### PHZ 3113 — Introduction to Theoretical Physics — Fall 2017

Course: PHZ 3113, Introduction to Theoretical Physics, Meeting times: MWF, Period 6 (12:50–1:40pm), room 1200 Physics
Instructor: J. N. Fry, Office: 2172, Phone: 392-6692, e-mail: fry#phys.ufl.edu, Office Hours: M 4:00pm; Tu/Th 1:00pm [schedule]
Grader: Keegan Gunther, Office: 1228, Phone: 392-9818 (?), e-mail: kgunther#ufl.edu, Office Hours: Monday Period 5 (11:45–12:25) or email for appointment

Course Description: This course presents an introduction to mathematical tools used in theoretical physics, with emphasis on practical uses rather than formalism. Where possible, connections will be made with physical examples, particularly from electrodynamics, statistical physics, and thermodynamics. Approximate schedule of topics will be

 Week Topics Physics Reading Notes 1 Introduction Infinite series, Asymptotics [Gauss's Law?] Chapter 4 Introduction 2 Partial derivatives Line integrals [Blackbody radiation?] Thermodynamics Sections 6–8 Chapter 5 Differential Calculus 3 Multiple integrals min/max with constraints Differentiating integrals Thermodynamics Chapter 6 Chapter 6 Exact and inexact differentials max/min with constraints Differentiation of integrals 4 Differentials Vectors, vector products Vector vs. scalar fields Chapter 7 Multiple integrals; vectors Vector and scalar fields 5 div, grad, and curl divergence theorem, Stokes's theorem Chapter 10   Chapter 11 div, grad, and curl; theorems 6 Dirac δ-function Curvilinear coordinates Chapter 13.1.3 Curvilinear coordinates 7 Applications of vector fields Electrodynamics Electrodynamics 8 Complex numbers Complex functions Analytic functions RLC circuits Chapter 24 Complex numbers Analytic functions 9 Complex integration Cauchy theorem Laurent series Chapter 24.10 Integration, Laurent series, Cauchy theorem 10 Linear vector spaces Linear operators Function spaces Quantum mechanics Chapter 19 Linear algebra Eigenvalue problems 11 Fourier series Fourier transforms Orthogonal functions Quantum mechanics Chapter 12 Fourier analysis 12 Second order equations, Bessel functions Orthogonal polynomials, Harmonic Oscillator Laplacian Chapter 17 13 Ordinary differential equations Partial differential equations Wave equation, heat equation Chapters 14, 15, 18 Chapters 20, 21

Prerequisites: PHY 2061, MAC 2313, or permission of the instructor.

Grading: Grading will be based 25% on periodic homework sets, and 25% each on three term exams. The term exams will tentatively be in class on September 22, [Exam 1 Solution] [Distribution] October 27, [Exam 2 Solution] [Distribution] and December 6 [Exam 3 Solution] [Distribution] Because the material is a sampler of many very different topics, there will be no cumulative final exam. Grading thresholds will be set as for an upper level course: an overall score of 40 will be worth a C, 50 will be worth a B, 60 a B+, 70 an A−, and 80 and up will be an A. I will retain the right to adjust the thresholds downwards (so 79 might become an A), but they will not go up. In addition, at each level there is a requirement on the number of homework sets turned in: 40% for a C, 50 for a B, etc. Students are expected to complete work at the time due, or as soon as possible in case of illness or other accepted, documented circumstance. There will be no last-minute makeups accepted.

The following paragraphs of advice on how to do well in Physics are lifted from one of my colleagues. (To put this into perspective, he also was once known to have his posted office hours during class meeting time.) This is your education, and you are free to make your own choices, but you should listen to what they say:
I do not plan to take daily attendance, but it is to your advantage to attend class. You may spend most of your time sleeping, but in between you will have the opportunity to learn what subjects I think are important, and you can then concentrate on these subjects during your reading. If by some unfortunate set of circumstances you do miss class, do not ask me if I said anything important — everything that I say is important. Instead, ask a classmate; she or he is likely to give an honest answer, and you won't offend me. There will be a substantial number of examples discussed in class that are not in the textbook, and examples in class often appear on tests. If you miss class you will not do well in this course.
Do the assigned homework. This is the drudge part of physics, but it is absolutely necessary. We will learn grand ideas and see their wondrous applications in class. But, your understanding is only superficial unless you can apply these same grand ideas to completely new circumstances. In course work, this is usually done with homework problems. Do not be surprised if the homework is frustrating at times; solving one challenging problem makes the next much easier. And homework problems often appear on tests. Doing all of the homework is the easiest way to improve your grade. Not doing homework is the easiest way to lower your grade.

Required text:

• K. F. Riley, M. P. Hobson, and S. J. Bence, Mathematical Methods for Physics and Engineering, 3rd Ed. (Cambridge University Press 2006).

Other useful books:

This and that:
Physical Constants from the Particle Data Group
Math trivia, Akira Hirose Math Notes
Sir George Gabriel Stokes, Leonhard Euler, The Euler Archive
Rope around the Earth
Harmonic sums  ∑ 1/n, ∑ (−1)n+1/n logarithmic ∑ 1/n − ln(N) Euler's constant γE   sin n/n. ∑ sgn(sin n)/n
Closed form solutions for the evolution of density perturbations in some cosmological models, E. J. Groth and P. J. E. Peebles, Astron. & Astrophys. 41, 143 (1975).
Black Body energy density
Some Series Expansions, a sample calculation
death star
George Green, An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism (1828) [arXiv] [google books]
a curl free field, a divergence free field
More than you wanted to know about δ-functions from
Fourier expansion of square wave Fourier expansion of triangle wave Fourier expansion of delta function
Bessel functions, more about Bessel functions
Hn(x) exp(−½x²),   Ln(x) exp(−½x),   Pn(x)
Hermite expansion of sin(x), Taylor expansion of sin(x)
Legendre polynomial expansion of step function, Bessel function expansion of step function

Homework: Problem solving is a skill learned only through practice. Take advantage of the homework as an opportunity to learn how to recognize the right approach to a problem before it becomes exam time. While I encourage you to discuss the assignments with each other, what you turn in must represent your own work. As we also do when publishing research articles: if you obtain significant information from a published or human source, cite that source. This will often be as little as "Jackson, eq. (9.98)". If you work together, please identify other members of your working group. And, please, be sure that in the end your elegant solution in fact answers the question asked!

1. Homework 1. Solution.
2. Homework 2. Due September 8 September 15. Solution.
3. Homework 3. Due September 15 September 22. Solution.
4. Homework 4. Due October 4. Solution.
5. Homework 5. Due October 13. Solution.
6. Homework 6. Due October 23. Solution.
7. Homework 7. Due November 10 November 13. Solution.
8. Homework 8. Due November 20. Solution.
9. Homework 9. Due December 4. Solution.

sample tests (coming soon)
Test 1 Fall 07, Test 1 Fall 08.
Test 2 Fall 07, Test 2 Fall 08.
Test 3 Fall 07, Test 3 Fall 08.

University Policies: Students are expected to know and comply with the University's policies regarding academic honesty and use of copyrighted materials. Cheating, plagiarism, or other violations of the Academic Honesty Guidelines will not be tolerated and will be pursued through the University's adjudication procedures.
“Students requesting classroom accommodations must first register with the Disabilities Resources Program, located in the Dean of Students Office, P202 Peabody Hall. The Disabilities Resources Program will provide documentation to the student, who must then deliver this documentation to the instructor when requesting accommodations.”