Instructor

Professor William Loinaz
Office: 223 Merrill Science Center
Phone: (413) 542-7968
email: waloinaz [AT] amherst [DOT] edu
Office Hours:
MTWThF 9:30-10:30 am, MW 1:30-3 [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: David Zhang, Rohan Mazumdar

Course Information

Course Catalog Description:

Schedule

• Class: MWF 12:00-12:50 pm, Th 1-1:50 pm, Merrill 315
• Problem Session (informal): Monday evening, time 9-10 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. 5): 25%
• Second Midterm (Tues. 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.]

• 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 8	Infinite series Sept 7: Intro to infinite series Geometric series (finite and infinite). Some useful series. Convergent and divergent series defined. Sept 9: Convergence (positive series) 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. Sept 10: 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.	Read: Boas, Chap. 1 PS 1 -- Problems: 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 [due Tues. Sept. 14, 11:59 pm]
2. September 13	Series / Complex numbers Sept 13: Conditionally convergent series / Power series Conditionally convergent series can be rearranged to sum to any value (Riemann series theorem). Power series defined. Convergence of power series. Interval of convergence. Allowed manipulations of power series. Taylor series expansions around the origin. Sept 15: 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. Addition, subtraction, and multiplication of complex numbers. Sept 16: Complex infinite series 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. Disc of convergence generalizes the interval of convergence. Rules for manipulating complex power series are similar to those for real power series. Sept 17: Elementary functions of complex numbers Euler's formula. Powers and roots of complex numbers. Exponential functions, trig functions, and hyperbolic trig 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 [due Tues. Sept. 21, 11:59 pm]
3. September 20	Complex numbers / Linear algebra Sept 20: Elementary functions of complex numbers / Applications of complex numbers: SHO 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: Applications of complex numbers: SHO, AC circuits Simple harmonic oscillator using complex numbers. Damped, sinusodally driven (AC) LRC series circuit using complex numbers. Sept 23: Applications of complex numbers: n-source interference / Intro to linear algebra n-source interference using complex numbers. 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. Sept 24: Solving systems of linear equations by Gaussian elimination / Determinants Solving systems of linear equations using Gaussian elimination. Possible outcomes: no solutions, unique solution, infinitely many solutions. Define rank of matrix. 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.	Read: Boas, start Chap. 3 PS 3 -- Problems: see Problem set 3
4. September 27	Linear algebra Sept 27: Determinants / Basics of vectors Sept 29: Analytic geometry with vectors / Matrix operations Sept 30: Matrices: multiplication, inverses, functions of matrices Oct 1: Linearity and linear transformations	Read: Boas, Chap. 3 PS 4 -- Problems: see Problem set 4
5. October 4	Linearity and linear transformations Oct 4: Rotations and reflections: 2D and 3D Oct 5: Exam 1 7-10 pm Merrill 220 Covers all we've done in class up through Friday Oct. 1 and everything in the book up to middle of p. 117. Oct 6: Linear dependence and independence / Homogeneous equations Oct 7: Homogeneous equations / Matrix trivia Oct 9: Linear vector spaces	Read: Boas, Chap. 3 No new problem set
6. October 11	Eigenvalues and eigenvectors Oct 11: Break Oct 13: Eigenvalues, eigenvectors, diagonalizing matrices Oct 14: Geometric interpretation of similarity transformations and diagonalization Oct 15: Diagonalizing hermitian matrices	Read: Boas, Chap. 3 PS 5 -- Problems: see Problem set 5
7. October 18	Applications of similarity transformations Oct 18: Orthogonal rotations in 3D / Powers of matrices Oct 20: Simplifying equations for conic sections / Normal modes of vibrating systems Oct 21: General vector spaces Oct 22: Introduction to multivariable calculus / power series in two variables	Read: Start Boas, Chap. 4 PS 6 -- Problems: see Problem set 6
8. October 25	Multivariable calculus: differential calculus Oct 25: Total differentials for functions of one and two independent variables Oct 27: Chain rule / implicit differentiation Oct 28: Implicit differentiation / reciprocals of derivatives Oct 29: Extremum problems: one variable, two variables, and extrema with constraints	Read: Boas, Chap. 4 PS 7 -- Problems: see Problem set 7
9. November 1	Multivariable calculus: differential calculus Nov 1: Lagrange multipliers Nov 3: Lagrange multipliers Nov 4: Change of variables / Differentiating integrals Nov 5: Multiple integrals	Read: Boas, Chap. 4, start Chap. 5 PS 8 -- Problems: see Problem set 8
10. November 8	Multivariable calculus: integral calculus Nov 8: Applications of multiple integrals Nov 10: Applications of multiple integrals / Change of variable in integrals (2D) Nov 11: Cylindrical and spherical coordinates / Jacobian determinants Nov 12: Jacobian determinants / Surface integrals / Triple scalar product	Read: Boas, Chap. 6, and read "div, grad, curl, and all that" PS 9 -- Problems: see Problem set 9
11. November 15	Vector calculus Nov 15: Vector triple products / differentiating vectors Nov 16 (evening): Exam 2 Nov 17: Differentiating vectors / directional derivatives and gradients Nov 18: Gradients / the "del" operator Nov 19: Vector calculus	Read: Problems: (see last week)
12. November 29	Vector calculus Nov 29: curls, gradients, and path independence of line integrals Dec 1: Calculating potentials / Green's theorem Dec 2: Green's theorem / flux Dec 3: Divergence theorem	Read: Boas, Chap. 6; div, grad, curl, and all that PS 10 -- Problems: see Problem set 10
13. December 6	Fourier series / ODEs Dec 6: Stokes theorem Dec 8: Stokes theorem / Fourier series Dec 9: Fourier series / first order ODEs Dec 10: first order ODEs / second order homogeneous ODEs with constant coefficients	Read: Boas, Chap 6, and Div, Grad, Curl, and All That PS 11 -- Problems: see Problem set 11
14. December 13	2nd order differential equations with constant coefficients Dec 13: second order ODEs with constant coefficients Dec 15: second order ODEs with constant coefficients	Read: Problems: