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Jacob Shapiro's Teaching Page at the Physics Department of Princeton U.

Contact

Please e-mail me at jacobshapiro@princeton.edu.

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Teaching

Analysis 1 Recitation Sessions

The course website contains logistical information as well as the homework and their solutions. Below are "scripts" (summaries) of the recitation sessions I held:

If you plan to submit your homework, it would make me very happy if you used LyX.

Analysis 2 Recitation Sessions

The course website contains logistical information as well as the homework and their solutions. Below are "scripts" (summaries) of the recitation sessions I held:

If you plan to submit your homework, please consider typing it into the computer using, for example, .

Full hand-written notes (in German, 91MB) were kindly provided by Simon Vonlanthen.

Quantum Field Theory 2 Recitation Sessions

The course website contains logistical information as well as the homework and their solutions. Below is some relevant material:

If you plan to submit your homework, please consider typing it into the computer using, for example, .

Analytical Mechanics Recitation Sessions

The course website contains logistical information as well as the homework and their solutions, the lecture notes, and forums in which you may ask questions.
I warmly recommend the book by V. I. Arnold which you may download electronically freely as ETHZ students. Another book to consider is H. Goldstein's.
Below is some relevant material from the sessions I held:
I usually will provide the unredacted solutions after the submission date has passed, for those people who are struggling with the German official solutions.
WeekSummary of Recitation SessionRedacted or Full Solutions
INo classes
IIOrganization info, some simple gradient exercises, and hints for HW1Full Solutions of HW1
IIICommon pitfalls for HW1 and hints for HW2Full Solutions for HW2
IVCommon pitfalls for HW2 and hints for HW3Full Solutions for HW3
VCommon pitfalls for HW3 and hints for HW4Full Solutions for HW4
VICommon pitfalls for HW4Full Solutions for HW5
VIIa discussion about natural units and the difference between central and conservative forcesFull Solutions for HW6
VIIINo summary of the recitation session this week.
Most of the presentation which was done in class is contained in the (redacted) solutions.
Full Solutions for HW7
and a Mathematica notebook for the plots.
IXSome remarks about natural frequenciesFull Solutions for HW8
XNo summary for this weekFull Solutions for HW9
XINo summary for this weekFull Solutions for HW10
XIIA short note about Legendre Transformations
A note about Hamilton's Least Action Principle seen as zero of the Frechet derivative of the action
Full Solutions for HW11
XIIIFlowsFull Solutions for HW12
XIVThe Hamilton-Jacobi equation and Poincare TransformationsFull Solutions for HW13

If you plan to submit your homework, please consider typing it into the computer using, for example, .

Mechanics of Continua Recitation Sessions

The course website contains logistical information as well as the homework and their solutions, the lecture notes, and forums in which you may ask questions.
Below is some relevant material from the sessions I held:
I usually will provide the unredacted solutions after the submission date has passed, for those people who are struggling with the German official solutions.
WeekSummary of Recitation SessionRedacted or Full Solutions
ISome Reminders from Analysis 2 and Linear AlgebraRedacted Solutions of HW1
IIDifferential Geometry Perspective on Curvilinear Coordinates, Official Sol-n of HW1Q2Redacted Solutions of HW2
IIINoneRedacted Solutions of HW3
IVNoneRedacted Solutions of HW4
VNoneRedacted Solutions of HW5
VIThere will be a note about the finite element method to solve the Navier equation.Not yet
VIINoneHints for HW7

Additional Material:

If you plan to submit your homework, please consider typing it into the computer using, for example, .

General Relativity Recitation Sessions

The course website contains logistical information as well as the homework and their solutions, the lecture notes, and forums in which you may ask (public) questions.

As for textbooks (in order of relevance to you):

Proseminar in Disordered Transport

During the spring semester of 2018 I had the pleasure to mentor three graduate students in Oded Zilberberg's Proseminar on transport in disordered media. What my group concentrated on mainly dealt with using super-Gaussian integrals (like path integrals) a la Efetov's 1995 manuscript to re-write the DC conductivity of a disordered material, and after a stationary phase approximation, derive a non-linear sigma model. This model can then be analyzed, and ultimately one can prove Poisson statistics in a localized regime, or non-zero conductivity can be shown in the delocalized regime. The students gave oral and written reports, the latter of which are available below:

Calculus I Lecture -- Math UN1101 (Section 02)

Columbia's fine print: General information:
Location:207 Mathematics Building
Time:Mondays and Wednesdays 4:10pm-5:25pm (runs through January 23rd until May 6th 2019 for 28 sessions)
Recitation SessionsFridays 2pm-3pm in Hamilton 602 run by Donghan Kim. First session on Feb 1st, 2019. Attendance not mandatory but warmly recommended.
Office hours:Tuesdays 6pm-8pm and Wednesdays 5:30pm-7:30pm (or by appointment) in 626 Mathematics (starting Jan 29th)
Teaching Assistants:
TAs office hours:Will be held in the help room (502 Milstein Center) at the following times: – Mat: Fridays 10am-12pm. – Donghan: Thursdays 4pm-6pm. – Ziad: Tuesdays 4pm-6pm.
Misc. information:Calculus @ Columbia
Getting help:Your best bet is the office-hours, and then the help room. If you prefer impersonal communication, you may use the Piazza website to pose questions (even anonymously, if you're worried). TAs will monitor this forum regularly.
Textbook:Lecture notes are available and will be updated on a weekly basis. I will do my best to follow the the Columbia Calculus curriculum so as to make sure you can go on to Calculus II smoothly. I will use material from various textbooks, some of which include: Spivak, Apostol, Courant and sometimes Stewart just to set the timeline (since this is what Columbia's curriculum is based upon).
Homework assignments:Assignments will appear on this website after before the Monday lecture every week and are due at the the Monday lecture of the following week. You do not have to hand in assignments every week, but you may present your solutions to the TAs or me to gain extra credit (see below) You must hand-in your assignments weekly to a satisfactory level in order to be able to take the exam. If there are reasons why you cannot hand-in your assignment at some week please write me an email directly.
Grading:There will be two midterms during lecture time (see below for dates) and one final (after the last lecture). Your grade is (automatically) the higher of the following two options: [Option A] The final carries 50% weight, the midterms each carry 25% weight for a total of 100% of your grade. [Option B] The final carries 40% weight, the midterms each carry 25% weight for a total of 90% of your grade. The remainder 10% is given to you if you succeed in accomplishing the following task at least three times during the semester: show up (no appointment necessary) to one of the office hours of the TAs or me, successfully orally present a solution to one of the homework assignments whose solution has not been published yet (should take you not more than 10 minutes max), and in the same occasion submit a neatly written down solution to the thing you just presented. Due to the results of the first midterm I have decided to change the rules a bit. You are now required to hand-in homework assignments weekly. If you do to a satisfactory level you may come to the exam and will get 10 points of your final grade. I am still undecided about how to divide the grades between the final and the second midterm, but you will not be negatively affected in any way if you scored low on the first midterm.

Tentative Schedule (will be updated to reflect what happened in class as the weeks elapse):
DateWeekLecture #ContentsSpecial events
Wed Jan 23I1SetsFirst class
Mon Jan 28II2Sets and functionsHW1 published (note typos corrected!); HW1 solutions published
Wed Jan 30II3Functions
Mon Feb 4III4Limits of sequencesHW2 published ; HW2 solutions published
Wed Feb 6III5Limits of sequences
Mon Feb 11IV6Limits of functionsHW3 published ; HW3 solutions published
Wed Feb 13IV7Limits of functions and continuityPractice Midterm 1 published Practice Midterm 1 Detailed Solutions published (note: After careful review and getting some feedback, I have decided that the actual midterm will be of the same format, but contain less questions on each part, and also that partial credit will be given to your calculation (contrary to the instructions in the practice midterm as it stands now) in case your answer is incorrect. So your explanation could help you salvage points if your final answer is wrong. As before, the material for the midterm is everything in the lecture notes from the beginning up to and not including derivatives).
Mon Feb 18V8Review
Wed Feb 20V9Midterm IMidterm 1 and Midterm 1 solutions
Mon Feb 25VI10Derivatives 3HW4 published ; HW4 solutions published
Wed Feb 27VI11Derivatives 4
Mon Mar 4VII12Derivatives 5HW5 published (typo fixed) HW5 Solutions published
Wed Mar 6VII13Derivatives 6
Mon Mar 11VIII14Derivatives 7HW6 published ; HW6 Solutions published
Wed Mar 13VIII15Derivatives 8
Mon Mar 25IX16Review
Wed Mar 27IX17Midterm 1.5Practice Midterm 1.5 published ; Practice Midterm 1.5 Solutions published ; HW7 published HW7 Solutions published ; Midterm 1.5 published ; Midterm 1.5 Solutions published ;
Mon Apr 1X18Integrals 1HW8 published ; HW8 Solutions published
Wed Apr 3X19Integrals 2
Mon Apr 8XI20Integrals 3HW9 published ; HW9 Solutions published
Wed Apr 10XI21Integration: Fundamental theorem of calculus
Mon Apr 15XII22Applications of derivatives: extremal pointsHW10 published ; HW10 Solutions published ; Practice Midterm 2 published ; Practice Midterm 2 Solutions published
Wed Apr 17XII23Applications of derivatives: Convexity
Mon Apr 22XIII24Review of practice midterm 2
Wed Apr 24XIII25Midterm 2Midterm 2 published ; Midterm 2 Solutions published
Mon Apr 29XIV26Review towards finalHW11 published ; HW11 Solutions published
Wed May 1XIV27Review towards final
Mon May 6XV28Review towards finalPractice Final published ; Practice Final Solutions published ; HW12 published ; HW12 Solutions published
Mon May 13 4:10pmXV*Final published and Final Solutions published .

PHY103 - Newtonian mechanics

No material has appeared here--all content was collected on Princeton's canvas website.

PHY104 - Electricity and magnetism