Instructor

Professor William Loinaz
Office: 223 Merrill Science Center
Phone: (413) 542-7968
email: waloinaz [AT] amherst [DOT] edu
Office Hours:
M 1:30-2:30, W 1:30-3:00 [subject to change as the semester goes on].
For my scheduled office hours, you can either drop in or make an appointment. To meet with me at some other time, it will be easiest if you email me for an appointment.
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: Shenglan Qiao, Neha Wadia

Course Information

Course Catalog Description:

Schedule

• Class: MWF 11:00-11:50 am, Th 1-1:50 pm, Merrill 315
• Problem Session (informal): TBA, but probably Monday evening, time 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 (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 (Wed. Oct. 5): 25%
• Second Midterm (Wed. Nov. 16): 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 (4th edition)
  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.]
• Electricity and Magnetism, E. M. Purcell [an elegant and sophisticated intro electromagnetism textbook. Includes a treatment of AC circuits using complex numbers.]

• 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 [sometimes used as a 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 5	Infinite series Sept 7: Course Logistics / Intro to Infinite Series Geometric series (finite and infinite). Some useful series. Sept 8: Convergence (positive series) Convergent and divergent series defined. Convergence defined via a limit of partial sums. Test for convergence: Preliminary test. Absolutely convergent series defined. Tests for convergence of series of positive terms: (1) Comparison test (2) Integral test Sept 9: Convergence (positive and alternating series) Tests for convergence of series of positive terms: (2) Integral test, (3) Ratio test, (4) "Special" comparison test. Alternating series test. Introduce conditionally convergent series. Conditionally convergent series can be rearranged to sum to any value (Riemann series theorem).	Read: Boas, Chap. 1 Problems: none this week (no grader yet!)
2. September 12	Series / Complex numbers Sept 12: Power Series Power series defined. Convergence of power series. Interval of convergence. Allowed manipulations of power series. Taylor series expansions around the origin. Sept 14: Power series / Defining and representing complex numbers Taylor series expansions around a general point. Complex numbers from solutions to the quadratic equation. The imaginary number i. General complex number as real part + imaginary part. Complex numbers as points in the Argand diagram. Polar representation. Complex conjugate of a complex number. Sept 15: Complex numbers: algebra, infinite series Addition, subtraction, multiplication, and division of complex numbers. Modulus of a complex number. Complex equations. Partial sums of complex series. Convergence, absolute convergence of a complex series defined. An absolutely convergent series is convergent. Tests for convergence. Complex power series. Sept 16: Complex power series Disc of convergence generalizes the interval of convergence. Rules for manipulating complex power series are similar to those for real power series. Euler's formula.	Read: Boas, Chap. 2 PS1 -- Problems: 1.2.6, 1.4.6, 1.5.4, 1.6.30, 1.9.22, 1.15.30, 1.15.31, 1.15.32, 1.16.2, 1.16.10, 1.16.14, 1.16.18 [due 11:59 pm Tuesday Sept. 20, 2011]
3. September 19	Complex numbers Sept 19: Elementary functions of complex numbers Powers and roots of complex numbers. Exponential functions, trig functions, and hyperbolic trig functions of complex numbers. Sept 21: Elementary functions of complex numbers Logs of complex numbers. Complex roots and powers of complex numbers. Inverse trig and inverse hyperbolic trig functions of complex numbers. Application: Simple harmonic oscillator using complex numbers. Sept 22: Complex numbers in physics applications Simple harmonic oscillator using complex numbers. Why is the harmonic oscillator so important and ubiquitous in physics? Because for a potential with a stable equilibrium point, for sufficiently small excursions around the equilibrium point the potential the potential looks like a harmonic oscillator. Show this explicitly with Taylor series expansion of potential about stable equilibrium point. Set up the damped, sinusodally driven (AC) LRC series circuit problem. Sept 23: AC circuits using complex numbers Damped, sinusodally driven (AC) LRC series circuit using complex numbers. Talk about the importance of resonance phenomena generally in physics.	Read: Boas, finish Chap. 2, start Chap. 3 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 [due 11:59 pm Tuesday Sept. 27, 2011]
4. September 26	Linear algebra Sept 26: Matrices and Gaussian elimination Matrices, matrix notation, transpose of a matrix. Start to talk about solving systems of linear equations using row reduction Gaussian elimination. Express systems of linear equations in matrix form. Solving systems of linear equations using Gaussian elimination. Possible outcomes: no solutions, unique solution, infinitely many solutions. Sept 28: Linear equations and determinants Relate categories of possible outcomes to relationships among (rank of M, rank of A, number of unknows). Calculate determinant of nxn square matrix, where n=1, n=2, and n general. Some relations to help calculate determinants more quickly. Sept 29: Vectors Cramer's rule for solving systems of linear equations using determinants. Algebra of vectors, geometric and in terms of components. Cartesian unit vectors. Dot product: its calculation and its properties. Cross product: its calculation. Einstein summation convention, Kronecker delta function. Sept 30: Analytic geometry with vectors / Matrix operations	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
5. October 3	Linearity and linear transformations Oct 3: Matrix multiplication / Inverse of a matrix Oct 5: Functions of matrices / linearity Oct 5: Exam 1 7-10 pm location TBA Oct 6: Transformations in the plane: general linear and orthogonal Oct 7: Rotations and reflections in 2D and 3D / Linear independence	Read: Boas, Chap. 3 PS 4 -- Problems: Boas, 3.5.13, 3.5.37, 3.5.44, 3.6.6, 3.6.17, 3.6.30, 3.7.25, 3.7.33, 3.8.16, 3.8.21
6. October 10	Title Oct 10: Break Oct 12: Title Oct 13: Title Oct 14: Title	Read: Boas, Chap. 3 PS 5 -- Problems: Boas, 3.9.15, 3.9.17, 3.10.2, 3.10.4, 3.10.10, 3.11.16, 3.11.19, 3.11.30
7. October 17	Applications of similarity transformations Oct 17: Title Oct 19: Title Oct 20: Title Oct 21: Title	Read: Start Boas, Chap. 4 PS 6 -- Problems: Boas 3.11.35, 3.11.43, 3.11.46, 3.11.51, 3.11.60, 3.11.62
8. October 24	Multivariable calculus: differential calculus Oct 24: Title Oct 26: Title Oct 27: Title Oct 28: Title	Read: Boas, Chap. 4 PS 7 -- Problems: see Problem set 7
9. October 31	Multivariable calculus: differential calculus Oct 31: Title Nov 2: Title Nov 3: Title Nov 4: Title	Read: Boas, Chap. 4, start Chap. 5 PS 8 -- Problems: 4.1.5, 4.1.14, 4.1.20, 4.1.22, 4.2.6, 4.4.1, 4.4.9, 4.4.15, 4.5.6, 4.6.9 [due Wednesday, November 9, 11:59 pm]
10. November 7	Multivariable calculus: integral calculus Nov 7: Title Nov 9: Title Nov 10: Title Nov 11: Title	Read: Boas, Chap. 6, and read "div, grad, curl, and all that" PS 9 -- Problems: 4.7.6, 4.7.16, 4.7.23, 4.7.25, 4.8.5, 4.9.9, 4.10.5, 4.11.2, 4.11.5, 4.11.10, 4.12.5, 4.12.6, 4.12.16, 5.2.6, 5.2.10 [due 11:59 pm, Tuesday November 29, 2011]
11. November 14	Vector calculus Nov 14: Title Nov 16: Title Nov 16 (evening): Exam 2 Covering through the end of Chap. 4. Nov 17: Title Nov 18: Title	Read: Problems: (carried over from last week)
12. November 28	Vector calculus Nov 28: Title Nov 30: Title Dec 1: Title Dec 2: Title	Read: Boas, Chap. 6; div, grad, curl, and all that PS 10 -- Problems: 5.2.22, 5.2.40, 5.2.48, 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 [due 11:59 pm, Tuesday December 6, 2011] Problem set 10
13. December 5	Fourier series / ODEs Dec 5: Title Dec 7: Title Dec 8: Title Dec 9: Title	Read: Boas, Chap 6, and Div, Grad, Curl, and All That PS 11 -- Problems: 6.8.16, 6.8.18, 6.8.19, 6.8.20, 6.9.3, 6.9.12, 6.10.6, 6.10.9, 6.11.8, 6.11.14, 6.11.21, 6.12.26, 6.12.30 [due 11:59 pm, Tuesday December 13, 2011]
14. December 12	2nd order differential equations with constant coefficients Dec 12: Title Dec 14: Title	Read: Problems: