Physics 106bc - Topics in Classical Physics - Electrodynamics
Winter and Spring Quarter, 2024
Course Homepage

Overview and Intended Learning Outcome

Ph106b will be devoted to fundamentals of electrostatics and magnetostatics, including boundary-value problems, multipole expansions, and electrostatics and magnetostatics in matter.  Ph106c will cover electrodynamics, including conservation laws, potential theory, electromagnetic waves, and radiation as well as the relationship between special relativity and electrodynamics.

Ph106bc covers electrodynamics at a level of sophistication beyond the introductory Ph1bc sequence.  You will see much material that is familiar to you, but we will take a more rigorous approach, analyze more challenging physical situations, and also consider many topics not seen in Ph1bc.  It is impossible to emphasize how important the core physics courses Ph106 and Ph125 are: these teach you the basic frameworks and techniques that you must know to do any physics.

The intended learning outcome of both Ph106b and Ph106c is for students to acquire the ability to calculate electric and magnetic potentials, fields, energies, and forces in a variety of basic physical configurations combined with an understanding of the underlying physical principles and calculation techniques.  This outcome requires both an understanding of principles as well as the ability to apply them to do calculations! 

Quick Links

Announcements: see Canvas pages: Ph106b, Ph106c (accessible only to students registered for the course)

Syllabus and Schedule, Problem Sets, and Solutions

Below you will find the outline of Ph106bc.  I will update the details of the topics covered in lectures and suggested reading as the term progresses.  Assignments and exams will be made available via Canvas, about a week before the due date, so no effort is made here to list them.

The problem sets and solutions are only accessible via Canvas.  (Lecture notes are available to anyone.)

Keep a copy of the lecture notes and problem sets handy on your computer or a USB stick.  Websites go down occasionally (seemingly especially during holidays), and a very modest bit of foresight can prevent this from disrupting the problem set due date schedule.  If there is a problem set update, or a lecture notes update relevant to a problem set, at a very late date and there is an outage (in the 24 hrs before a set is due), this policy will be suspended.

In the suggested reading, G stands for Introduction to Electrodynamics by Griffiths, LN for Lecture Notes, HM stands for Classical Electromagnetism by Heald and Marion, and J for Classical Elecrodynamics by Jackson.  Reading given in parentheses is optional (intended only to tell you where material is drawn from).  The numbers in parentheses after each LN section listing and at the end of each day's lecture is the number of LN slides (to manage lecture pace).
Ph106b: Electrostatics and Magnetostatics
Week/TA Tuesday Lecture Thursday Lecture
Jan 1
TA: N/A
No PS/OH this week!

1.
Introduction to Course
LN 1.1: Course Material (5)
LN 1.2: Notation (1)
Basic Electrostatics I:
LN 2.2: Assumptions (1)
LN 2.3: Coulomb's Law, Electric Field (5)
LN 2.3: Dirac Delta Function (3)
LN 2.4: Integral Form of Gauss's Law (6)
LN 2.4: Differential Form of Gauss's Law (4)
(25)
Reading: G 2.1-2.2.3
Jan 8
TA: Colin
2.
Basic Electrostatics II:
LN 2.4: Dirac Delta Function Redux (3)
LN 2.5: Curl E = 0 (4)
LN 2.6: Electric Potential (6)
LN 2.7: Techniques (1)
LN 2.8: Boundary Conditions (9)
LN 2.9: Poisson's and Laplace's Equations (2)
(25)
Reading: G 2.2.4-2.3
3.
Basic Electrostatics III:

LN 2.10: Electric Potential Energy (8)
LN 2.11: Conductors (10)
(18)
Reading: G 2.4-2.5.3 (J 1.11)
Jan 15
TA: Alfred
PS delayed to Tuesday evening due to holiday
4.
Basic Electrostatics IV:
LN 2.12.3-5: Capacitance (19)
(19)
Reading: G 2.5.4 (J 1.11)
5. Advanced Electrostatics I:
LN 3.1: Laplace's Equation (6)
LN 3.2: Uniqueness Theorem (5)
LN 3.3: Method of Images (1+3)
(12)
Reading: G 3.1.1-3.1.4 (J 1.7)
Reading: G 3.1.5-3.1.6 (J 1.8-1.9)
Reading: G 3.2 (J 2.1-2.5)
Jan 22
TA: Gemma
6. Advanced Electrostatics II:
LN 3.3: Method of Images (cont.) (9)
LN 3.4: Green Functions (7)
(16)
Reading: G 3.2 (J 2.1-2.5)
Reading: (J 1.10)
7. Advanced Electrostatics III:
LN 3.4: Green Functions (6+3)
LN 3.4: Obtaining Green Functions from the Method of Images (4+5)
LN 3.5: Separation of Variables: General Considerations (4)

LN 3.6: Separation of Variables in Cartesian Coordinates (5)
(19+5)
Reading: (J 2.6-2.8)
Reading: G 3.3.1 (J 2.9)

Jan 29
TA: Colin
8. Advanced Electrostatics IV:
LN 3.6: Separation of Variables in Cartesian Coordinates (8)
LN 3.7: Separation of Variables in Spherical Coordinates: General Theory (0+6)
LN 3.8.1-3.8.4: Separation of Variables in Spherical Coordinates w/Azimuthal Symmetry (10)
(18+6)

Reading: G 3.3.2 (J 3.1-3.3)
9. Advanced Electrostatics V:
LN 3.8.5: Separation of Variables in Spherical Coordinates w/Azimuthal Symmetry (cont.) (11+1)
LN 3.9.1-3: Separation of Variables in Spherical Coordinates w/o Azimuthal Symmetry (4+3)

LN 3.9.4: Spherical Harmonic Expansion of Green Function (8)
(23+4)
Reading: (J 3.3)
Reading: (J 3.5-3.6)
Reading: (J 3.9-3.10)

Feb 5
TA: Alfred
PS this week will focus on practice midterm problems
10. Advanced Electrostatics VI:
LN 3.9.4: Spherical Harmonic Expansion of Green Function (cont.) (6)
LN 3.9.5: Examples of Using the Spherical Harmonic Expansion of Green Functions (12+5)

(18+5)
Reading: (J 3.9-3.10)
11.
Advanced Electrostatics VII:

LN 3.10: Multipole Expansion (12)
(12)
Reading: G 3.4 (J 4.2)
Feb 12
TA: Gemma
12.
Advanced Electrostatics VIII:
LN 3.10: Multipole Expansion (cont.) (3)
Electrostatics in Matter I:

LN 4.1: Polarizability and Polarization (6)
LN 4.2: The Electric Displacement Field (6)

LN 4.3: Linear Dielectrics (4+4)
(19+4)
Reading: G 4.1-4.4.1 (J 4.3)
13.
Electrostatics in Matter II:
LN 4.3: Linear Dielectrics (cont.) (3)
LN 4.4: Boundary Value Problems with Dielectrics (7)
LN 4.5: Electrostatic Energies and Forces on Dielectrics (10+1)

(20+1)

Reading: G 4.4.1 (J 4.3)
Reading: G 4.4.2 (J 4.4)
Reading: G 4.4.3-4.4.4 (J 4.7)

Feb 19
TA: Colin
PS delayed to Tuesday evening due to holiday
14. (Actually given on 2/22)
Electrostatics in Matter II:
LN 4.5: Electrostatic Energies and Forces on Dielectrics (8)
Magnetostatics I:

LN 5.2: Lorentz Force, Currents (7)
LN 5.3: Continuity Equation (2)
LN 5.4: Fields and Forces (5)
(22)
Reading: G 4.4.3 (J 4.7)
Reading: G 5.1-5.2.2 (J 5.1)
15. (Actually given on 2/25)
Magnetostatics II:
LN 5.5: Divergence of Magnetic Field (1)
LN 5.5: Curl of Magnetic Field, Ampere's Law (7)
LN 5.6: Potentials (16)
(24)
Reading: G 5.2.2-5.4.1 (J 5.2-5.5)
Feb 26
TA: Alfred
16.
Magnetostatics III:
LN 5.7: Boundary Conditions (11)
LN 5.8: Magnetic Multipoles (12)
(23)
Reading: G 5.4.2 (J 5.8)
Reading: G 5.4.3 (J 5.6)
17.
Magnetostatics IV:
LN 5.8: Magnetic Multipoles (cont.) (7)

Magnetostatics in Matter I:
LN 6.1: Paramagnetism and Diamagnetism (2)
LN 6.2: Potentials and Fields of Magnetized Materials (6+1)
LN 6.3: Auxiliary Field (2)
LN 6.3: Boundary Conditions on Auxiliary Field (6)
(23+1)
Reading: G 6.1-6.3.3 (J 5.7-5.8, 5.10)
Mar 5
TA: Gemma
18.
Magnetostatics in Matter II:
LN 6.3: Magnetic Permeability (7)
LN 6.4: Boundary Value Problems in Magnetic Matter (14)
(21)

Reading: G 6.4.1 (J 5.9-5.11)
19.
Magnetostatics in Matter III:
LN 6.4: Boundary Value Problems in Magnetic Matter
(cont.) (15+5)
LN 6.5: Nonlinear Magnetic Permeability (7)
(22+5)

Reading: G 6.4.1-2 (J 5.11-5.12)
Mar 12
TA: Colin

Final Exam Review during problem session
Problems from 2021-2023 exams, available on Canvas, will be used.
A poll will be sent out to determine which problems are of most interest.
N/A
Back to the top.

Ph106c: Electrodynamics
Week/TA
Tuesday Lecture Thursday Lecture
Apr 1
TA: N/A
No PS/OH this week!
20.
Electrodynamics I:
LN 7.1: Currents and Ohm's Law; Fields, charges and currents in wires (7)
LN 7.2: Motional Electromotive Forces (16)
(23)

Reading: G 7.1.1-7.1.3 (J 5.15)
21.
Electrodynamics II:
LN 7.3: Electromagnetic Induction, Faraday's Law (18)
LN 7.4: Inductance (5)
(23)

Reading: G 7.2.1-7.2.3 (J 5.15, 5.17)
Apr 8
TA: Jaeha
22.
Electrodynamics III:
LN 7.5.1-7.5.5: Magnetic Energy (15)
LN 7.5.6-7.5.7: Magnetic Forces (5)
(20)

Reading: G 7.2.4 (J 5.16)
23.
Electrodynamics IV:
LN 7.6.1-7.6.3: Displacement Current, Maxwell's Equations in Vacuum (9)
LN 7.6.4-5: Maxwell's Equations in Matter, Boundary Conditions (6)
Conservation Laws:
LN 8.1-8.2: Conservation of Charge, Energy (11)
EM Waves I:
LN 9.2.1: Electromagnetic Waves in Vacuum (4)
(30)
NOTE: LN 8.3-8.4 is being skipped, you are not responsible for it.
Reading: G 7.3.1-7.3.4 (J 6.1)
Reading: G 8.1, 8.3 (J 6.7)
Reading: G 9.2.1, 9.1.1-2
Apr 15
TA: Colin
24.
EM Waves II:
LN 9.2.2-9.2.7: Electromagnetic Waves in Vacuum (cont.) (13)
LN 9.3.1-9.3.3: EM Waves in Nonconducting Matter, Reflection and Refraction (7)
(20)

Reading: G 9.1-9.3.2 (J 7.1-7.3)
25.
EM Waves III:
LN 9.3.4-9.3.8: EM Waves in Nonconducting Matter, Reflection and Refraction (25)
(25)

Reading: G 9.3.3 (J 7.3)
Apr 22
TA: Jaeha
26.
EM Waves IV:
LN 9.4: EM Waves in Conductors (17)
(17)

Reading: G 9.4.2 (J 8.1)
27. EM Waves V:
LN 9.5: EM Waves in Dispersive Matter (15)
(15)
Reading: G 9.4.3 (J 7.5, HM 10.2, 10.4-10.5)
Apr 29
TA: Jaeha
28.
EM Waves VI:
LN 9.6-9.7: Transmission Lines (24)
(24)

Reading: G 9.5 (HM 7.1, J 8.2)
29.
EM Waves VII:
LN 9.8.1-9.8.4: Waveguides: Form of Solution (7)
LN 9.8.5-9.8.11: Waveguides: Boundary Conditions, Propagation Properties, Example Solutions (18)

(25)

Reading: G 9.5 (J 8.2-8.4)
May 6
TA: Colin
30.
EM Waves VIII:
LN 9.8.12-13: Waveguides: Energy (9+1)
LN 9.8.15: Waveguides with Finite Conductivity (15+1)
(24+2)

Reading: G 9.5 (J 8.5, 8.1)
31.
Potentials Revisited:
LN 10.1.1-4: Potential Formulation (8)
LN 10.2: Retarded Potentials and Fields (13+2)
NOTE: LN 10.1.5-10.1.6 is being skipped, you are not responsible for it.
(21+2)

Reading: G 10.1-10.2.2 (J 6.2-3, 6.5, HM 4.5, 8.1-8.2)
May 13
TA: Aike
32.
Review of Special Relativity:
LN 11.2.1-11.2.5: Definitions, Lorentz Transformation, Implications of Lorentz Transformation (12+8)
LN 11.2.7-11.2.8: Geometrical Interpretation, Light Cones, Causality, and Simultaneity (0+5)
LN 11.2.8-12: Four-Vectors, Invariant Norm, Tensors, Covariant and Contravariant Indices (9)
LN 11.2.13: Proper Time, Four-Velocity, and Velocity Addition (5)
(26+13)

Reading: G 12.1-2
33.
Relativity and Electrodynamics:
LN 11.3.1-11.3.3: Covariant Formulation of EM Sources and Potentials (5)
LN 11.3.4: Transformation of EM Fields (3+3)
LN 11.3.5: Field of a Moving Point Charge (3)
LN 11.3.5-11.3.8: Covariant Formulation of EM Fields and Maxwell's Equations (3+2)
LN 11.4: Relativistic Dynamics with EM Fields (3)
NOTE: LN 11.5-11.6 are being skipped, you are not responsible for that material.
(17+5)
Reading: G 12.2-3
May 20
TA: Aike
34.
Radiation I:
LN 12.1.1-12.1.3: Potentials and Fields of a Fixed-Velocity Point Charge (12+1)
LN 12.1.4: Potentials and Fields Radiated by an Accelerating Point Charge (7+1)
(19+2)

Reading: G 12.2.4
Reading: G 10.3.1-2, 11.2.1 (HM 8.3-8.5)
G 11.2.2-11.2.3 are being skipped, you are not responsible for this material.
35.
Radiation II:
LN 12.1.5: Power Radiated by an Accelerating Point Charge (3)
LN 12.1.6-12.1.9: Bremsstrahlung, Synchrotron Radiation, Lienard's Formula, Larmor's Formula (10)

LN 12.2.1-12.2.3: General Theory of Radiation (11)
(24)

Reading: G 11.2.1, 11.1 (HM 8.8, 8.6)
May 27
TA: Colin
PS delayed to Tuesday evening due to holiday
36.
Radiation III:
LN 12.2.5-6: Electric and Magnetic Dipole Radiation (12)
Applications of Radiation I:
LN 13.1: Classical Scattering (11+1)
(23+1)

Reading: G 11.1 (HM 9.1-9.3, 9.8)
Reading:
(HM 10.1, J 14.8)
37.
Applications of Radiation II:
LN 13.1: Classical Scattering (4)
LN 13.2: Antennas (22)
(26)

Reading: (HM 10.1, J 14.8)
Reading: (HM 9.4-9.5, 9.7, J 9.4)
Jun 3
TA: Aike
38. Optional Lecture -- never given
Advanced Potential Formulation:
LN 10.1.5: Lorentz Force Law in Potential Form (9)
LN 10.1.6: Gauge Transformations and Coupling of Matter to EM Fields (8)

Advanced Special Relativity I:

LN 11.5: Lagrangian Formulation of Relativistic Electrodynamics (7)
(24)
Reading: (J 12.1, HM 4.9)
Reading: (J 12.7, HM 14.10-11)
39. Optional Lecture -- never given
Advanced Conservation Laws:
LN 8.3: Conservation of Linear Momentum (9)
LN 8.4: Conservation of Angular Momentum (5)
Advanced Special Relativity II:

LN 11.6: Relativistic Conservation Laws (9)
Applications of Radiation III:
LN 13.3: Diffraction (14)
(37)
Reading: G 8.2 (J 6.7, HM 4.8)
Reading: (J 12.10, HM 14.12)
Reading: (HM 12, J 10.5)

Jun 10
TA: Jaeha
Final Exam Review during problem session
Problems from 2021-2023 exams, available on Canvas, will be used.
A poll will be sent out to determine which problems are of most interest.
Reading: N/A

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Vital Information

Ph106b and Ph106c have Canvas sites.  Caltech-privileged information, including problem sets, will be listed there since it is password-protected.  All public information will be posted to this site.

Location:
107 Downs

Time:
TuTh 10:30-11:55 am

Instructor:

Prof. Sunil Golwala, 302 Cahill, Mail Code 367-17.

Office hours: Thursday 9-11 pm, 4th floor Lauritsen.  If no one shows by the end of the first hour, or no one sends an email requesting the second hour, the OH may end early.

If conflicts prevent anyone from attending the above office hour, other arrangements can be made.  Contact the course instructor.

If you need to contact the course instruction outside of office hours, please try email first.  Meetings can be arranged outside of normal office hours, but spur-of-the-moment meetings are frequently not possible.  Please include "Ph106" in the subject line of your email so that it is recognized and responded to quickly.  See comments below about email and extensions.

Teaching Assistants:

Ph106b:
Zhaoyu (Gemma) Huai
Alfred Li
Colin Weller

Office hours:

We will have one problem session (on Monday) and two office hours (Wednesday, Friday) each week in addition to the instructor office hours on Thursday.

The problem session(s) and W/F office hours will be run by the TA who is grading that week's homework.  See the syllabus above for the relevant TA information.


Problem session: Monday 8-9 pm,
4th floor Lauritsen.  This is an interactive session in which the students will work together to solve problems.  The session may go past 1 hr depending on student and TA interest, but only attendance at the first hour is required to obtain credit as noted belowIf you cannot attend, email the course instructor to make special arrangements.

Problem session makeup: Wednesday 8-9 pm, 4th floor Lauritsen.  This session is intended mainly for those who have conflicts with M 8-9 pm, but you may attend either problem session.

Wednesday 7-8 pm,
4th floor Lauritsen: office hour, no planned agenda

Friday. 3-4 pm, 4th floor Lauritsen: office hour, no planned agenda; intended for last-minute questions for problem set due that day.

If you would like help on Tuesday, feel free to contact the TAs to arrange a special appointment.

If conflicts prevent anyone from attending the above problem session or office hours, other arrangements can be made.  Contact the course instructor.
Ph106c:
Jaeha Lee
Aike Liu
Colin Weller

Office hours: Same as Ph106b except:
Problem session makeup: Tuesday 8-9 pm, 4th floor Lauritsen.  This session is intended mainly for those who have conflicts with M 8-9 pm, but you may attend either problem session.

Wednesday 4-5 pm, 4th floor Lauritsen: office hour, no planned agenda

Feedback: I greatly appreciate student feedback; feedback prior to the end-of-term evaluations lets me modify the class to fit your needs.  In person, by email, by campus mail, whatever you like.  There will be a request for volunteers for course ombudspersons and a mid-term survey that will provide an opportunity for anonymous feedback.

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Textbook(s) and Lectures

Other texts are included in the Course Reserves, but these are the most useful.

Policies and Grading

The course will use the following policies on collaboration, honor code, assignment due dates and extensions, and credit:
  • Homework is due 7 pm Fri via Canvas.

  • Instructor or TA response to questions after 5 pm Friday should not be expected.

  • Extension requests should be sent to me, the course instructor, not the TAs.  I do not check email continuously, and typically not after 5:30 pm on weeknights (until possibly after 8 pm), so your extension requests must allow time for non-immediate response.

  • Extension requests must be based on conditions that could not be planned for or planned around: physical or mental health issue, family or other personal emergency, CASS accommodations, etc.  Other work (academic, research, other), extracurricular activities, etc. that were known about ahead of time and could be planned for are generally not considered acceptable reasons, though in some cases they can be.  The deans have reiterated this policy to instructors, with the goal of ensuring students do not have work piled up at the end of term due to extensions earlier in the term.  Do the best you can and turn in what you have if you did more than half the problem set, otherwise take the 50% credit extension and turn in the work a week late.

    If you have a CASS accommodation, please note it in your extension request.

  • Late work policy
    • You may turn any problem set up to 1 week late for 50% credit.  Splitting of sets is not allowed: Turn in what you have on time for 100% credit, or turn in more or all of the set late for 50% credit, but you may not do both.
    • You may have one silver bullet extension each for Ph106b and one for Ph106c.  A silver bullet provides a 1-week extension at full credit.  It does not push out the due date, so one cannot take an additional 1-week extension at 50% credit; it is a replacement of the 50% credit period by 100% credit.
    You do not need to request permission ahead of time for the above, just note it at the top of the submitted problem set.  Let us know if late work is occurring near the end of term so we don't miss giving credit for the work.

  • The grading split will be
    • 50% problem sets
    • 25% midterm exam
    • 25% final exam

  • Extra credit for problem session attendance: To encourage attendance at the Monday problem sessions, we will offer extra credit.  Here are the rules on the extra credit:
    • The extra credit will be added after the letter grade boundaries are decided, so students who do not attend will not be penalized.
    • Students who miss no more than one problem session in Ph106b or Ph106c (separately for the two courses) will be guaranteed one +/- grade increment of extra credit.  Students who attend fewer sessions will receive a proportional point increment.  The latter may or may not result in a +/- grade increment depending on the details of the person's numerical grade.
    • Extra credit does not apply to the A/A+ boundary: A+ grades must be earned on the basis of submitted work.
    • If you have a time conflict with the problem session time, contact the course instructor to identify an alternate solution.

  • Honor code and Collaboration policy

    • Use of mathematical software like Mathematica is allowed on homework, but will not be available for exams.  From a former colleague: It is absolutely essential that you develop a strong intuition for basic calculations involving linear algebra, differential equations, and the like.  The only way to develop this intuition is by working lots of problems by hand; skipping this phase of your education is a really bad idea.

    • HOMEWORK COLLABORATION AND REFERENCE POLICY

      You must first try the problems yourself.  If you get stuck, or are unsure of your answer, you may seek help from the TAs or the instructor (see office hours above). You may also seek help from other students in the course, but your solution must be the result your own understanding of the material and must be written up independently (e.g. not copied from someone else's solutions or from a jointly prepared solution). If you do work with other students on a problem set, you must identify the names of those with whom you worked with on the submitted work.  Don't let your colleagues show you how to do the problems; make sure they are helping you by "Socratic Method" -- asking you questions that will lead you to the insight you need for a particular problem.

      It is probably possible to find the solution to any reasonable problem in other textbooks, from previous years of Ph106, or on the internet. You must not seek solutions to the assigned problems from any such resource. In any case, this would be a foolish thing to do, since the assignments serve as practice for the midterm and final for which consulting outside sources is not allowed. You should also not consult others who have taken Ph106 in a previous year for copies of the problem sets, but of course you may request help as you would from a TA.

      Historically, performance on problem sets is much better than on exams (see below).  Some of this may be due to the exam time constraint, but some of it may also be due to problem set overcollaboration.  If you do not internalize the material via the problem sets, you will not do well on the exams.  So be very careful to follow the collaboration policies, not just because of the honor code, but for your own good.

      Here are some elaborations on the collaboration and reference policies, intended to supplement, not replace, the above policies:

      • On consulting tutors, TAs, fellow students, etc:

        Remember what the collaboration policy says: you must first try the problems yourself.  You can consult the instructor, TAs, tutors, fellow students, etc., but your solution must be the result of your own understanding.  You cannot ask other people to show you how to do a homework problem, or watch them do it, only discuss general issues and concepts with them, or work different examples.

        Generally, homework problems appear difficult because either the underlying physics or the calculational technique has not been understood.  Understand those and the homework is doable on your own.

      • On assisting fellow students:

        The same rules apply.  Don't tell your fellow students how to do a problem.  You can help them figure it out themselves by discussing relevant concepts, other examples, etc.  Helping another student without explicitly showing them how to do a problem is helpful to your own understanding, also, as you must have the concepts and techniques clear in your own head in order to effectively explain them to another student.  Use the "Socratic Method" -- ask questions that will lead your colleague to the insight needed to figure out the problem on their own.

    • EXAM COLLABORATION AND REFERENCE POLICY

      Exams are strictly non-collaborative!

      Exams are "open-book": You may consult your own notes (both in-class and any additional notes you take), Griffiths, and handouts and solution sets on this website.  No other textbooks (not even Jackson and Heald & Marion, since they are optional), no web sites, no other resources.

      In some instances, you may make use of notes taken from online resources. In particular, if you take the initiative to study beyond class material and you get lucky by finding or studying ahead of time a problem that is later assigned on homework or an exam, you get to benefit from your hard work. However, you may not go hunting for problems on the web after they have been assigned, and you must use your own notes (handwritten or electronic) on any materials you have found, not the original source material.


      The most extreme hypothetical is the case of finding on the web a problem that is assigned on homework or an exam.  If you find the problem before seeing the relevant homework or exam, and take notes on it in your own hand (real or virtual), then those notes are fair game for use while you are doing the homework or exam. If you see the homework or exam, then go searching on the web and find the problem, your notes on such a problem are not allowed. Even if you found the problem before you saw the exam and saved the solution on your computer, going back to that saved copy is also not allowed, since that would not be your own notes.


      While it follows the letter of the above policy, hunting down scores of problems ahead of time and copying them in one's own hand is strongly discouraged. Doing so clearly violates the spirit of the law, and the large amount of time it takes to find and copy these solutions could be much better spent learning the material.

      If you do make use of electronic resources and save them, one idea would be to create a "forbidden" folder on your computer that you know you may not consult during an exam.  This will prevent even accidental violations of the honor code.

      • You may use the previous years' exams and solutions posted on the Canvas website when doing problem sets or exams, but only those!  You may not use previous years' exams or solutions that are not available from this website or the Canvas website.

      • You may use any other materials provided by the instructor or TAs, including material from the problem sessions or office hours.

    • AI/ONLINE TUTORING POLICY

      This course will adhere to the PMA policy on the use of AI and online tutoring.  The portions of that policy relevant to this course are as follows (and are consistent with what is stated above about use of internet resources):

      A primary goal of education is to learn how to approach and how to think about problems. Rapidly evolving generative artificial intelligence tools (e.g. ChatGPT, Bard, etc), online tutoring services (e.g. Chegg) and internet resources (e.g. Google) have the potential to be powerful companions for learning. On the other hand, they also provide tempting shortcuts to solutions that can be seriously detrimental to student learning. The course policies below serve to ensure that artificial intelligence (AI), internet resources (IR) and online tutoring (OT) usage in our class is carried out responsibly and ethically.

      Permissible Uses of AI, IR & OT

      Augmenting learning: AI, IR & OT can be used as a virtual TA to help clarify concepts learned in class, to provide example problems/solutions that supplement course material, and to inquire about advanced topics beyond the scope of the course.

      Prohibited Uses of AI, IR & OT

      Generating solutions: Unless explicitly allowed by the instructor, AI, IR & OT cannot be used to generate answers to any class assignment (e.g. problem sets, quizzes, exams), even if the student revises or recreates the content with the exception of the scenario described above. If there is any confusion about AI, IR & OT policy, the student should seek clarification before using them for any assignment.

      Guidelines for Using AI, IR & OT in Permissible Cases

      Understanding and Learning: Students may use AI, IR & OT to enhance their learning. However, these should not replace primary methods of learning, such as attending lectures, reading assigned textbooks, participating in sections and office hours, and practicing independent problem-solving. Students should take advantage of the unique opportunities associated with being enrolled in-person at Caltech.

      Critical thinking: Students should note that material generated by AI, IR & OT may be inaccurate, incomplete, or otherwise problematic. Students should ensure they are learning from reliable sources. Beware that over-reliance on these tools may also stunt the development of independent thinking and creativity. 

      Consequences of Violating the AI, IR & OT Use Policy

      Any student who violates the AI, IR & OT use policy is subject to the same disciplinary actions as for a Caltech Honor Code violation.
  • Ditch day policy (Ph106c): 
    • If ditch day falls on a lecture day, I will reschedule the lecture for the Saturday following ditch day, probably at 2:00 pm.  If ditch day falls on a problem set due day or the day before (Thursday or Friday), the set due date will be delayed to the following Monday, usual time.  If that Monday is a holiday, then the set will be due Tuesday at the usual time.

    • A delayed problem set due date due to ditch day has no impact on later problem set due dates, including 50% credit and silver bullet extensions.  If ditch day falls just before a holiday weekend, pushing the due date to Tuesday, there is the prospect of a very short following week to do the next set.  Plan accordingly by starting the next set over the weekend while finishing the set that was due during the week of ditch day.

    • Office Hours: 
      • If ditch day falls on a Thursday, Thursday and Friday office hours will be rescheduled for Saturday/Sunday.  
      • If ditch day falls on a Friday, then causality requires that we not change the Thursday office hour schedule.
      • If Monday is a holiday, shift the above by one day, availability permitting.  
      • So, for those of you who might be making decisions on acausal information, take account of the above information.
Grade Distributions

Note the very strong final exam vs. midterm exam correlation and the weak total exam vs. homework correlation.  Too much collaboration on homework can leave one unprepared for the non-collaborative exams.

Ph106b (2024; note that all histograms are before extra credit):




Ph106c (2024; note that all histograms are before extra credit):





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