index

Lecture Instructor	Dr. Le Chen	lzc0090@auburn.edu
Class Time and Room	TR, 09:30 AM -- 10:45 PM	Parker Hall 354 (2022 Fall), 228 (2023 Spring)
Office hours	TR, 15:00 PM -- 15:50 PM	Parker Hall 203

When you send us emails, please do include the keyword Math 7000 or Math 7010 in the subject field of your email to ensure a timely response.
In case you want to make an appointment with the instructor via Zoom, here is the link:
https://auburn.zoom.us/j/8141875411

Course description

Applied mathematics consists of lots of analysis related topics; see the table of content of the textbook.

This is a sequence of two-semester courses -- Math 7000 and Math 7010. Through this sequence of two courses, we will cover the most parts of the textbook.

Textbook

"Principles of Applied Mathematics: Transformation and Approximation", Revised Edition, 2000, ISBN:0-7382-0129-4, by James P. Keener

Over the two semesters, we may cover the first eight chapters of the book:

Part I (Math 7000)
- Chapter 1: Finite dimensional vector spaces
- Chapter 2: Function spaces
- Chapter 3: Integral equations
- Chapter 4: Differential operators
Part II (Math 7010)
- Chapter 5: Calculus of variations
- Chapter 6: Complex variable theory
- Chapter 7: Transform and spectral theory
- Chapter 10: Asymptotic expansions

Department approval

This is a demanding course and it requires a great deal of work from your side. In order to successfully master the material and complete the course, you are expected to

Read the textbook and attend lectures.
Take the advantage of the office hours, which give you additional chance to interact with the instructor.
We will use Mathematica throughout the semester. Make
sure to have the access to it (consult COSAM IT) and learn how to use it.
Read solutions and any feedback you receive for each problem set.
Complete and submit weekly homework through Gradescope.
Complete both midterm test and the final exam.
Use appropriate etiquette and treat other students with respect in all discussions.
Do not hesitate to ask for help whenever needed.

Note: The syllabus was created in April 2022, and it is subject to changes during the semester.

There will be about one assignment for each chapter.
No late homework will be accepted.
You need to write full details of the problems and upload your solutions to gradescope.
- Go to Canvas --> Find this course --> Click Gradescope on the left panel.
- See below for more instructions on gradescope.
We will randomly select a few problems to grade and the rest will be checked only for completion.
You may need to use Mathematica, or Matlab/Python//Sage, to assist you for the homework.

There will be one midterm test during the class session:

Final exam will be cumulative.

	Part I (Math 7000)		Part II (Math 7010)
	Date/Time	Coverage	Date/Time	Coverage
Midterm Test	Oct. 4th, Tuesday	Chapters 1 - 3	Mar. 2nd, Thursday	TBA
Final Exam	Dec. 5th, Monday	Comprehensive	TBA	Comprehensive

Please note down the above dates. No late exam/test will be given.
Makeup exams will only be allowed in extreme circumstances. Exams cannot be made up without a
university-approved excuse. Any excuse must be submitted by the date of exam to be considered.
Please refer to the Tiger Cub for the list of acceptable reasons for being absent from an exam or
a test. Makeup exam/test has to be scheduled and made up in a timely manner.
More details will come during the semester.

Notify the instructor if you are not able to participate in a lecture due to illness or some other emergency.
Attendance will not be directly counted into your final score.
But sufficient attendance will make your eligible for grade curving at the end of semester.

The final score will be determined as follows:

Based on the final score (plus potential bonus points), the final letter grade will be
determined as follows:

Grade (+)		Grade		Grade (-)
		A	92%-100%	A-	90%-91.9%
B+	87%-89.9%	B	82%-86.9%	B-	80%-81.9%
C+	77%-87.9%	C	72%-76.9%	C-	70%-71.9%
D+	67%-67.9%	D	67%-67.9%	D-	60%-61.9%
		F	0%-59.9%

Below is the tentative schedule that may change during the semester:

	Part I		Part II
Week	Tuesday -- Thursday	Coverage	Tuesday -- Thursday	Coverage
1	08/16 -- 08/18	1.1 - 1.2	(01/10) -- 01/12	6.1
2	08/23 -- 08/25	1.3 - 1.4	01/17 -- 01/19	6.2
3	08/30 -- 09/01	1.5 - 1.6	01/24 -- 01/26	6.3
4	09/06 -- 09/08	2.1 - 2.2	01/31 -- 02/02	6.4 - 6.5
5	09/13 -- 09/15	2.2, 3.1	02/07 -- 02/09	7.1 - 7.2
6	09/20 -- 09/22	3.2	02/14 -- 02/16	7.3 - 7.4
7	09/27 -- 09/29	3.2 - 3.3	02/21 -- 02/24	7.5
8	10/04 -- (10/06)	Midterm Exam	02/28 -- 03/02	Midterm Exam
9	10/11 -- 10/13	3.4	03/14 -- 03/16	10.1 - 10.2
10	10/18 -- 10/20	3.5 - 3.6	03/21 -- 03/22	10.2 - 10.4
11	10/25 -- 10/27	4.1	03/28 -- 03/30	10.5
12	11/01 -- 11/03	4.1	04/04 -- 04/06	5.1
13	11/08 -- 11/10	4.2	04/11 -- 04/13	5.2
14	11/15 -- 11/17	4.2	04/18 -- 04/20	5.3 - 5.4
15	11/29 -- 12/01	4.3	04/25 -- 04/27	Reviewing

Chapter/Section	Slides	Slides	Lecture Notes
Chapter 1: Finite dimensional vector spaces	presentation	compact
1.1. Linear vector spaces	pres.	comp.
1.2. Spectral theory for matrices	pres.	comp.
1.3. Geometrical significance of eigenvalues	pres.	comp.	Notes
1.4. Fredholm alternative theorem	pres.	comp.
1.5. Least squares solutions -- Pseudo inverses	pres.	comp.	Notes
1.6. Applications of eigenvalues and eigenfunctions	pres.	comp.	Notes
Chapter 2: Function spaces	presentation	compact
2.1. Complete vector spaces	pres.	comp.	Notes
2.2. Approximation in Hilbert spaces	pres.	comp.	Notes, Notes
Chapter 3: Integral equations	presentation	compact
3.1. Introduction	pres.	comp.	Notes
3.2. Bounded linear operators in Hilbert space	pres.	comp.	Notes
3.3. Compact operators	pres.	comp.	Notes
3.4. Spectral theory for compact operators	pres.	comp.	Notes, Notes
3.5. Resolvent and pseudo-resolvent kernels	pres.	comp.	Notes, Notes
3.6. Approximate solutions	pres.	comp.	Notes
3.7. Singular integral equations	pres.	comp.	Notes
Chapter 4: Differential operators	presentation	compact
4.1. Distributions and the delta function	pres.	comp.	Notes Notes Notes Notes
4.2. Green function	pres.	comp.	Notes Notes
4.3. Differential operators	pres.	comp.	Notes
4.4. Least squares solutions	pres.	comp.
4.5. Eigenfunction expansions	pres.	comp.
Chapter 5: Calculus of variations	presentation	compact
5.1. The Euler-Lagrange equations	pres.	comp.
5.2. Hamilton principle	pres.	comp.
5.3. Approximation methods	pres.	comp.
5.4. Eigenvalue problems	pres.	comp.
Chapter 6: Complex variable theory	presentation	compact
6.1. Complex valued functions	pres.	comp.	Notes
6.2. The calculus of complex functions	pres.	comp.	6-2-1 and 6-2-2 6-2-3 6-2-4
6.3. Fluid flow and conformal mappings	pres.	comp.	6-3-1 6-3-2 6-3-2
6.4. Contour integration	pres.	comp.	6-4 6-4 6-4
6.5. Special functions	pres.	comp.	6-5-1 6-5-2
Chapter 7: Transform and spectral theory	presentation	compact
7.1. Spectrum of an operator	pres.	comp.
7.2. Fourier transforms	pres.	comp.	7-2-1 7-2-1, 7-2-1, 7-2-1
7.3. Related integral transforms	pres.	comp.	7-3-1
7.4. Z transforms	pres.	comp.
7.5. Scattering theory	pres.	comp.
Chapter 8: Partial differential equations	presentation	compact
8.1. The Poisson equation	pres.	comp.
8.2. The wave equation	pres.	comp.
8.3. The heat equation	pres.	comp.
8.4. Differential-difference equations	pres.	comp.
Chapter 9: Inverse scattering transform	presentation	compact
9.1. Inverse scattering	pres.	comp.
9.2. Isospectral flows	pres.	comp.
9.3. Korteweg-deVries equation	pres.	comp.
9.4. The Toda lattice	pres.	comp.
Chapter 10: Asymptotic expansions	presentation	compact
10.1. Definitions and properties	pres.	comp.	10-1
10.2. Integration by parts	pres.	comp.	10-2
10.3. Laplace method	pres.	comp.	10-3 10-3
10.4. Method of steepest descents	pres.	comp.	10-4 Some codes for plotting the complex functions
10.5. Method of stationary phase	pres.	comp.	10-5

We will use gradescope to handle submissions of homework, which allows
us to provide fast and accurate feedback on your work.
As soon as grades are posted, you will be notified immediately so that you can log in and see your
grades and feedback.
If you have any questions regarding Gradescope, please send your message to
- help@gradescope.com
Printer+scanner or tablet
- The easiest way to submit the homework/tests/exams is the following steps:
  1. print the given template;
  2. complete the problem sets;
  3. scan the resulting paper (make sure it is legible);
  4. upload the scanned file to gradescope.
- Alternatively, if you have a tablet that you can write on it, you may simply write on the
  template pdf file and upload the resulting file.
- Make sure that you make the correct association of your solutions to the problems.
- Double check your scan quality and make sure your solutions are legible.
The following short video (1 minutes 40 seconds) shows the basic usage of gradescope, which should
explain everything you need to be able to do.

More instruction will be available towards the Fall 2022.

Students should familiarize themselves with Auburn honor code here
- https://www.auburn.edu/academic/provost/academic-honesty/.
Students are encouraged to share ideas and solutions on problem sets and labs, but must
express those ideas in their own words in their submitted work.
Students are not authorized to view or use the work of another student during exams.

Your success in this class is important to me. We will all need accommodations because we all learn differently. If there are aspects of this course that prevent you from learning or exclude you, please let me know as soon as possible. Together we will develop strategies to meet both your needs and the requirements of the course.

I encourage you to visit the Office of Accessibility to determine how you could improve your learning as well. You can register and make a request for services from the Office of Accessibility. In this case, please do inform me of such requests. See the following link for more information:

https://accessibility.auburn.edu/

According to Auburn University policies: http://auburn.edu/administration/aaeeo/H&D.php


Auburn University is committed to providing a working and academic environment
free from prohibited discrimination and harassment and to fostering a nurturing
and vibrant community founded upon the fundamental dignity and worth of all its
members. Auburn University prohibits harassment of its students and employees
based on protected classes and works to eliminate prohibited behavior from its
academics and employment through corrective measures and education.

The Office of AA/EEO oversees compliance with the Policy Prohibiting Harassment
of Students, the Policy Prohibiting Harassment of Employees, and the Policy on
Sexual and Gender-Based Harassment and Other Forms of Interpersonal Violence.

Protected classes are race, color, sex (which includes sexual orientation,
gender identity, and gender expression), religion, national origin, age,
disability, protected veteran status, or genetic information.

Auburn University also prohibits retaliation against any individual for opposing
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policies.

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Math 7000/7010: Applied Mathematics I/II

2022 Academic Year, Auburn University

Contacts

Course description

Textbook

Coverage

Prerequisite

Students obligations and tips

Homework

Test and exam

Attendance

Assessment

Tentative schedule

Slides

Gradescope

Miscs

Honor code

Accessibility

Harassment and Discrimination

Acknowledgement