Instructor

Professor William Loinaz
Office: 223 Merrill Science Center
Phone: (413) 542-7968
email: waloinaz [AT] amherst [DOT] edu
Office Hours: MWF 11 am - 12 pm
You're also welcome to drop by my office. If I'm in and free I'm happy to meet with you, but it's not so often during the day that I'm in and I'm free.

Grader: Matt Herman

Course Information

Course Catalog Description:

Schedule

• Class: Tuesday and Thursday 10:00-11:20, Merrill 211
• Problem Session (informal): Monday 10-11 pm, Physics student lounge
  

Requisites

Course requirements

• Attendance: Come to class. Lectures and in-class discussion will generally NOT duplicate the text, so don't assume you can just "get it from the book". It's your affair how you allocate your time and I won't explicitly penalize you for being absent, but if you're going to be absent please do me the courtesy of letting me know in advance, if possible. It's a small class--I'll notice if you're missing. And if you're consistently absent I'll want to know why. If you arrive late, please enter quietly at the back of the classroom. Obviously it will be your responsibility to find out what happened in the class you missed.

• Homework: I'll assign weekly problem sets, due Tuesdays@11:59 pm. You may leave your homework in my mailbox near the physics department office, or of course you may give it to me personally (please do NOT leave it in the box beside my office or stick it under my door). Homework submitted late without prior arrangement will receive a 50% penalty if submitted within three days of the due date (i.e. by Sunday @11:59 pm), and will receive no credit after that.

  Why do the homework?
  Since you're juniors, you've all figured this out by now. But, I'll say it anyway...

  I can't emphasize enough the importance of working the problems. In some of your classes homework is primarily evaluative; the point is for you to demonstrate what you've learned from the readings and lectures. In physics the homeworks are primarily instructional; you learn physics primarily by doing working problems. You must work the problems, think about the results, and understand any mistakes you've made if you wish to attain the type of understanding of the subject required of a working physicist. In at nutshell: If you can't work problems you don't know physics. I (or a grader) will grade the problems, and I'll hand out solutions. I encourage you to read the solutions and understand any mistakes immediately. If something doesn't make sense, ask me about it right away---don't wait until right before an exam.

  Homework extensions
  If you've got a good reason why you need an extension, come talk to me in advance. I'll usually grant the extension for some additional reasonable amount of time that we agree upon. However, I will not grant a homework extension without penalty if you ask for it on the day the homework is due, so don't ask for one. In general, life will be easier for both of us if you do your best to finish the problem set on time and hand in as much as you've been able to complete by the deadline. [If you need such a last-minute or post-facto extension due to extenuating circumstances (e.g. death in the family, sudden illness, travel problem), consult the Dean of Students or your Class Dean formally make such a request to me and suggest a rescheduled due date. You should also take this route if you need an extension but you don't want to tell me why (say, it's for personal or legal reasons). If you explain your reason to a Dean and the Dean tells me it's OK, that's good enough for me.]

• Exams: There will be two mid-term exams and a final, and these will serve as the primary evaluative mechanisms for the course. The exams will be closed-book, and all course material (lectures, handouts, text readings and homeworks) are fair game for the exam. I'll give you relevant formulae, so the exams will be not be memorization exercises. I tend to like problems that ask that you derive results utilizing key derivations from class, then use the result to do something new.

• Extensions: In the interest of fairness I will hold fast to the deadlines and policies above. In particular, I won't grant extensions to homeworks on the day they're due, and I won't reschedule the exam for an individual to a different day from the rest of the class. Should circumstances render such rescheduling unavoidable, you'll need to have the Dean of Students or your Class Dean contact me with a formal request for an extension and a suggested rescheduled time. Such matters should be taken care of before the exam if at all possible. If the matter is personal or confidential, the Deans need not provide me with any particulars, only their opinion that the rescheduling is reasonable.

  The College requires that all written work for a course except for a final be submitted by 5 pm on the last day of classes. The physics department takes this deadline seriously. After that day/time, no homework will be accepted.

Statement of Intellectual Responsibility: particulars for this course

• I strongly encourage you to discuss the homework problems with your classmates---discussing and debating the concepts and procedures is a very effective way to learn. However, the final write-ups of your assignments should be your own. For example, the copying homework solutions in part or in whole from other students (current or prior) or from other sources (commercial or otherwise) is unacceptable. I don't mind if you use other texts to learn from, and if the answer to a homework problem is worked as a example in some other text you may utilize it (although you should first try to solve it on your own as best you can). But in that case you should make an explicit reference to the source in your homework, and of course you still need to explain the solution to the problem in your own words. It goes without saying, but I'll say it anyway: tests are written without help.
• If you have any questions about what is or is not acceptable under this policy, please ask us. In all cases, the spirit of the Statement of Intellectual responsibility will take precedence over legalistic convolutions of the text.

How to get the most from this class:

• Come to class awake and on time.

• Do the relevant reading and read through the problems assigned for the week before the lecture (I'll announce the readings and problems in class and post them on the website). Even if you don't understand the readings fully at the time, try to get the broad outline of the material so you'll have some hooks on which to hang the ideas that we talk about in class.

  The roles of lectures and textbooks
  Lecture will not be a regurgitation of the text, a summary of all you need to know for the course, or a how-to guide for the homework. Rather, I'll try delve deeper into selected points. In lecture I'll cover material and do demonstrations related to the readings, but I won't feel obliged to be comprehensive in those places where I feel the text is adequate and I may focus only on a few points that I feel are particularly interesting or subtle. You shouldn't expect to understand what's going on without close study of the readings, and you should come to class with questions you have on the readings. Further, after we settle into the semester a bit, I expect the classes will become less lecture-oriented and more participatory; it will be difficult to reap the maximum benefit from that format if you're not sufficiently prepared to fully participate.

• Ask questions: in class, after class, during office hours, in problem sessions, in the hallways. Ask the questions you think you're supposed to know the answer to, the questions you're sure everyone else knows the answer to (they don't), questions about the overarching logic or the minute details, questions about the points or conclusions that weren't made that seem like they should follow. If individual arguments, their interconnection, or the entire point of the lecture don't seem clear to you, ASK. The main benefit to taking a class, especially at a small school like Amherst, is that you can ask questions of the experts.

• Work the problems: Start early. Try all of them. Struggle with them awhile yourself---some will be clear, simple exercises meant to familiarize you with a procedure, others will be meant to stretch your understanding (some will be intentionally vague, so that you have to clarify the picture before solving the problem). Be sure you can state what ideas (mathematical and physical) are being utilized in each problem; even if you still can't solve the problem you're most of the way there. The ability to work problems is not sufficient to claim an understanding of the physics, but it is a necessary step.

  For the problems you can't solve, talk to classmates, attend the problem sessions, or ask me. When you ask me, either try to give you just enough of a hint to get you through, or I'll guide you through the problem with a series of leading questions. I'll never just tell you how to do it. If you run out of time and don't finish the set, start earlier next week. When the solutions come out, look over them right away, before you've forgotten all of the points you were confused about. You think you'll just get clear on it before the next exam, but there's never as much time as you think.

• If things aren't going as you'd like, take an active role in improving your situation. Use all of the resources at your disposal. Step 1 is almost always to come talk to me. If you don't understand what's going on in lecture, the book, or the problems, if you feel like you can't keep up, come talk to me. I can help you, and I can point you to additional resources. Don't hide.

  On the other hand, if you find the class too slow for your liking, if you have questions that you aren't getting answers to, if you'd like more detail, if you are frustrated that we aren't digging deeply enough, if you crave more applications, come talk to me. I'm very happy to provide you with additional materials or explanations that will will stimulate you and challenge you at whatever level you can handle.

  One word of warning: Amherst College students tend to have lots of extracurriculars of all types. I support this, and I am occasionally willing to be flexible to facilitate your participation in range of activities, but don't let your extracurriculars overshadow your academics. If you become concerned that your courses are getting in the way of your extracurriculars, you've got the wrong mindset. Remember why you're here.

Grading:

• Homework: 20%
• First Midterm: 25%
• Second Midterm: 25%
• Final: 30%

Textbooks:

• Classical Mechanics (5th edition)
  Author: Tom W. D. Kibble
  ISBN: 1860944353
  Publisher: Imperial College Press
  [This will be the main course text. A copy of this book is on reserve at the Library]
  

• Classical Mechanics (1st edition)
  Author: John Taylor
  ISBN: 1-891389-22-X
  Publisher: University Science Books
  [This book has often been used as the text for this course over the past few years. I like it, although it's received mixed review from students. At a similar level to Kibble, but with more detail.]
  
  
• Classical Dynamics of Particle and Systems (5th edition)
  Author: Stephen Thorton and J. B. Marion (deceased)
  ISBN: 0-534-40896-6
  Publisher: Thomson Brooks-Cole
  [Sometimes used as a text for this course. The prose is a bit dry, but there's plenty of detail.]
  
  
• Physics (vol. 1), Hans Ohanian [a good general text for review of introductory material. used as Physics 23/32 text in the past.]
  
  
• Lectures in Physics, R. P. Feynman [Feynman's insights are always unique and worthwhile. You appreciate them more as you get older.]

• Div, Grad, Curl and All That (4th ed.), H. E. Schey [A usable introduction to vector calculus in a style that physicists find comfortable.]
• Mathematical Methods in the Physical Sciences (3rd ed.), Mary L. Boas [a comprehensive introductory mathematical physics book. very popular around here.]
• Mathematical Handbook (Schaum's Outline Series), Murray R. Spiegel [a convenient compendium of useful mathematical formulae, including integrals and special functions at a low, low price.]
• Basic Training in Mathematics, R. Shankar [textbook for Physics 27]

Mathematica Tutorials

We will use Mathematica fairly extensively in the homework, to obtain numerical solutions to problems that are not analytically solvable and to simplify plotting of results. If you've never used Mathematica before, or haven't used it much, the tutorials will help you get started. They were written by Professor Emeritus Bob Hilborn and revised by Rebecca Erwin '02. If you download the file and save it to the desktop with a .nb suffix in the name, your computer will recognize it as a Mathematica notebook and will start up Mathematica automatically when you double-click on the icon, provided you have Mathematica installed. Mathematica is installed on lots of the college's public machines, including on the computers in the Physics Department computer lab. Alternately, you can pay the $140 or so to buy the student version.

• Intro
  
• Functions
  
• SymbolicManipulation
  
• Plots
  
• Lists and Arrays
  
• Solving Differential Equations Numerically
  
• Complex Numbers
  
• Fourier Analysis
  
• Programming
  
• Statistics
  
• Input-Output Issues
  
• Solving Equations Numerically
  

Lecture Schedule

Week	Notes	Hmwk	Other
1. September 1	Space, Time, and Newton's Laws / Vectors Sept 2: Intro and Logistics / Space, time, and vectors Scope of classical mechanics, and scope of the course. Space and time: the background manifold we'll use. Geometrical vectors: define vectors as quantities that transform under rotations as the displacement. [Handouts: Student information sheet ] Sept 4: More about vectors Write general vectors in terms of orthonormal basis vectors. Einstein summation convention. In 2D, compare, contrast, and convert between Cartesian and polar basis vectors. Products of vectors and the geometrical interpretation: scalar and vector products. Levi-Civita symbol and Kronecker delta. Differentiation of vector functions: definition, versions of familiar calculus rules. Beware: basis vectors in non-cartesian coordinates have non-trivial derivatives! [Handouts: Vector analysis with diagrams (pp. 7-11 of Stedman's Diagrammatic Methods in Group Theory)]	Read: Kibble, Chap. 1 and Appendix A Problems: [Due Tuesday 9/9/08, 11:59 pm] Chap. 1: 7, 8, 10 Appendix A: 7 Chap. 2: 3, 7
2. September 8	Vectors / Newton's Laws / Linear Motion Sept 9: Vectors / Newton's Laws Differentiation of vectors: position, velocity, and acceleration in polar coordinates. Diagrammatic argument that derivatives of radial and polar vectors "make sense." Interpretation of terms in expression for acceleration vector. Finite rotations are not vectors (infinitesimal rotations are). Reference frames defined (inertial frames particularly important). Mass and force defined rather casually. Newton I addresses natural state of motion, serves to define inertial frames. Newton II is the "workhorse." Newton III (strong form and weak form). Consequence of Newton III: conservation of linear momentum for composite systems. Failures of NIII (in relativity, in electrodynamics). Linear motion: conservative forces and energy conservation. Sept 11: Linear Motion Conservative forces and conservation of energy: When F=F(x), can always find a first integral of motion (fn of x and v) which is constant in time. Show that T+V=E is constant in time. Show how the potential energy landscape can be used to give qualitative description of motion evey without explicit solution (stable and unstable equilibria, turning points). Small oscillations about equilibrium: Taylor expand about equilibrium point. Only second order and higher terms in small displacement are nonzero. If equilibrium is stable, displacements may remain small for all time; not so if unstable. In stable equilibrium, leading term is usually quadratic: harmonic oscillator potential. Harmonic oscillator potential: possible motions for SHO and inverted SHO potentials. Equation of motion. 2nd order linear ODE--general solution has two linearly independent terms and two constants of integration. Linear ODEs satisfy superposition principle. Show that superposition of solutions is also a solution for linear equations, and that it's not true in general for nonlinear equations. Guess solutions of exponential form, solve.	Read: Kibble, Chap. 2 Problems: Kibble, Chap. 2: 8, 9, 15, 20, 26, 30
3. September 15	Energy and Angular Momentum Sept 16: Title Sept 18: Title	Read: Problems:
4. September 22	Central Conservative Forces Sept 23: Title Sept 25: Title	Read: Problems:
5. September 29	Noninertial reference frames Sept 30: Title Oct 1: Exam 1 (7-9 pm) Oct 2: Title	Read: Problems:
6. October 6	Potential theory Oct 7: Title Oct 9: Title	Read: Problems:	Exam practice: P43F04 exam 1
7. October 13	Two-body and Many-body problems Oct 14: Fall Break Oct 16: Title	Read: Problems:
8. October 20	Rigid body motion Oct 21: Title Oct 23: Title	Read: Problems:
9. October 27	Lagrangian mechanics Oct 28: Title Oct 30: Title	Read: Problems:
10. November 3	Small oscillations and normal models Nov 4: Title Nov 6: Title	Read: Problems:
11. November 10	Hamiltonian mechanics Nov 11: Title Nov 13: Title	Read: Problems:	Exam practice: P43F04 exam 2
12. November 17	Geometry of dynamical systems Nov 18: Title Nov 19 (evening): Exam 2 Nov 20: Title	Read: Problems:
13. December 1	Chaos in Hamiltonian systems Dec 2: Title Dec 4: Title	Read: Problems:
14. December 8	Geometric mechanics Dec 9: Dec 11: Reading period	Read: Problems: