MATH 4581 - Classical Mathematical Methods in Engineering

3 Credit hours - Spring 2026 - CRN34628 (BG) and CRN33763 (BU)
(Dec 30, 2025 Version)

Lectures: Tuesday, Thursday in person in Skiles154.
Lectures run from 12:30 to 13:45. Handwritten lectures will be posted in Canvas. Lectures will be recorded, and recordings placed in Media Gallery. Students may also watch lectures remotely through Zoom. A link will be sent before classes.

Instructor Information

Doron Lubinsky, lubinsky@math.gatech.edu
Tuesday, Thursday 11:00-12:00 via Zoom or in person in Skiles 237A.

General Information

Description
The main repository for the course are the folders in "Files" in Canvas. The course provides an introduction to classical analytical methods for solving partial differential equations. The main tools will be separation of variables, Fourier series and the Laplace transform. The topics to be covered are:

(1) Fourier series and Fourier integrals

(2) The Sturm-Liouville Theorem

(3) The heat equation

(4) The wave equation

(5) Laplace and Poisson equations

(6) Laplace transform

(7) Heat flow using the Laplace transform.

Course Goals and Learning Outcomes

• Computing Fourier series and study their convergence.
• Using separation of variables on the heat and wave equations.
• Using polar and cylindrical coordinates for the Laplace and Poisson equations
• Applying the method of eigenfunction expansions
• Computing Laplace transforms and applying them to ordinary differential equations
• Applying the Laplace transforms to heat flow problems

Course Requirements & Grading

There will be regular Homework, 2 midterm tests, and a final exam. All students must take the final exam.

The items are weighted as follows:
Homework: 35%
Midterm tests: 40% (Each midterm counts 20%)
Final exam: 25%
No extra credit.

Description of Graded Components

Homework
There will be regular graded homework, throughout the course. Homeworks will be posted on Gradescope, and students must upload their solutions to Gradescope. Here are tentative deadlines for the Homeworks:
Homework 1: Monday 2 February at 11pm
Homework 2: Thursday 12 February at 11pm
Homework 3: Monday 2 March at 11pm
Homework 4: Monday 16 March at 11pm
Homework 5: Monday 13 April at 11pm

Midterm Tests
There will be 2 midterm tests, written during class.
TENTATIVE dates of tests:
Test 1: Tuesday 24 February
Test 2: Tuesday 31 March
It is emphasized that these test dates may be changed due to unforeseen circumstances.

Final Exam
The final exam will be comprehensive.
The final exam is on Thursday May 7 from 11:20am-2:10pm in the classroom.

Makeup Tests
These will only be given where there is a medical certificate provided, or approved university absence.

Grading Scale

You can be guaranteed at least the following grades if your percentage lies in the specified range:

There will also be a curve that might allow e.g. an A for a grade slightly lower than 90%. This is decided at the end of the course based on the distribution of final percentages in the class.

See http://registrar.gatech.edu/info/grading-system for more information about the grading system at Georgia Tech.

Course Materials

Course Text
Boundary Value Problems, 6^th edn., by David Powers, Academic Press, Elsevier, 2010.
Additional Materials/Resources

A final percent of 90+, 80+, 70+, 60+ guarantees a grade of respectively A, B, C, D respectively, though there will be a curve on the final percentage that could yield e.g. an A for a lower grade.
All grades will be posted on Canvas.

7. Honor Code
Please review the Georgia Tech Honor Code.

8. Piazza
The class link is https://piazza.com/gatech/spring2026/math4581bu/home