Information

Instructor: Yimin Zhong (yimin.zhong@auburn.edu)

Office: Parker 242

Office Hours: TTh 10:45am - 12:15pm

Class Schedule: TTh 9:30am - 10:45am

Classroom Location: Parker 250

Course Website: on Canvas

Important Dates:
- 01/28/26 -- Last day to drop from the course with no grade assignment.
- 04/17/26 -- Last day to withdraw from course with no grade penalty. "W" assigned.

Textbook

⊕ Principles of Applied Mathematics by James Keener, 2018

⊕ Applied Mathematics by David Logan, 3rd (2006) or 4th edition, 2013

Reference Textbooks

⊕ Linear Integral Equations by Rainer Kress, 3rd edition, 2014

⊕ Ordinary Differential Equations and Dynamical Systems by Gerald Teschl, 2012

⊕ Functional Analysis: Introduction to Further Topics in Analysis by Elias Stein, Rami Shakarchi, 2011

⊕ Introduction to the Calculus of Variations by Bernard Dacorogna, 2025

⊕ Principles of Partial Differential Equations by Alexander Komech, Andrew Komech, 2009 (for the distribution part and Green's function)

Course Prerequisites

Solid knowledge in vector calculus, linear algebra, and ordinary differential equations.

Course Description

This course will cover vector spaces, function spaces, dynamical systems, asymptotic approximation, perturbation theory, distributions, differential operators, compact operators, complex analysis, Fourier transforms, calculus of variations, and more.

Topics to be covered

Distribution and Green's function, Sobolev space

Variational Calculus, some convex analysis

Some physics

Homework

○ Homework will be posted on Canvas after every topic.

○ You have 2 weeks to complete each set.

Exams

The course MATH 7010 has one in-class midterm and a final exam. The final will be comprehensive (testing material from the beginning). The dates are: 02/19 (Midterm), and the final exam date (TBA).

Late Homework

Late homework is officially accommodated in the following three circumstances:

○ Illness or other extraordinary personal circumstances.

○ Religious observance

○ Varsity athletic participation

Otherwise, late submission will NOT be accepted.

Grading

○ Regular Homework (40%);

○ In-class Midterm (20%);

○ The Final Exam (40%);

○ Exams are closed-book and closed-note. Calculators without graphical or programming functions are allowed.

○ Final score scale: 90 -- 100 (A) || 80 -- 89 (B) || 70 -- 79 (C) || 60 -- 69 (D) || 0 -- 59 (F)

Policy on Generative Models

In principle, you can use the generative models to assist you in completing the homework/programming problems, but you cannot use them in any of the exams.

ADA Policy

Students who need accommodations are asked to submit their approved accommodations through AU Access electronically and to make an individual appointment during the first week of classes or as soon as possible if accommodations are needed immediately.

Academic Honesty

All portions of the Auburn University Student Academic Honesty Code (Title XII) found in the [Student Policy eHandbook](https://www.auburn.edu/student_info/student_policies/) will apply to this class. All academic honesty violations or alleged violations of the SGA Code of Laws will be reported to the Office of the Provost, which will then refer the case to the Academic Honesty Committee.