Phys 3033: Analytical Methods in Physics

Fall 2015    Welcome! This course will introduce you to many of the mathematical tools you need to be an effective physicist. While this will not be an easy class, if you do decide to exert the mental effort to assimilate the material well, I believe it will be rewarding!
  1. Class venue/time: 249 MWAH, MWF 1-1:50 pm
  2. Office: 373 MWAH
  3. E-mail: chuxx302
  4. Office hours: Fridays from 2-3 pm (right after class), on MWAH's 2nd floor conference room. You should e-mail me if you wish to set up a time to meet outside of these times.
  • Disability resources     If you have a disability that you think I should know about, and if you need special accomodations, please feel free to speak to me after class or e-mail me to set up a meeting.    
  • Academic integrity     You are encouraged to discuss with your classmates the material covered in class, and even work together on your assignments. However, the work you turn in must be the result of your own effort. If I find that you copied your work from some place else, you will immediately receive zero credit for that particular piece of work. If you plagarized your classmate, your classmate will also receive zero credit for her/his/their work, unless (s)he/they can prove to my satisfaction (s)he/they were unwilling participant(s) of your dishonesty.
Syllabus and Grading Scheme

The rough chronology of the course will be as follows.
  • Complex numbers
  • Linear algebra 
  • Advanced calculus, including 
    • Calculus on the complex plane
    • Fourier Transforms/Series
    • Asymptotic methods
    • Differential geometry
    • Partial differential equations
The grading scheme in this course will go as follows. Roughly top 1/3 of the class will get A, middle 1/3 B and bottom 1/3 C. I will use plus/minus letter grades, e.g. A+, whenever appropriate. I wish to reward hard work during the semester, so I will give most weight to the homework you turn in.

The midterm and final are papers you would write on topics I describe below. (The font size should be 12 pts.) Your writing will be judged firstly by the accuracy, breadth and depth of the content; but also by the clarity of the exposition. Turn in your papers by e-mailing them to me. If you write your paper on MS Word, please convert it to Open Office format before sending it to me. Extra credit will be given if you write your paper in LaTeX; if you do, just e-mail me your TeX file.

Homework (60%):     I will assign problem sets from the lecture notes posted here. I recommend starting your homework as soon as possible -- do not wait until the day before it is due to do it!

Note: I will not accept late homework -- just turn in whatever you have done at the time/day it is due.
  1. Due Monday 14 September, in class: Problems 1.0.1 through 1.0.14.
  2. Due Friday 25 September, in class: Problems 2.1 through 2.17.
  3. Due Thursday 15 October, 12 noon: Problems 3.1 through 3.18.
  4. Due Monday 2 November, in class: Problems 3.19 through 3.32.
  5. Due Monday 23 November, 5 pm: Problems 3.33, and 4.1 through 4.18.
  6. Due Saturday 12 December, 12 noon: Problems 4.19, 4.21, 4.22, 4.28, 4.29; 7.1-7.4, 7.9-7.11, 7.12, 7.14-7.18.
Midterm (15%) (Due Wed, 4 November, 11:59 pm):    Write a 5-10 page introduction to the Sturm-Liouville theory of ordinary differential equations and orthogonal functions. Your paper should explain how linear algebra plays a central role. Other aspects you may wish to cover include important properties of the orthogonal functions and what sort of physical applications they have.

Final (25%) (Due Wed 16 December, 11:59 pm):     Write a 10-20 page introduction to group theory. Your paper should explain the basic axioms that define a group, and may cover questions that include but need not be limited to: What is the Lie algebra of a group? What is a representation of a group? What groups, and which of its representations, are important in physics? What are symmetries, and how are groups related to their description in both classical and quantum physics?

Note added Friday 11 December: The total for the final will be 25 points. You can turn it in until Friday 18 December 11:59 pm, but I will take 3 points off if you turn it in on Thursday 17 Dec and 6 points off on Friday 18 Dec.

Current Grades (Updated 12 December):
  • 1-4:     41.8 through 58.6 %
  • 5-8:     17.71 through 30.7 %
  • 9-13:   0 through 17.65 %
Lecture Notes & Problems

I will be teaching from my lecture notes below. The main shortcoming of my lecture notes is that there are no figures - this is why you need to come to class, where I will supply them whenever necessary...
  • Lecture Notes (Note added 2017: Link points to end-2015 version of lecture notes.)   I will continue to update/edit these notes throughout the semester, so check back regularly. Do let me know if you find any errors, typos, etc.
Mathematical Methods Texts
This course does not have a required textbook. However, I encourage you to seek out different ways of looking at the material discussed in class.

General Asymptotics Linear Algebra and Group Theory Special functions
Complex analysis
Differential geometry
Numerical methods
(Mostly links to amazon.com - out of convenience; not an endorsement of their business practices.)

Other Mathematical Resources
Online
Books (Mostly links to amazon.com - out of convenience; not an endorsement of their business practices)
Acknowledgements

While developing this course, I have taken inspiration from several of the textbooks listed above. The previous installment of Phys 3033, taught by Prof. John Hiller, can be found here.

Disclaimer

The views and opinions expressed in this page are strictly those of mine (Yi-Zen Chu). The contents of this page have not been reviewed or approved by the University of Minnesota.