
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
; V118;
Lect. B pp 13  
L2  9/9  Fields, vector spaces, $\nabla \lambda, \nabla\cdot\vec D, \vec \nabla\times\vec B, \nabla^2 \lambda$  Lect. B pp. 414; AW3253; V3742  
L3  9/14  Integration, Helmholtz' theorem  Lect. B pp. 1418; AW5461,6465,95100  
HW1  9/19  Homework Assignment # 1: .  
L4  9/16  Vector space, matrices, dual space,norm  Lect. C ; V4363  
L5  9/21  Manifolds, metric, geodesic, 1forms  Lect. D pp.19; V92114,13537; AW151  
HW2  9/26  Homework Assignment # 2: .  
L6  9/23  vector fields, nforms. exact and closed  Lect. D, pp. 914.  
L7  9/28  Integration, Stokes' theorem, Hodge dual, Laplacian; Orthogonal coordinates  Lect. E pp. 18; AW304308; V116134  
L8  9/30  E&M in 4D $F^{\mu\nu}, {\bf d*F=*J}$, Separation of variables  Lect. E pp 89 Lect. F ; pp 16; AW554560  
HW3  10/3  Homework Assignment # 3: . [Postponed to Oct. 5 in class]  
L9  10/5  Some special functions; Infinite series;  Lect F pp 36; Lect. G pp. 12.  
L10  10/7  Elliptic integral, Generating functions, $B_n$, extended trapezoid rule and EulerMcClaurin formula. $\zeta(s)$  Lect. G, pp. 310.  
L11  10/12  Infinite products, $\Gamma(a,x), \Gamma(x), E_1(x)$ Asymptotic expansion. Complex Variables.  Lect. G, pp. 1115; Lect. H p. 1; AW403420  
Pr 1  10/13  Project 1: .  
L12  10/14  Contour integrals, analytic continuation, poles,  Lect. H pp. 17; AW420442  
Midterm Exam 
10/19  Midterm exam  
L13  10/21  poles, Branch points and cuts.  Lect. H, pp 813; AW447470  
HW5  10/24  Homework Assignment # 5: .  
L14  10/26  $B(x,y)$; MittagLeffler,Steepest Descents;  Lect. H, pp 1318. AW489495;  
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. 16. AW562564  
HW6  10/31  Homework Assignment # 6: .  
L16  11/2  Solutions of Bessel's equation. Selfadjointness  Lect. I pp 712, AW565587  
L17  11/4  measures, completeness, orthogonal polynomials  Lect. I pp 1214, AW622651 Lect. J pp 15  
HW7  11/7  Homework Assignment # 7: .  
L18  11/9  Important functions: $\Gamma(z), B(u,v)$. $\Gamma(2z), \psi^{(n)}(z)$.  Lect. K
pp 17  
L19  11/11  erfc, Bessel, $J_\nu$, Hankel, Neumann.  Lect. K pp712  
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 pp1321  
L21  11/18  Associated Legendre Polynomials $P^m_\ell$, Spherical Harmonics. Hermite, Laguerre, other orthogonal polynomials.  Lect. K pp 2127.  
L22 
11/23 at 1:40 
Fourier Analysis. Integral transforms: Fourier, Laplace, Hankel, Mellon. Convolution.  Lect. L
pp 16
Lect. M pp 19  
    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 49. Lect. O pp 12  
L24  12/2  Special Relativity  Lect. O pp 29  
L25  12/7  Equivalence Principle, Vierbein and Metric  Lect. P pp 19  
L26  12/9  Parallel Transport  Lect. Q pp 16  
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 19  
Exam  12/20 811AM 
Final exam, Hill 009 