Physics 227, Autumn 2022


Marcel den Nijs

Office: PAB B429
Department of Physics
University of Washington
Seattle, WA 98195

10:30 am - 11:20 am
Mo, Tu, We, Th, Fr
PAA A118


This is the first quarter of the Physics elementary mathematical physics course sequence.

This course covers topics from chapter 1-7 of "Mathematical Methods in the Physical Sciences" by Mary Boas, augmented with additional Physics oriented applications. This includes infinite series and power series, complex numbers and complex functions, linear algebra and eigenvalue problems, partial differentials and multiple integrals, vector analysis and line integrals, and finally Fourier series and Fourier transforms. In other words, the course stacks-up a lot of topics, and this tower could easily collapse into you unless you shield yourself by not falling behind.

One purpose of this course is to present basic mathematics from a more applied and physics point of view compared to the Mathematics Department offered courses you might have taken already or will take soon. Another purpose is to become sufficiently fluent in using these mathematical tools before taking the next level physics courses such that by then you can better focus on physics concepts, e.g., in quantum mechanics, electro magnetism, and statistical physics.

The background and preparation of the students taking this course is typically quite varied, depending heavily on which Math courses they took already as well as their high school experience. Students seated near you might seem to have a hard time or already to know it all. That more likely reflects preparation instead of ability. You might want to volunteer to help other students or ask them questions yourself. Explaining material to others is one of the best methods to deepen your own understanding.

This course meets 4 times each week in lecture style mode, Mo-Tu-We-Fr. It also meets on Thursdays in tutorial mode led by both the TA's and the instructor, focussed on the homework due the next day and on learning to use the Mathematica software. The Midterms also take place on Thursdays,


All course materials will be posted on Canvas. These include the homework assignments, homework solutions, the solutions to the weekly quizzes and the 2 midterms, example Mathematica codes, my lecture notes, and other documents for this course. Canvas includes discussion options to encourage communication among students.

The lectures will be blackboards based while projecting also the posted lecture notes. The lectures will be taped using ZOOM and will be posted on Canvas. Taking photographs of the blackboards is encouraged, and I expect some of you to volunteer posting them in the Canvas discussion area.


You need to have a hard copy or an e-book version of "Mathematical Methods in the Physical Sciences" by Mary Boas.

You need to have easy access to the Mathematica software. This is different from software platforms such as MathLab, that support pure numerical data analysis type operations. Mathematica does algebra for you.

The UW site license allows students free installation of Mathematica on their laptops. For instructions on how to download the software and how to install it, look for "Software for the UW" under IT Connect inside MyUW. Ask fellow students or the TA's during the first week Thursday tutorial for help. Example codes are posted inside Canvas.

In this class you need to use Mathematica a lot, but only for basic useful tasks, like performing simple but tedious algebra, plotting functions to easily visualize them, and to look-up items that required thirty years ago thick books listing tables (of prime numbers for example) and integral identities.

Mathematica is powerful and its code is compact, but its grammar is unguessable at times. Therefore it pays to build a library of codes and start each new task by modifying a previous one. Adding Mathematica to your toolbox is very useful in your future Physics courses and for research. That is why the Physics department requires Mathematica in this course. I will provide example codes with the hw problems such that only minor adjustments in the codes will be required.


Weekly Homework (HW) assignments are posted on Canvas. They are due each Friday before midnight as an upload into Canvas, except for a few that are due on a Monday morning, e.g., HW1 at the start of the second week of instruction (a short one). No HW is due during the weeks of the 2 midterms (see below). Homework will be graded by the TA's. Each HW assignment is worth 10 points. Unfortunately it is impossible for the TA's to grade everything in detail. Therefore they will spot grade the HW. You will receive up to 5 points for "volume" and one randomly chosen question will be graded in detail for the remaining 5 points.

Every Tuesday, we have a short Quiz at the start of the lecture, 15 minutes long. The Quizzes are in-person and paper based; unless CoVid reverts us into online teaching mode. Each quiz will be graded in full detail and is worth 10 points. Each quiz is based on the Homework that was due the previous Friday or the Midterm that took place on the Thursday before.

Solutions of that homework/midterm will be posted in Canvas typically on Saturdays. For HW due on Monday mornings the solutions will be posted at noon on Monday. Questions about the HW solutions can be addressed during office hours (see below).

The first of two Midterms takes place on Thursday October 27 and the second one on Thursday November 17.
Each Midterm counts for 100 points.

The Final exam takes place on Monday, December 12, 8:30-10:20 pm, in PAA A118.
The final is comprehensive and counts for 150 points.

All in-person quizzes and exams are closed book tests. Calculators are not needed but basic non-programmable versions are allowed during quizzes and exams. All internet connectivity must be turned off and unaccessible during quizzes and exams.

For each Midterm and the Final you prepare and bring one sheet with formula's or what ever you like to write onto it. I do not care about the size of your note sheet nor the font you use (you can bring a magnifying glass), as long as size and reading it does not interfere with your neighbors and their space. Information retrieval is a core feature; write too little and you do not have it; write too much and you can not find it.


Office hours are on Monday morning at 11:30 am -12:30 pm in-person in my office (room B429) and/or on Zoom. This is not rigid. You are invited to come to my office or contact me at any time with questions, comments, and suggestions, or whatever; provided I am not preoccupied with something urgent. There are quiet study areas near my office on the fourth floor. You can always e-mail me.


To qualify for credit in this course you must participate in the two midterm exams, and also take the final exam. Failing to do so results into an automatic 0.0 grade. I will honor special circumstances of course, but you need to inform me in a timely manner.

All HW and test scores will be posted on Canvas by points scored only.

Your course grade will be determined from the combined scores in each category, approximately as follows: HW counts for 15% of your total score. (I will drop your lowest HW set score.) The Quizzes count also for 15% of your total score. (I will drop your lowest Quiz score.) Each Midterm counts for 20%, and the Final for 30% of your total score. These relative weights come close to simply adding-up all your posted scores.

The course grade calculation is more complex than simply proportional to your total score. By mid-quarter I will announce what score will be required to earn a 2.0 grade, and also, but only more approximately, where the 3.0 and4.0 thresholds will likely be.


UW guidelines strongly recommend everybody to wear masks at all times inside UW facilities.

Students who require SPECIAL ACCOMMODATIONS or encounter special (un)expected circumstances during the quarter should contact me as early as possible, so we can address these in a timely fashion (before the next short test). See also: Disability Resources for Students .

The RELIGIOUS ACCOMMODATIONS policies of the UW can be found at


home page of Marcel den Nijs, Physics Department URL