Course Web Site and Preliminary Syllabus

Mathematical Physics

Phy 301: Methods of Analytical Physics, Department of Physics & Astronomy, College of Engineering, Forestry, & Natural Sciences, University of Idaho, 2010 Fall, 3 hours, 3 credit hours.

Don't Panic
This is so cool.
Unchain your inner nerd.
In science, we are slaves to the truth---only error can set us free.
To be is to be the value of a variable.
                W.V. Quine (1908jun25--2000dec25), ``From a Logical Point of View'', p. 15

The course mottos: very reassuring I think.

Warning: This syllabus is subject to change at the discretion of the instructor. Any changes will be announced in class as well as made on this page.


  1. Instructor Information
  2. Syllabus Items
  3. Tentative Schedule
  4. Section 1 Posting grades by anonymous alias is allowed by NAU rules, but ordinary emailing grades (as opposed to GPS emailing grades) is not (see Ferpa Rules on Grades). You will need the supersecret username and password access the grade posting. The password protection adds a bit of security.
  5. Section 2 A fictitious section for testing purposes.
  6. Math Lectures These have only begun to be created.
  7. University Sites of Relevance Note Drop/Add day is 2010sep09.
  8. University Policy Statements for syllabi. A brief review after Instructor Information should be done.
  9. Class rosters for NAU faculty only This class is Phy 301 (5006).

  1. Instructor Information
  2. Instructor:
    Dr. David Jeffery, Physical Science Building, Rm 212, Tel: 928-523-9542, Email: David.Jeffery AT (also jeffery AT, jeffery AT, Office hours: as on instructor schedule. (If you need to see the instructor for sure, make an appointment. I'm usually happy to see students at any time that I'm relatively free.)

  3. Syllabus Items
    1. Jump in with Questions? at any time, of course.

    2. Course Web Site: The course web site URL is

      which is the page you are maybe viewing right now. This page is the preliminary syllabus and includes Syllabus Items and Tentative Schedule.

      This page is/will be/may be linked from the official physics department UG physics course page.

    3. Place and Time:

      1. Physical Science Building 321, TR 9:35--10:50 am (physics class schedulel)

    4. Pre/Corequisites: As specified in the online UG physics course page.

      1. Math 239: Differential Equations which is a corequisite. But to get into Math 239: Differential Equations, you had to have Math 238: Calculus III: Vector Calculus. In this class, there will be some overlap with differential equations, but we will try to avoid repeating vector calculus even though review of that might be very useful.

    5. Breaks: No breaks for 50-minute lectures. But in 75 minute lectures we will probably break for 5 minutes (and not more) at about the 45 minute mark.

    6. Textbook: Weber & Arfken, 2004, Essential Mathematical Methods for Physicists (hereafter Weber or WA as convenient). See also the publisher's Weber site and Google books Weber site which has online detailed contents.

      This is a somewhat more pedagogical version of the classic Arfken book: Arfken & Weber, 2005, Mathematical Methods for Physicists (hereafter usually Arfken). Yours truly actually uses Arfken (1970) as a reference---since that is the edition of Arfken that he's had for three dog ages.

      Weber is, of course, pretty good. All the good stuff presented with explication and enough rigor for most physicists.

      I have to admit that sometimes the pedagogy stuff is an annoyance to me. I prefer to see the general result and then specialize for examples: i.e., I like the original Arfken style better. But this may just be a matter of taste. Also maybe fewer, but choicer words would help in some cases I think.

        But all instructors think that about their texts.

      Alien mesmerized by words Alien mesmerized by words.

      There are also a few typos, wrong internal references (which happen all the time in revised editions), and even occasionally (in my view) subpar explication. Students (and instructors) shouldn't be afraid to challenge the text: usually the text is right, but even Arfken nods.

      Nonetheless you will probably treasure this book and keep it after the binding falls apart and it is in piles of fragments.

      We will hew pretty closely to Weber since, among other things, the instructor's knowledge is nearly textbook thin on many, but not all topics.

      We only cover part of Weber since there is more in Weber than can be covered in two semesters (maybe even three semesters) and we have only one: see Tentative Schedule below.

    7. Nature of the Course: This is an intermediate course in the math needed by physicists and also some engineers and others in physical sciences.

      There are lots of proofs, but the rigor is a bit low. The proofs are physicsy proofs often.

      In some cases, we just say someone has proved the result: e.g., the completeness of sets of Sturm-Liouville eigenfunctions. Even Weber (p. 511) and Arfken (1970, p. 443) give up on this one and just refer to Courant & Hilbert (1953, Vol. 1, Chap. 6, Sec. 3)---they pass the buck to great granddad.

      Much of the material will reappear in quantum mechanics, electromagnetism, and other physics contexts. There will be a synergy with those other courses.

      Some items might be continuously useful all your lives. Others you may never see again---but your darkness will have been enlightened---briefly anyway.

      ../../astro/astlec/lec000/infinity_eternity.png Math helps.

      Earthrise Earthrise from Apollo 11, 1969jul16. Credit: NASA.

      Alien consigning math to the flames Not in this course.

      This course will NOT be straight lecturing.

      You need to take notes, but you also will be challenged to solve questions in class in real time. So have your pen and paper handy.

      It's not going to be just passive learning.

      It's going to be at least somewhat active learning. Learning is literally forming neural connections in the brain. It takes training---it's like weight lifting.

      Some questions will be easy; some will be harder. A minute or so for easy ones up to maybe 5 minutes for really hard ones.

      Some questions are meant to be worked out individually, but others can be discussed and worked on in groups. Sometimes I just expect someone to answer the question in ordinary classroom fashion. There's no hard line between the three possibilities.

      I imagine most of you know each other already, but right now we will take a couple of minutes for you to introduce yourselves to your neighbors---even if you are already know them.

      Meanwhile I'm going to circulate quiz 1. It's voluntary, but it'll be me an idea of who you-all are and allow you to request posting of grades online by anonymous alias which is allowed by NAU rules, but email and telephone communication of grades is not (Ferpa Rules on Grades). A sample of online grade posting is the fictitious section 2 grades.

        Yours truly does NOT use Blackboard Vista---mostly because I'm used to doing what I do, but also Blackboard Vista is will disappear in 2011 and there's not much sense in learning it now.

      For anonymous alias, I require a signature.

      Actually, I will require a signature for all handed in work.

      Your signature, as always, is your mark of genuineness.

      I will also circulate a seating plan---no you don't have to sit in the same place ever again, but it will help me get started at learning names.

      Time passes---ready for me to go on?

      Is this a hard or an easy course?

      Fairly hard, but that's no change for any of us.

    8. Homeworks: There will be at least one homework for each chapter. I might break the homeworks up into a, b, c, etc. in some cases. They will usually be due about a week after the material has been covered.

      The homeworks will be posted along with their due dates online on the Tentative Schedule below. There is some flexibility about due dates.

      You will need the SUPERSECRET username and password access to the homeworks and solutions. (They are the same as for the grade posting. The username/password is just for a bit of extra security. The posted grades are really protected by the anonymous aliases.

      You get 5 marks just for a complete homework and maybe 5 marks for a marked question chosen by the instructor. I hope to mark one question on each homework, but I'm not sure of the time I'll have available. Maybe I can get a grader to help out.

      The solutions will be posted on the the Tentative Schedule eventually.

      Typically about 50 to 70 % or more of the full-answer exams questions will be drawn from the homeworks or, in the case of the FINAL, past exams also. Questions that reappear on the exams might be tweeked a bit from previous versions.

      Homeworks will count 10 % or so of the final grade.

      All homeworks count the same no matter what they are marked out of.

      Homeworks should be done with full effort.

      Study Weber and your notes. Then tackle the problems. At least at first try not to look back at notes or text. Try to drag the solution out by memory and thought. Try anything. Then look for help in text or notes. Then ask colleagues or yours truly for help.

      Looking up solutions online is FORBIDDEN.

      Lots of solutions are out there: Wikipedia, Wolfram MathWorld, Mathematical Physics Lectures (yours truly's very meagre start on a set of online mathematical physics lectures), etc.

      But it doesn't do you much good to just look at a solution---at least not until you've thought really hard about the problem---and it's FORBIDDEN.

      You have to form long-term memory with long-term neural connections of the subject material.

      You are all in STEM---you need those long-term neural connections---and most of the homework grades will be just for doing the work anyway.

    9. Exams: There will be 2 in-class exams of 75 minutes and a 2-hour COMPREHENSIVE FINAL.

      The in-class exams cover the material up to some cut-off point that will be announced in class and on the course web page in the Tentative Schedule.

      The final is about 50 % weighted or more on material since the last in-class exam and about 50 % weighted or less on all the material that came before the last in-class exam.

      The tentative dates for the exams are:

            Exam        Date     Solutions (posted post-exam)
            Exam 1      Sep30 R   Exam 1 solutions
            Exam 2      Dec09 R   Exam 2 solutions 
            Final Exam  Dec14 T   Final Exam solutions
                                  The final is at 7:30--9:30 am in the regular class room
                                  as specified by 
                                  Finals schedule for 2010 Fall.

      The exams will mainly consist of full-answer questions. A few easy multiple-choice questions may be included at the start as a warm-up. NO scantrons are needed.

      The exams are closed book.

      Calculators are permitted only for calculational use which may be slight. No saved formulae, solutions, programs---you are on your honor.

      Cell phones MUST be turned off and be out of sight.

      Make-up exams are possible, but students must ask for them promptly and avoid knowing anything about given exams.

    10. Evaluation and Grading: The 3 grading categories, their weightings, and their drops are:
            homeworks                  10 % or so   1 drop
            2 in-class exams           35 % or so   no drop
            1 comprehensive final      55 % or so   no drop
      Note that yours truly is leaving myself a bit of wiggle room on weighting. I don't think I will wiggle, but sometimes anomalies arise and a bit of wiggling is expedient.

      Each in-class exam is worth 22.5 % or so of the final grade.

      Attendance is NOT kept and NO marks are assigned for attendance. Students are encouraged to keep good attendance. Attendance keeps all of us yoked to the material and moving forward.

        In any course, just showing for the lectures keeps the student at least partially up to date just in itself.

        It's hard to fall completely behind if you attend lectures.

        And there is lots of evidence that good attendance correlates with achievement---but don't ask me to produce this evidence---it's what deans tell me.

      There are absolutely NO extra credits.

      Letter grades will be assigned per NAU grading policy--which allow instructors some freedom of interpretation on how do determine ``average''.

      The instructor uses a curve to automatically assign letter grades during the semester---if there are enough students to make a curve meaningful---if there arn't, the instructor just decides on letter grades.

      There is NO fixed scale.

      The curve is only used for current total grade: individual items (tests, etc. are NOT curved).

      For these curved grades the instructor uses an 11-grades scale: A,B+,B,B-,C+,C,C-,D+,D,D-,F. There are no pluses or minues with A and F.

      The final grades are decided on by the instructor directly---the curve is NOT used, except as a guide.

      In this course, I expect that the class GPA will be in the B- range (i.e., about 2.7) or a bit higher---but I am rather parsimonious about A's---just being in the upper half of the class is not enough.

      There do NOT have to be any D's or F's---the curve is NOT used for final grades.

      The NAU grading policy has only 5 levels, of course: A,B,C,D,F.

      The instructor will submit MIDTERM GRADES and FINAL GRADES as scheduled in the 2010 fall academic calendar.

      Remember that after an instructor has submitted FINAL GRADES, any adjustments (except for purely clerical errors) are NOT easy.

      This is true for any course.

      Students should make any queries about their final grades before the instructor submits them.

        About grades: they are important, but they are not everything.

        They are a measure of what you learn in a course: the learning itself is what counts ultimately.

        If you've worked hard in a course and learnt a lot, then that helps you will all the following courses and all the rest of your life.

        The best strategy is to work hard in a course subject to all other constraints in life.

        Of course, if you need a specific grade for some particular thing (e.g., a scholarship), don't undershoot.

        Don't imagine you can fine tune your effort just to get that specific grade.

      Aliens and Grades Beware of aliens bearing grades.

  4. Tentative Schedule of Topics from Weber
  5. No dated schedule has ever been adhered to by the instructor---except in summer semesters where it's easy to do.

    So there are no dates in this Tentative Schedule.

    But we have 8 chapters scheduled in my current plan and 15 weeks of classes, and so we will count on covering a chapter every two weeks or so.

    It is hoped we will cover all the scheduled chapters in the given order, but some omissions and permutations may occur.

    Additions are not too likely, but if we have time there is lots to add.

    The detailed contents of Weber have been used below.

    1. Chapter 1: Vector Analysis


      Since the material of this chapter has been covered by the students before, we will only cover selected topics for a bit of review and to bring out facets of particular interest.

      But the students are expected to know the whole chapter---since they have covered the material in earlier courses.

      1. 1.2: Scalar or Dot Product In brief.
      2. 1.3: Vector or Cross Product Just a short review primarily to introduce the Einstein summation rule (WA-146) and the Levi-Civita symbol (WA-153) and show its utility in doing proofs using cross products and curls. I suppose Levi-Civita invented his symbol.
      3. 1.4: The Triple Scalar Product and the Triple Vector Product In brief.
      4. 1.5: Gradient Just a short review of gradients and a look at Lagrange multipliers.
      5. 1.6: Divergence In brief with a brief look at the continuity equation.
      6. 1.7: Curl In brief with the Levi-Civita symbol.
      7. 1.8: Successive Applications of Del In brief, with the Levi-Civita symbol.
      8. 1.9: Vector Integration In brief.
      9. 1.10: Gauss's Theorem In brief.
      10. 1.11: Stokes's Theorem In brief.
      11. 1.12: Potential Theory In brief.
      12. 1.13: Gauss's Law and Potential Theory In brief.
      13. 1.14: Dirac Delta Function In brief.

    2. Chapter 2: Vector Analysis in Curved Coordinates and Tensors


      There is great material in this chapter and some of it we will relegate to more specialized courses.

      1. 2.3: Orthogonal Coordinates
      2. 2.4: Differential Vector Operators This covers the general expressions for Euclidean space for gradient, divergence, the Laplacian, and curl.
      3. 2.5: Spherical Polar Coordinates An important case and an example of specialization from the general case of Section 2.4.
      4. 2.6: Tensor Analysis We will do this section and some more of the chapter to be decided on.
      5. 2.7: Contraction and Direct Product Maybe.
      6. 2.8: Quotient Rule Maybe.
      7. 2.9: Dual Tensors Maybe.

    3. Chapter 5: Infinite Series We will do Sections 5.1--5.7.

      1. 5.1: Fundamental Concepts
      2. 5.2: Convergence Tests
      3. 5.3: Alternating Series Concerned with Liebniz criterion and absolute convergence.
      4. 5.4: Algebra of Series Concerned mainly with rearrangement of series.
      5. 5.5: Series of Functions Concerned mainly with uniform convergence.
      6. 5.6: Taylor Expansion
      7. 5.7: Power Series
      8. 5.8: Elliptical Integrals
      9. 5.9: Bernoulli Numbers
      10. 5.10: Asymptotic or Semiconvergent Series

    4. Chapter 6: Functions of a Complex Variable I We will do Section 6.1 only.

      1. 6.1: Complex Algebra
      2. 6.2: Cauchy-Riemann Conditions
      3. 6.3: Cauchy's Integral Theorem
      4. 6.4: Cauchy's Integral Formula
      5. 6.5: Laurent Expansion

    5. Chapter 7: Functions of a Complex Variable II:


    6. Chapter 8: Differential Equations


    7. Chapter 9: Sturm-Liouville Theory---Orthogonal Functions: We will probably cover this whole chapter.

    8. Chapter 11: Legendre Polynomials and Spherical Harmonics: We will probably cover this whole chapter. The Legendre polynomials and spherical harmonics are important examples of complete sets of eigenfunctions. They turn up as important entities in quantum mechanics among other things.

    9. Chapter 14: Fourier Series: We may cover this chapter depending on time depending on time available.

    10. Chapter 15: Integral Transforms: We may cover Sections 15.1--15.7 on the Fourier transform depending on time available.

    11. Chapter 16: Partial Differential Equations: We may cover some parts of this chapter depending on time available.

    12. Chapter 17: Probability: We may over some of this chapter if there is any time.