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Physics 464/511,
Fall 2016


The syllabus will list the topic and readings for each lecture, the homework assignments, and the exams. But timing may vary --- we will progress as we can, so we may fall a bit behind.

This is preliminary, especially below the line that says so.

The syllabus is subject to change, often without advance notice, but the changes, other than timing, will probably be small for the material above the “preliminary” line. These changes will occur in response to the speed with which we cover material, individual class interests, and possible changes in the topics covered.

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My materials are generally available in view mode, indicated by , (one page per side, for viewing) and in print mode, indicated by , (two pages per side, for more efficient printing).

Supplementary readings in Vaughn pages xx are indicated Vxx, and in Arfken and Weber (6th Ed) as AWxx. These are often review of material I assume you know, or more exposition than I can cover.

  Date Topic Reading
L1 9/7 Math preliminaries Lect. A ; V1-18;
Lect. B pp 1-3
L2 9/9 Fields, vector spaces, $\nabla \lambda, \nabla\cdot\vec D, \vec \nabla\times\vec B, \nabla^2 \lambda$ Lect. B pp. 4-14; AW32-53; V37-42
L3 9/14 Integration, Helmholtz' theorem Lect. B pp. 14-18; AW54-61,64-65,95-100
HW1 9/19 Homework Assignment # 1: .
L4 9/16 Vector space, matrices, dual space,norm Lect. C ; V43-63
L5 9/21 Manifolds, metric, geodesic, 1-forms Lect. D pp.1-9; V92-114,135-37; AW151-
HW2 9/26 Homework Assignment # 2: .
L6 9/23 vector fields, n-forms. exact and closed Lect. D, pp. 9-14.
L7 9/28 Integration, Stokes' theorem, Hodge dual, Laplacian; Orthogonal coordinates Lect. E pp. 1-8; AW304-308; V116-134
L8 9/30 E&M in 4-D $F^{\mu\nu}, {\bf d*F=*J}$, Separation of variables Lect. E pp 8-9 Lect. F ; pp 1-6; AW554-560
HW3 10/3 Homework Assignment # 3: .  [Postponed to Oct. 5 in class]
L9 10/5 Some special functions; Infinite series; Lect F pp 3-6; Lect. G pp. 1-2.
L10 10/7 Elliptic integral, Generating functions, $B_n$, extended trapezoid rule and Euler-McClaurin formula. $\zeta(s)$ Lect. G, pp. 3-10.
L11 10/12 Infinite products, $\Gamma(a,x), \Gamma(x), E_1(x)$ Asymptotic expansion. Complex Variables. Lect. G, pp. 11-15; Lect. H p. 1; AW403-420
Pr 1 10/13 Project 1: .
L12 10/14 Contour integrals, analytic continuation, poles, Lect. H pp. 1-7; AW420-442
10/19 Midterm exam
L13 10/21 poles, Branch points and cuts. Lect. H, pp 8-13; AW447-470
HW5 10/24 Homework Assignment # 5: .
L14 10/26 $B(x,y)$; Mittag-Leffler,Steepest Descents; Lect. H, pp 13-18. AW489-495;
L15 10/28 Differential Equations of Physics, singular (regular and essential) and ordinary points; Frobenius' method. Fuchs' theorem, Wronskian. Lect H p18. Lect. I pp. 1-6. AW562-564
HW6 10/31 Homework Assignment # 6: .
L16 11/2 Solutions of Bessel's equation. Self-adjointness Lect. I pp 7-12, AW565-587
L17 11/4 measures, completeness, orthogonal polynomials Lect. I pp 12-14, AW622-651
Lect. J pp 1-5
HW7 11/7 Homework Assignment # 7: .
L18 11/9 Important functions: $\Gamma(z), B(u,v)$. $\Gamma(2z), \psi^{(n)}(z)$. Lect. K pp 1-7
L19 11/11 erfc, Bessel, $J_\nu$, Hankel, Neumann. Lect. K pp7-12
HW8 11/14 Homework Assignment # 8: .
HW9 11/21 Homework Assignment # 9: .
Pr 2 11/23 Project 2: .
L20 11/16 spherical Bessel, Legendre Polynomials, multipole moments $P_\nu$. Lect. K pp13-21
L21 11/18 Associated Legendre Polynomials $P^m_\ell$, Spherical Harmonics. Hermite, Laguerre, other orthogonal polynomials. Lect. K pp 21-27.
L22 11/23
at 1:40
Fourier Analysis. Integral transforms: Fourier, Laplace, Hankel, Mellon. Convolution. Lect. L pp 1-6
Lect. M pp 1-9
- - - 11/25 No class. Happy Thanksgiving
HW10 12/5 Homework Assignment # 10: .
What follows is very provisional, may change greatly, especially the timing
L23 11/30 Green's functions. Special Relativity Lect. M pp 4-9. Lect. O pp 1-2
L24 12/2 Special Relativity Lect. O pp 2-9
L25 12/7 Equivalence Principle, Vierbein and Metric Lect. P pp 1-9  
L26 12/9 Parallel Transport Lect. Q pp 1-6  
HW11 12/12 Homework Assignment # 11: . Not to be handed in or graded.
L27 12/14 Geodesic Deviation, Curvature, and the Field Equation Lect. R pp 1-9
Exam 12/20
Final exam, Hill 009

  Joel Shapiro (
  Last modified: Wed Dec 14 09:29:59 2016