Professor: Brandon Seward
(pronouns: they/them or he/him)
Email: bseward@ucsd.edu
Lecture: MWF 11:00-11:50 in Warren Lecture Hall (WLH) room 2205
Lecture Recordings: On our
Canvas page under the Media Gallery tab
Office Hours: Monday 1:00 - 2:30 and Wednesday 2:30 - 4:00 in AP&M 5739
Teaching Assistant: Juno Seong
Email: jseong@ucsd.edu
A01 Discussion: Tues. 4:00am-4:50am in AP&M 5402
A02 Discussion: Tues. 5:00am-5:50am
in AP&M 5402
Office Hours: Thurs. 2:00-6:00 pm in Humanities and Social Sciences (HSS) 3071
Course Description: Second
course in a rigorous three-quarter sequence on real analysis. Topics
include: differentiation, integration, sequences and series of
functions, some special functions.
Textbook (Available on Canvas): Principles of Mathematical Analysis by Walter Rudin, 3rd edition
. We will cover Chapters 5 through 8.
Additional Study Materials: On Canvas
Homework: Homework
will be due most weeks on Fridays at 11:59 PM, except on weeks in
which we have a midterm it will be due on the following Monday at 11:59 PM. No late
homework
will be accepted, but your lowest homework score will be dropped when
computing your final grade. On each assignment, a few problems will be
graded for correctness, while the others will be graded simply for
completion. We will use
Gradescope
for turning in homework. When registering for gradescope, please
register using your "@ucsd.edu" email address and use Entry Code EJZEB2
.
Homework 1 (Due Friday April 12):
Chapter 5 problems 2, 4, 6, 8, 9, 17, 26
Homework 2 (Due Friday April 19):
Chapter 5 problems 11, 15, 22 and Chapter 6 problems 1, 2, 3, 4
Homework 3 (Due Monday April 29):
Chapter 6 problems 5, 6, 7, 8, 10
Homework 4 (Due Friday May 3):
Chapter 6 problems 9, 11, 12, 13(abd), 15, 17, 19
Homework 5 (Due Friday May 10):
TBA
Homework 6 (Due Friday May 17):
TBA
Homework 7 (Due Wednesday May 29):
TBA
Homework 8 (Due Friday May 31):
TBA
Homework 9 (Due Friday June 7):
TBA
Exams:
All exams will be in-person. If you miss a midterm no makeup exam will
be given. Instead your final exam will count towards 60% of your final
grade.
Grading: Your final grade will be the maximum of the following two weighted averages:
- 20% Homework, 20% First Midterm, 20% Second Midterm, 40% Final Exam.
- 20% Homework, 20% Best Midterm, 60% Final Exam
Special Accommodations:
Students requiring accommodations should provide an OSD letter of
certification and OSD accommodation recommendation as
soon as possible.
Approximate Course Schedule
Week
|
Monday
|
Wednesday
|
Friday
|
1
|
April 1
The derivative of a real function
|
April 3
The derivative of a real function
Mean value theorems
|
April 5
The continuity of derivatives
L'Hospital's rule
Derivatives of higher order
|
2
|
April 8
Taylor's theorem
Differentiation of vector-valued functions
|
April 10
Differentiation of vector-valued functions
Definition and existence of the integral
|
April 12 (HW 1 Due)
Definition and existence of the integral
|
3
|
April 15
Definition and existence of the integral
|
April 17
Definition and existence of the integral
Properties of the integral
|
April 19 (HW 2 Due)
Properties of the integral
|
4
|
April 22
Properties of the integral
Integration and differentiation
|
April 24
First Midterm
Practice Exam, Solutions
First Midterm Solutions
|
April 26
Integration of vector-valued functions
Rectifiable Curves
|
5
|
April 29 (HW 3 Due)
Discussion of the main problem
Uniform convergence
|
May 1
Uniform convergence and continuity
Uniform convergence and integration
|
May 3 (HW 4 Due)
Uniform convergence and differentiation
|
6
|
May 6
Equicontinuous families of functions
|
May 8
Equicontinuous families of functions
The Stone--Weierstrass theorem
|
May 10 (HW 5 Due)
The Stone--Weierstrass theorem
|
7
|
May 13
The Stone--Weierstrass theorem
|
May 15
The Stone--Weierstrass theorem
Power series
|
May 17 (HW 6 Due)
Power series
|
8
|
May 20
Power series
The exponential and logarithmic functions
|
May 22
Second Midterm
|
May 24
The exponential and logarithmic functions
The trigonometric functions
|
9
|
May 27
Memorial Day Holiday
|
May 29 (HW 7 Due)
The trigonometric functions
|
May 31 (HW 8 Due)
The algebraic completeness of the complex field
Fourier series
|
| 10 |
June 3
Fourier series
|
June 5
Fourier series
|
June 7 (HW 9 Due)
Fourier series
The Gamma functions
|
11
|
Friday June 14, 11:30 AM -- 2:30 PM
Final Exam
|