Mathematical Methods in Physics

Phys 314, Fall 2025

Course Web Page

Brooks Thomas

Hugel 020
Physics Department
Lafayette College
730 High St.
Easton, PA 18042

Phone: (610) 330-5207
Email: thomasbd@lafayette.edu

Contact Info

Physics at Lafayette

Other Resources

• My Personal Home Page
• Lafayette Physics Department
• Physics Courses

• List of NSF REU Sites
• APS Resources for Students
• Society of Physics Students (SPS)
• CU*iP
• SACNAS
• National Society of Black Physicists

Course Materials and Other Useful Links

• Syllabus
• Resources and Demos Page
• Course Moodle

Textbooks

• Mary L. Boas, Mathematical Methods in the Physical Sciences, 3rd Ed. (Wiley, 2006).
• H. M. Schey, Div, Grad, Curl, and All That, 4th Ed. (W. W. Norton & Co., 2005).
• Brooks Thomas, Slightly Disturbed: Oscillations, Waves, and the Mathematics Behind Them (lecture notes).

Instructor Drop-In Hours

My instructor drop-in hours this semester will be held in Hugel 125. (These are sometimes referred to as "office hours," but in this case that's a misnomer in this case because Hugel 125 is not my office.) These drop-in hours are listed below:


• Mon., 3:00 - 4:00 PM
• Wed., 1:30 - 3:30 PM
• Fri., 1:00 - 2:00 PM

The default assumption is that my drop-in hours will take place in person. However, if the need arises for you to attend my drop-in hours virtually at any point during the semester (e.g., because of a winter-weather emergency or an illness), please email me in advance to schedule a virtual drop-in-hours meeting.

Course Schedule

Note: readings marked "Boas" are from Mathematical Methods in the Physical Sciences by Mary L. Boas, readings marked "Schey" are from "Div, Grad, Curl, and All That" by H. M. Schey, and readings marked "Thomas" are supplementary readings from my own lecture notes.



Date	Topic	Reading	Homework
Week 1
8/25	Differential Equations: Physics with Feedback
8/27	Taylor Series	Boas 1.1 - 1.3, 1.12 - 1.13, 1.15; Thomas 2.1 - 2.3, 2.6 - 2.7
8/29	Fourth Hour: Basic Mathematica Operations
Week 2
9/1	Working with Series, Tests of Convergence	Boas 1.4 - 1.11, 1.14; Thomas 2.4 - 2.5
9/3	Complex Numbers	Boas 2.1 - 2.16; Thomas 3.1 - 3.5	HW 1 Due
9/5	No Class Meeting
Week 3
9/8	Special Functions and Their Series Expansions	Boas 11.1 - 11.11
9/10	Ordinary Differential Equations, Separation of Variables	Boas 8.1 - 8.2; Thomas 4.1 - 4.2
9/12	Fourth Hour: Differential Equations in Mathematica		HW 2 Due
Week 4
9/15	First-Order Linear Differential Equations	Boas 8.3 - 8.4; Thomas 4.3 - 4.4
9/17	Higher-Order Linear Differential Equations	Boas 8.5; Thomas 5.1 - 5.3
9/19	Brooks in Canada (No Class Meeting)		HW 3 Due
Week 5
9/22	Brooks in Canada (No Class Meeting)
9/24	The Method of Undetermined Coefficients	Boas 8.6 - 8.7; Thomas 5.4
9/26	Laplace Transforms	Boas 8.8 - 8.9	HW 4 Due
Week 6
9/29	Green's Functions, Part I: Delta Functions and Impulses	Boas 8.11; Thomas 8.1 - 8.3
10/1	Green's Functions, Part II: A Symphony of Spikes	Boas 8.12; Thomas 8.4 - 8.5
10/3	Fourth Hour: Pre-Exam Review Session		HW 5 Due
Week 7
10/6	Midterm Exam 1
10/8	Coupled Differential Equations, Matrix Operations	Boas 3.1 - 3.6; Thomas 9.1 - 9.3, 9.6 - 9.7
10/10	Fourth Hour: An Introduction to Python
Week 8
10/13	Fall Break (No Class Meeting)
10/15	Brooks in Brazil (No Class Meeting)
10/17	Brooks in Brazil (No Class Meeting)
Week 9
10/20	Vector Spaces and Hilbert Space	Boas 3.14, 12.6
10/22	Linear Algebra	Boas 3.7 - 3.10; Thomas 9.4 - 9.5, 9.8
10/24	Practice with Green's Functions		HW 6 Due
Week 10
10/27	Basis Transformations	Boas 3.10 - 3.11; Thomas 9.9
10/29	More Things, More Springs!	Thomas 9.10
10/31	Brooks in Colorado Springs (No Class Meeting)
Week 11
11/3	From Oscillations to Waves	Thomas 9.11
11/5	Fourier Series	Boas 7.1 - 7.6; Thomas 7.1 - 7.3
11/7	Evaluating Fourier Coefficients	Boas 7.7, 7.9; Thomas 7.4	HW 7 Due
Week 12
11/10	Campus-Wide Power Outage (No Class Meeting)
11/12	Midterm Exam 2
11/14	Fourth Hour: Differential Equations in Python
Week 13
11/17	The Fourier Transform	Boas 7.12; Thomas 7.5 - 7.7
11/19	Div, Grad, Curl, and All That	Boas 6.1 - 6.7; Schey p. 1 - 9, p. 42 - 54, p. 82 - 91, p. 131 - 144
11/21	Fourth Hour: Chaotic Systems in Python		HW 8 Due
Week 14
11/24	No Class Meeting
11/26	Thanksgiving Break (No Class Meeting)
11/28	Thanksgiving Break (No Class Meeting)
Week 15
12/1	Line Integrals and Green's Theorem	Boas 6.8 - 6.9; Schey p. 63 - 75, p. 115 - 121
12/3	Stokes's Theorem and Conservative Fields	Boas 6.11; Schey p. 91 - 104
12/5	Fourth Hour: Machine Learning		HW 9 Due
Final Exam
12/10	Final Exam: 4:00 - 7:00 PM in Hugel 017