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.
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.]
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.
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.
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.
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.
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.
|1. September 7||
Sept 8: Intro to infinite series
Geometric series (finite and infinite). Some useful series.
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||
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|
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||
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||
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||
Oct 12: Break
Oct 14: Eigenvalues, eigenvectors, diagonalizing matrices
Oct 15: Geometric interpretation of similarity transformations and diagonalization
Oct 16: Diagonaizing hermitian matrices
|7. October 19||
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||
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||
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||
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||
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
|12. November 30||
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||
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||
Dec 14: second order ODEs with constant coefficients