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	HW 2 Due
9/12	Fourth Hour: Differential Equations in Mathematica
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 - 8.7; Thomas 5.1 - 5.4	HW 3 Due
9/19	Brooks in Canada (No Class Meeting)
Week 5
9/22	Brooks in Canada (No Class Meeting)
9/24	Laplace Transforms, the Dirac Delta Function	Boas 8.8 - 8.9, 8.11; Thomas 8.1 - 8.2
9/26	Consider the Source: The Method of Green's Functions	Boas 8.12; Thomas 8.3 - 8.5
Week 6
9/29	Coupled Differential Equations, Matrix Operations	Boas 3.1 - 3.6; Thomas 9.1 - 9.3, 9.6 - 9.7
10/1	Linear Algebra	Boas 3.7 - 3.10; Thomas 9.4 - 9.5, 9.8	HW 4 Due
10/3	Fourth Hour: Pre-Exam Review Session
Week 7
10/6	Midterm Exam 1
10/8	Vector Spaces and Hilbert Space	Boas 3.14, 12.6
10/10	Fourth Hour: An Introduction to Python
Week 8
10/13	Fall Break (No Class Meeting)
10/15	Basis Transformations	Boas 3.10 - 3.11; Thomas 9.9	HW 5 Due
10/17	Eigenvalues, Eigenvectors, and Normal Modes	Boas 3.12; Thomas 9.10
Week 9
10/20	Div, Grad, Curl, and All That	Boas 6.1 - 6.7; Schey p. 1 - 9, p. 42 - 54, p. 82 - 91, p. 131 - 144
10/22	Line Integrals and Green's Theorem	Boas 6.8 - 6.9; Schey p. 63 - 75, p. 115 - 121	HW 6 Due
10/24	Fourth Hour: Differential Equations in Python
Week 10
10/27	The Divergence theorem and the Continuity Equation	Boas 6.10; Schey p. 11 - 41
10/29	Stokes's Theorem and Conservative Fields	Boas 6.11; Schey p. 91 - 104	HW 7 Due
10/31	Fourth Hour: Chaotic Systems in Python
Week 11
11/3	Fourier Series	Boas 7.1 - 7.6; Thomas 7.1 - 7.4
11/5	The Fourier Transform	Boas 7.7, 7.12; Thomas 7.5 - 7.7	HW 8 Due
11/7	Fourth Hour: Pre-Exam Review Session
Week 12
11/10	Midterm Exam 2
11/12	Partial Differential Equations, the Laplace Equation	Boas 13.1 - 13.2
11/14	Fourth Hour: Machine Learning I
Week 13
11/17	Waves and the Wave Equation	Boas 13.4
11/19	The Diffusion and Schrödinger Equations	Boas: 13.3	HW 9 Due
11/21	No Class Meeting
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	Bessel Functions: Laplace on a Cylinder	Boas 12.12 -12.20, 13.5; Schey 128 - 131
12/3	Spherical Harmonics: Laplace on a Sphere	Boas 13.7 - 13.8; Schey 124 - 127	HW 10 Due
12/5	Fourth Hour: Machine Learning II
Final Exam
TBA	Final Exam: TBA