Caltech California Institute of Technology

Caltech Division of Physics, Mathematics and Astronomy

Physics 106a - Topics in Classical Physics, Sep-Dec 2019.

Physics 106a is a 10-week intermediate course in the application of basic principles of classical physics to a wide variety of subjects, including special relativity.
Ph106b will continue with topics in Electromagnetism, including radiation. Ph106c (no longer required for the physics option) will go in more depth on electromagnetism and optics, including boundary value problems and green functions, transmission lines and waveguides, field-theoretic conservation theorems, antennas, scattering, and diffraction.

This website (for Ph 106a only) is: (pdf)

This website is under construction for Fall 2019 - expect it to change significantly!


Please watch this space for announcements regarding Ph 106a; things like rescheduling of lectures, typos in assignments, etc. It is your responsibility to keep up to date with the course information.

  • 12/19/19: Final Exam solutions and Final Grade Distributions posted.
  • 12/6/19: Please fill out the TQFR! And ... have a great winter break!
  • 12/6/19: Alvin will hold a review session on Tuesday 12/10 at 5pm in B157 West Bridge.
  • 12/7/19: Assignment 7 solutions posted.
  • 12/6/19: Final exam posted. Assignment 7 solutions will be posted tomorrow. Please check back for the solutions to the final!
  • Note that Assignment 7 is due in two weeks, Friday 12/6/19. The final exam will be posted on 12/6/19, due 12/13/19.
  • 11/23/19: With apologies for the delay, Assignment 7 and Assignment 6 solutions are posted. Typos in Assignment 5 solutions are fixed.
  • 11/19/19: Typo fixed in problem 3b of Assignment 6 .
  • 11/16/19: With apologies for the delay, Assignment 6 and Assignment 5 solutions are posted.
  • 11/8/19: Assignment 5 is way too long, so leave out problem 3! (You are welcome to do it, but not for credit).
  • 11/9/19: Midterm grade distributions posted.
  • 11/8/19: Assignment 5 posted. Assignment 4 solutions posted. Midterm solutions typos in solutions to problems 1b and 4e fixed.
  • 11/7/19: Assignment 4 problem 4d: fixed some confusing notation.
  • 11/5/19: Assignment 4 problem 1c asked for a plot out to t=4, but it needs to go out to t=5. Now changed.
  • 11/2/19: Assignment 4 posted. Apologies for the delay!
  • 11/2/19: Midterm solutions posted.
  • 10/26/19: Assignment 3 solutions posted. Apologies for the delay!
  • 10/26/19: Assignment 2 solutions were incomplete; now fixed.
  • 10/25/19: Midterm posted. The midterm covers material through Lecture 7 (10/24/19: damped, driven SHO). It is due Friday 7pm, 1 November, 2019. This coming week, The TAs will review the material covered through the beginning of the term.
  • 10/24/19: The order of the lactures is being re-arranged, starting with Lecture 8, which now covers normal modes of oscillation (it used to be Lecture 19). Subsequent lectures will be moved around, as well; stay tuned!
  • 10/21/19: Added a potentially helpful figure to Assignment 3 problem 1.
  • 10/18/19: Assignment 3 posted. Solutions 2 posted.
  • 10/17/19: Ombudsperson for Ph 106a - Gabriel Woolls, gwoolls AT Please talk with Gabriel if you have concerns or suggestions about this class. (You are also welcome to talk with me, or the TA's, or use this anonymous feedback form).
  • 10/17/19: The TAs will hold office hours on Tuesdays 5-9 pm, Wednesdays 10:30-midnight, and Thursday 5-9 pm, all in B157 West Bridge.
  • 10/16/19: Assignment 2 updated with clarification of problems 2d and 3b.
  • 10/12/19: Assignment 2 posted. Assignment 1 solutions posted.
  • 10/4/19: Assignment 1 posted. Typo in L3 fixed. Problem 3b: that's ln(z), not log10(z).
  • As noted below, you are welcome to use Mathematica if you find it helpful in assignments. It is not to be used for exams.
    Ph 2 ab or Ph 12 abc, Ma 2.

    Tuesdays and Thursdays, 10:30-11:55, 103 Downs.
    Any changes will be announced well in advance. Please arrive on time!

    Instructor: Prof. Alan J. Weinstein
    Office: 354A West Bridge; Mail Code: 100-36; Phone: x2166; E-mail: ajw AT

    Teaching assistants:

    Textbook for Phys 106a:
    Analytical Mechanics by L.N. Hand and J.D. Finch, Cambridge University Press (1998) (on amazon).

    Much of the structure, pacing, notation, etc. is taken from this text. It is far from perfect: it doesn't have a review of elementary Newtonian mechanics; it has typos; many people think the explanations are often unclear. Looking at other texts can always help.

    Recommended texts: On reserve at Fairchild Library. Use these texts for alternate explanations or for additional problems or examples.
    • Classical Mechanics by Goldstein, Poole, and Safko (3rd edition): This is a classic textbook (I was taught the subject using an earlier edition, back in the 70s).
    • Classical Mechanics by John Taylor: a nice book, with more review of the basics than Hand and Finch, but slightly less advanced than the level of the class; it will need supplementing with other reading in a few places.
    • Mechanics by Landau and Lifshitz: classic but terse.
    • Classical Dynamics of Particles and Systems by Thornton and Marion: not as advanced as class text, and does not cover all the material, but good supplement if you find the jump from earlier classes to Ph106 too large.

    Approximately 50% problem sets, 15% midterm, 35% final exam.

    Problem Sets:
    • Problem sets and exams will be posted below on Friday of each week, due on the following Friday at 7pm in the Physics 106 IN box by the East Bridge mailboxes, and returned to the Physics 106 OUT box by the East Bridge mailboxes.
    • To satisfy FERPA privacy rules, please make sure you have a FERPA waiver filed with PMA. Else, please choose a 6 or 7 digit code and email this to me and the TAs before the first assignment is due. You will use this, and not your name, to label the assignments you hand in.
    • If your name, and not just your numerical code, appears on the assignment, you will have to pick it up directly from the TAs.
    • Solution sets will be posted on the web.
    • You are strongly encouraged to check your work when it is returned to you.
    • Corrections to problems may be posted in the Announcements section above. If you are having trouble with a problem, be sure to check this page to see if a correction has been posted, and feel free to contact me if you think a problem has errors in it or seems overly difficult.
    • Problem sets are essential for mastering the material in this class!

    Midterm and final exams during appropriate weeks of the term (5th and 10th). Both will be take-home and "limited" open-book (only the text and class notes allowed); see Honor Code section below. The final exam will be comprehensive.

    • OFFICIAL policy: Work (the entire problem set) will be accepted up to one week late at 1/2 credit, no credit thereafter. Please put a note at the top of your problem set if it is late. You do not need to contact me or the TAs to turn in a problem set late for 1/2 credit. You must hand in the assignment in one piece (i.e.\ not a fraction on time for full credit, and the rest late for partial credit).
    • Students may request extensions from the corresponding grader (see emails above) a day or more in advance. Extension requests are governed by the honor system.
    • One extension (for up to one week) is allowed without question (your silver bullet). Please put a note at the top of your problem set that you are using your silver bullet.
    • Extension requests should be accompanied by a good excuse (eg, physical or mental illness), and should be accompanied by a letter from a doctor or the dean.
    • You must request the extension (by email to me and the TAs) before the problem set is due. (This is not necessary for your silver bullet).
    • Please put late or extension problem sets in the corresponding grader's mail box, and email them.
    • Late papers make far more work for the graders, who have their own set of pressures and deadlines as graduate students. There is no entitlement to extensions, so please do not be demanding.

    Honor Code and Collaboration policy:
    • Work is governed by the honor system.
    • You may not use sources that contain the answer to a problem or to a very similar problem. If you have come across such material in the past, so much the better; but you shouldn't go back and reference that material when working on the problem set.
    • In particular, do not use solution sets from previous years, or problem/solution books, at any time. Exams and their solutions from past years are not to be used in any fashion.
    • Collaboration is permitted on problem sets, but then you should go off alone and write it up; the work you hand in must be your own, and honestly reflect your own understanding of the material.
    • The midterm and final are not collaborative. For these you may consult your own notes (both in-class and any additional notes you take), the text by Hand and Finch, and handouts and solution sets on this website. You may not use other textbooks, the web (except for the current Ph106 website), or any other resources.
    • Mathematica or similar software may be used in problem sets for getting past some mathematical chore (if it's to the point of obscuring the physics for you). However, it is usually much better to master the mathematical analysis yourself without help from such software. If you chose to use it anyway, make sure you simplify the result as much as possible, so that it is easy to see what the math is telling you.
    • Mathematica or similar software may not be used in exams, unless explicit stated on the exam.
    • Please attend class, and section meetings!
    • Please ask questions of the TA's and the prof.
    • Please clearly write your ID number (NOT your name), date, assignment number on all of your assignments and exams. Clearly mark the problem numbers and answers.
    • Please write as neatly as possible. A human being is trying to read your work well enough to give credit!

    I greatly appreciate student feedback; feedback prior to the end-of-term TQFR evaluations lets me modify the class to fit your needs. If you want to send an anonymous comment about the course to me, click here.
    I also welcome any comments in person, by email to ajw AT, by campus mail, whatever you like.

    Lecture schedule and reading, fall term:

    Week (Tuesday) Tuesday Lecture Thursday Lecture Assignment
    (by Friday PM)
    October 1
    1. Review of Newtonian Mechanics
    Reading: Notes; HF §1.1; T Chs. 1,3,4; GPS §1.1-2
    Your favorite elementary mechanics text
    2. Variational Approach
    Reading: Notes; HF §2.1-5; T Ch6, §7.1-2
    Assignment 1,
    due next Friday.
    (TA: Alvin)
    October 8
    3. The Lagrangian
    Reading: Notes
    4. Constraints, Virtual Work...
    Reading: Notes; HF §2.6-9; T §7.3-9
    Assignment 2
    (TA: TBD)
    A1 Solutions
    October 15
    5. Variational Approach with Constraints
    Reading: Notes; HF §2.6-9; T §7.3-10
    6. Equilibria and Oscillations
    Reading: Notes; HF Ch 3; T Ch 7
    Assignment 3
    (TA: TBD)
    A2 Solutions
    October 22
    7. Driven, Damped Oscillations
    Reading: Notes; HF Ch 3; T Ch 7
    8. Resonant response
    Reading: Notes; HF Ch 3; T Ch 7
    Midterm Exam
    (TA: TBD)
    A3 Solutions
    October 29
    9. Normal modes Part 1
    Reading: Notes; HF Ch 9; T Ch 11
    10. Normal Modes Part 2
    Reading: Notes; HF Ch 9; T Ch 11
    Assignment 4
    (TA: TBD)
    Midterm Solutions
    November 5
    11. Central Forces: Bound States I
    Reading: Notes; HF Ch 4; T Ch 8
    12. Central Forces: Bound States II
    Reading: Notes; HF Ch 4; T Ch 8
    Assignment 5
    (TA: TBD)
    A4 Solutions
    November 12
    13. Central Forces: Scattering States
    Reading: Notes; HF §4.7, prob 4.28; T Ch 14
    14. Hamiltonian Dynamics I
    Reading: Notes; HF Ch 5; T Ch 13
    Assignment 6
    (TA: TBD)
    A5 Solutions
    November 19
    15. Hamiltonian Dynamics II
    Reading: Notes; HF Ch 5; T Ch 13
    16. Special Relativity I
    Reading: Notes; HF Ch 12; T Ch 15
    Assignment 7
    (TA: TBD)
    A6 Solutions
    November 26
    17. Special Relativity II
    Reading: Notes; HF Ch 12; T Ch 15
    No assignment
    (TA: TBD)
    A7 Solutions
    December 3
    18. Special Relativity III
    Reading: Notes; HF Ch 12; T Ch 15
    19. Special Relativity IV
    Reading: Notes; HF Ch 12; T Ch 15
    Final Exam
    (TA: TBD)
    Fin Solutions

    Acknowledgements: Most of the lecture notes and problem sets / solutions for this class were developed by Prof. Michael Cross. Many thanks to him!

    Last Updated: Dec 6, 2019
    Alan Weinstein/ajw AT