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PHYS 228 A: Elementary Mathematical Physics

Summer Term: 
Meeting Time: 
MTThF 12:00pm - 1:00pm
PAA A118
Pavel Bolokhov

Syllabus Description:

Welcome to Physics 228 — the second course on Mathematical Physics. The course will be moving quite fast and it is important that you are organized and stay on top of the material. While challenging and demanding, hope this course will be an exciting, entertaining and illuminating experience for you!


Focus of Physics 228

This course provides a deeper look into the theory of electricity and magnetism. We shall study:

  • ordinary and partial differential equations
  • complex analyticity
  • Laplace transforms
  • orthogonal polynomials and special functions
  • spherical harmonics


Learning Outcomes

Upon successful completion of this course you will be familiar with:

  • complex analysis and residue integrals
  • analysis of differential equations by variety of methods
  • Dirac delta function, Green functions
  • solving partial differential equations via separation of variables
  • using Mathematica to target basic analytical needs


Required Course Materials


M.Boas, Mathematical Methods in the Physical Sciences, 3rd Ed., Wiley


Administrative Information

Instructor: Pavel A. Bolokhov Class meets: Mon Wed Thu Fri 12:00–1:00pm
Office: PAB 424 PAA 118
Email: Office hours: Tue 2:30–5:00pm
Teaching assistant: Joseph Merritt TA office: PAB 235
TA email: TA office hours:
Teaching assistant: Tanner Rase TA office: PAB 229
TA email: TA office hours:
Teaching assistant: Huangyu Xiao TA office: PAB 223
TA email: TA office hours:

Help: if you have a physics question and cannot attend office hours, email me or drop by to set an appointment. If you have a personal question, feel free to email me



Students are responsible for all material covered in lectures. Please ask questions in class (highly encouraged), or drop by for office hours, or email your question (that might be more difficult to do, so use that as the last resort in special circumstances). Do every attempt to ask a question in person

Read the necessary chapter contents before the corresponding lecture. This will make attending a lecture a more complete experience and make it easier to follow the class material

As an additional resource, please take a look at the lecture notes of Professor Steve Ellis. You may find them useful for homework or for clarification of class material

Lecture notes:



  • Homework will be assigned each week
  • Assignments will be collected on paper
  • Lowest homework score will be dropped
  • If you earn 90% of the total possible points at the end of the quarter, you will get a full credit
  • Experience shows that students who spend time on homework problems get better scores on exams
Homework 1 Homework 2 Homework 3 Homework 4 Homework 5



There will be one mid-term test and a final examination. For either tests you can bring one sheet of formulas. You will also want spare paper. Smartphones have to be left at the front of the class

The final examination grade will replace the mid-term grade if it turns out to be higher

The final examination is on the final day of the class

Sample problems and their solutions are available

Final test sample problems are available, and the formula sheet for the final test



Quiz 1 Quiz 2 Quiz 3 Quiz 4
Quiz 5 Quiz 6 Quiz 7 Quiz 8


Grading Policy

  • homework is 25%
  • the mid-term is 30%
  • the final exam is 30%
  • quizzes are 15%

In addition, an adjustment of up to ±5% may be applied to the final grade based on my subjective evaluation of such intangibles as attitude, preparedness, effort, class participation etc


Study Center

  • Students are encouraged to gather and work cooperatively in small groups in the Physics Study Center
  • The Physics Study Center is located in room AM018 of Physics and Astronomy Auditorium. To reach it, go down the stairs that circle behind the Foucault pendulum and proceed toward the end of the hall
  • Teaching assistants will be available for consultation during many portions of the day if your study group needs assistance, but staffing levels will not support much individual attention. The Study Center is staffed from approximately 9:30am to 4:30pm on weekdays. A schedule of who is staffing the physics study center can be found here: Study Center Hours

Access and Accomodations

If you have a temporary health condition or permanent disability that requires accommodations, you can have special access and accommodations. Your experience in this class is important to me. If you have already established accommodations with Disability Resources for Students (DRS), please communicate your approved accommodations to me at your earliest convenience so we can discuss your needs in this course

If you have not yet established services through DRS, but have a temporary health condition or permanent disability that requires accommodations (conditions include but not limited to; mental health, attention-related, learning, vision, hearing, physical or health impacts), you are welcome to contact DRS at 206-543-8924 or or disability.uw.eduDRS offers resources and coordinates reasonable accommodations for students with disabilities and/or temporary health conditions.  Reasonable accommodations are established through an interactive process between you, your instructor(s) and DRS.  It is the policy and practice of the University of Washington to create inclusive and accessible learning environments consistent with federal and state law


Academic Integrity

Academic integrity is essential in this course. You are encouraged to work together and discuss homework problems but the assignments you submit should be your own work. You may not give or receive help on quizzes or exams. Consider and take note that the following is considered cheating of one or the other form:

  • looking at or copying published or online solutions for homework problems
  • looking at or copying solutions that have previously been turned in for credit
  • copying another student's solutions to homework or examination problems
  • failing to acknowledge significant resources, other than the course textbook, that you used
  • failing to acknowledge significant collaboration with your classmates

In this course, you are considered to have been informed about the types of cheating and academic dishonesty, and warned that such dishonesty will not be tolerated


Time Table

Time table shows the important dates and an approximate distribution of the course material. The table is subject to changes when necessary

The schedule below shows the guidelines for reading prior to each lecture. This may shift as necessary to accommodate our rate

Date No. Topic Reading
Mon Jun 18 0 Introduction
Tue Jun 19 1 First Order Equations 8.1–8.3
Thu Jun 21 2 First and Second Order Equations 8.4–8.6
Mon Jun 25 3 First and Second Order Equations 8.4–8.6
Tue Jun 26 4 Analytic Functions 14.1–14.3
Thu Jun 28 5 Laurent Series, Residue Theorem 14.4–14.6
Mon Jul 2 6 Using the Residue Theorem 14.7
Tue Jul 3 7 Using the Residue Theorem 14.7
Thu Jul 5 8 More complicated residue integrals 14.7
Mon Jul 9 9 More complicated residue integrals 14.7
Tue Jul 10 10 Laplace Transform 8.8
Thu Jul 12 11 Inverse Laplace transform (Bromwich integral) 14.7
Mon Jul 16 12 Dirac delta function 8.11
Tue Jul 17 13 Using delta functions for ODE 8.11
Thu Jul 19 14 Green Functions 8.12
Mon Jul 23 15 Variational calculus 9.1–9.2
Tue Jul 24 16 Using variational calculus 9.3–9.4
Thu Jul 26 Midterm Examination 8, 14, 9
Mon Jul 30 17 Lagrangian Mechanics 9.5–9.6
Tue Jul 31 18 Legendre's equation 12.1–12.2
Thu Aug 2 19 Rodrigues' formula. Generating function 12.4–12.5
Mon Aug 6 20 Legendre Series 12.6–12.9
Tue Aug 7 21 Fuchs Theorem, Frobenius' method 12.21, 12.11
Thu Aug 9 22 Gamma and Beta functions 11.2–11.5
Mon Aug 13 23 Curvilinear coordinates 10.8
Tue Aug 14 24 Equations in spherical coordinates 13.7
Thu Aug 16 25 Spherical harmonics. Conformal maps 13.7, 14.9–14.10
Fri Aug 17 Final Examination


Catalog Description: 
Applications of mathematics in physics with emphasis on the mechanics of particles and continuous systems. Develops and applies computational methods, both analytic and numerical. Prerequisite: minimum 2.0 grade in PHYS 227. Offered: WS.
GE Requirements: 
Natural Sciences (NSc)
Section Type: 
Last updated: 
October 17, 2018 - 9:41pm