Physics 464 and 511 Syllabus

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Physics 464/511, Fall 2016
Syllabus

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

Midterm
Exam 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
8-11AM Final exam, Hill 009

	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 $F^{\mu\nu}, {\bf dF=J}$, 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
Midterm Exam	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 8-11AM	Final exam, Hill 009

Joel Shapiro (shapiro@physics.rutgers.edu)

Last modified: Wed Dec 14 09:29:59 2016