Instructor

Professor William Loinaz
Office: 223 Merrill Science Center
Phone: (413) 542-7968
email: waloinaz [AT] amherst [DOT] edu
Office Hours: Wed 1:30-2:30 pm, Th 11-12 am, Th 2-3 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: Ojeh Bikwa, Emine Altunas

Course Information

Course Catalog Description:

Schedule

• Class: MWF 12:00-12:50 pm, Th 1-1:50 pm, Merrill 211
• Problem Session (informal): Monday evening, time 8-9 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 (tenatively) 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 Friday @11:59 pm), and will receive no credit after that.

  Why do the homework?
  Since you're sophomores and 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 (Tues Oct. 6): 25%
• Second Midterm (Tues. Nov. 17): 25%
• Final: 30%

Textbooks:

• Mathematical Methods in the Physical Sciences (3rd edition)
  Author: Mary L. Boas
  ISBN-13: 978-0471198260
  Publisher: Wiley
  [a comprehensive introductory mathematical physics book. very popular around here. This will be the main course text. A copy of this book is on reserve at the Library.]
  
• Div, Grad, Curl, and All That: An Informal Text on Vector Calculus
  Author: H. M. Schey
  ISBN-13: 978-0393925166
  Publisher: W.W. Norton & Co.
  [A usable introduction to vector calculus in a style that physicists find comfortable. A copy of this book is on reserve at the Library.]

• Physics (vol. 1 & 2), Hans Ohanian [a good general text for review of introductory physics material. used as Physics 23/24 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.]

• 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 [previous textbook for Physics 27]

Mathematica Tutorials

We may use Mathematica 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 7	Infinite series Sept 8: Intro to infinite series Geometric series (finite and infinite). Some useful series. [Handouts: ] Sept 9: Convergence (positive series) Definition of convergent and divergent series. Illustrate dangers of manipulating divergent (and even some convergent) series. Convergence of series as limit of sequence of partial sums. Tests for absolute convergence of series/convergence of positive terms: (1) comparison test, (2) integral test. Sept 10: Convergence (alternating series) Convergence of series of positive terms (cont'd): (3) ratio test, (4) "special" comparison test. Alternating series. Conditionally convergent series. Convergence or divergence of series is not affected by multiplying by a nonzero constant or changing a finite number of terms. Two convergent series may be added term-by-term. Power series. Sept 11: Power series Range of values of x for which power series converges is the "interval of convergence." In the interval of convergence, the power series defines a function. Rules for manipulating power series (in the interval of convergence). Expanding functions in about some point in a Taylor series. If a function is make of simpler parts, we can expand the parts in power series and combine the expansions.	Read: Boas, Chap. 1 PS 1 -- Problems: Boas, 1.2.6, 1.4.6, 1.5.4, 1.6.30, 1.9.22, 1.15.32, 1.16.2, 1.16.10, 1.16.14, 1.16.18
2. September 14	Complex numbers Sept 14: Defining and representing complex numbers Sept 16: Complex infinite series Sept 17: Elementary functions of complex numbers Sept 18: More elementary functions of complex numbers	Read: Boas, Chap. 2 PS2 -- Problems: Boas, 2.5.21, 2.5.48, 2.5.60, 2.6.13, 2.7.15, 2.10.25, 2.11.18, 2.16.9, 2.16.10, 2.16.12
3. September 21	Complex numbers / Linear algebra Sept 21: Applications of complex numbers: AC circuits Sept 23: Applications of complex numbers: n-source interference / Intro to linear algebra Sept 24: Solving systems of linear equations by Gaussian elimination Sept 25: Determinants	Read: Boas, Chap. 3 PS 3 -- Problems: Boas, 3.2.13, 3.2.14, 3.2.18, 3.3.4, 3.3.17, 3.4.20, 3.4.23, 3.5.13, 3.5.37, 3.5.44 [It's optional to check your problems by computer for those problems in which you're told to do so.]
4. September 28	Linear algebra Sept 28: Basics of vectors Sept 30: Analytic geometry with vectors / Matrix operations Oct 1: Matrices: multiplication, inverses, functions of matrices Oct 2: Linearity and linear transformations	Read: Boas, Chap. 3 PS 4 -- Problems: Boas, 3.6.6, 3.6.17, 3.6.30, 3.7.25, 3.7.33, 3.8.16, 3.8.21, 3.9.15, 3.9.17, 3.11.16, 3.11.19, 3.11.30, [3.11.43, 3.11.51 --- these last two problems are carried over to next week's problem set.] (due Thurs. Oct. 16, 11:59 pm)
5. October 5	Linearity and linear transformations Oct 5: Rotations and reflections: 2D and 3D Oct 6: Exam 1 (7-10 pm) Oct 7: Linear dependence and independence / Homogeneous equations Oct 8: Homogeneous equations / Matrix trivia Oct 9: Linear vector spaces	Read: Finish Boas, Chap. 3 PS 5 -- Problems: Boas, Chap. 3: [carried over from last problem set: 3.11.43, 3.11.51], 3.11.35, 3.11.46, 3.12.3, 3.12.7, 3.12.14, 3.12.18
6. October 12	Eigenvalues and eigenvectors Oct 12: Break Oct 14: Eigenvalues, eigenvectors, diagonalizing matrices Oct 15: Geometric interpretation of similarity transformations and diagonalization Oct 16: Diagonaizing hermitian matrices	Read: Problems:
7. October 19	Applications of similarity transformations Oct 19: Orthogonal rotations in 3D / Powers of matrices Oct 21: Simplifying equations for conic sections / Normal modes of vibrating systems Oct 22: General vector spaces Oct 23: Introduction to multivariable calculus / power series in two variables	Read: Start Boas, Chap. 4 PS 6 -- Problems: Boas: 3.14.7, 3.14.15, 4.1.5, 4.1.14, 4.1.20, 4.1.22, 4.2.6, 4.4.1, 4.4.9, 4.4.15 (dues Tuesday, Oct. 27)
8. October 26	Multivariable calculus: differential calculus Oct 26: Total differentials for functions of one and two independent variables Oct 28: Chain rule / implicit differentiation Oct 29: Implicit differentiation / reciprocals of derivatives Oct 30: Extremum problems: one variable, two variables, and extrema with constraints	Read: Boas, Chap. 4 PS 7 -- Problems: Boas: 4.5.6, 4.6.9, 4.7.6, 4.7.16, 4.7.23, 4.7.25, 4.8.5, 4.9.9, 4.10.5, 4.11.2
9. November 2	Multivariable calculus: differential calculus Nov 2: Lagrange multipliers Nov 4: Lagrange multipliers Nov 5: Change of variables / Differentiating integrals Nov 6: Multiple integrals	Read: Boas, Chap. 4, start Chap. 5 PS 8 -- Problems: Boas: 4.11.5, 4.11.10, 4.12.5, 4.12.6, 4.12.16, 5.2.6, 5.2.10, 5.2.22, 5.2.40, 5.2.48
10. November 9	Multivariable calculus: integral calculus Nov 9: Applications of multiple integrals Nov 11: Applications of multiple integrals / Change of variable in integrals (2D) Nov 12: Cylindrical and spherical coordinates / Jacobian determinants Nov 13: Jacobian determinants / Surface integrals / Triple scalar product	Read: Boas, Chap. 6, and read "div, grad, curl, and all that" PS 9 -- Problems: Boas 5.3.30, 5.4.13, 5.5.10, 5.6.11, 6.3.18, 6.4.6, 6.6.3, 6.6.13, 6.7.8, 6.8.7 [due Tues. Dec. 1, 11:59 pm]
11. November 16	Vector calculus Nov 16: Vector triple products / differentiating vectors Nov 17 (evening): Exam 2 Nov 18: Differentiating vectors / directional derivatives and gradients Nov 19: Gradients / the "del" operator Nov 20: Vector calculus	Read: Problems:
12. November 30	Vector calculus Nov 30: curls, gradients, and path independence of line integrals Dec 2: Calculating potentials / Green's theorem Dec 3: Green's theorem / flux Dec 4: Divergence theorem	Read: Boas, Chap. 6; div, grad, curl, and all that PS 10 -- Problems: Boas, 6.8.13, 6.8.16, 6.9.3, 6.9.12, 6.10.6, 6.10.9, 6.11.8, 6.11.14, 6.11.21, 6.12.30
13. December 7	Fourier series / ODEs Dec 7: Stokes theorem Dec 9: Stokes theorem / Fourier series Dec 10: Fourier series / first order ODEs Dec 11: first order ODEs / second order homogeneous ODEs with constant coefficients	Read: Boas, Chap 7.1-7.11 and Chap. 8.1-8.7 Problems: suggested problems (not to turn in): 7.2.6, 7.4.16, 7.5.9, 7.7.1, 7.8.15, 7.9.11, 8.2.16, 8.3.5, 8.4.10, 8.5.12, 8.6.25, 8.6.36, 8.7.5
14. December 14	2nd order differential equations with constant coefficients Dec 14: second order ODEs with constant coefficients	Read: Problems: