II)
22	11	Dominated Convergence
23		Final Exam Review
24		Final Exam

Homework

Here is the schedule of homework, which is always due on at 11:59 pm. You will submit the homework on Canvas.

Note: The homework solutions are written by Peiyan Li, who has gladly volunteered to release his solutions. Beware of minor mistakes.

Homework	#	Date	Solutions
Homework 1	7	Friday, July 8	Solutions
Homework 2	7	Tuesday, July 12	Solutions
Homework 3	7	Friday, July 15	Solutions
Homework 4	8	Tuesday, July 19	Solutions
Homework 5	8	Friday, July 22	Solutions
Homework 6	9	Friday, July 29	Solutions
Homework 7	9	Wednesday, August 3	Solutions
Homework 8	11	Sunday, August 7	Solutions
Homework 9	11	Wednesday, August 10	Solutions