Search Rutgers   Search Physics Physics 464/511 Fall 2016 Lecture Notes   You will need an Adobe Acrobat Reader to view or print some of these files, the ones with .pdf extensions. If you don't have one, it is available for free: Lecture Notes Here are the short introduction to all the lectures Here are my full notes intended for the lectures.

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Latexed Lectures are available in full format for easier on screen reading, shown by the icon . They are also given reduced to two pages/side for more efficient printing, linked with .

Topics	Reference	Pages	Last Mod
Mathematical Preliminaries	Lecture A:	1-5	9/7/16
Vector Spaces and Fields	Lecture B:	1-19	9/12/16
More on Vector Spaces	Lecture C:	1-8	9/12/16
Manifolds	Lecture D:	1-14	9/22/16
Integration of n-forms	Lecture E:	1-9	9/26/16
Separation of Variables; Curvilinear Coordinates	Lecture F:	1-6	10/5/16
Infinite Series	Lecture G:	1-15	10/12/16
Review of Complex Variables	Lecture H:	1-18	10/24/16
Differential Equations	Lecture I:	1-14	10/25/16
Classical Orthogonal Polynomials	Lecture J:	1-5	11/3/16
Some particular important functions	Lecture K:	1-27	11/07/16
Fourier Analysis	Lecture L:	1-6	11/22/16
Integral Transforms	Lecture M:	1-9	11/23/16
Numerical Methods	Lecture N:	1-7	11/29/16
Special Relativity	Lecture O:	1-9	11/29/16
Equivalence Principle, Vierbein and Metric	Lecture P:	1-9	12/8/16
Parallel Transport	Lecture Q:	1-6	12/8/16
Geodesic Deviation, Curvature, and the Field Equations	Lecture R:	1-9	12/8/16

Supplementary Notes

• Vector Identities from cover of Jackson, or all on one sheet version.
• Notes on using indices correctly. view, print, This seems trivial, but I have seen many students have difficulties.
• Notes on totally antisymmetric tensors, or Levi-Civita symbols, ε_μνρ..., in 3-D Euclidean space: (view), (print), and in higher dimensional Euclidean or Minkowski space: (view), (print), including their use with matrices and determinants. The Levi-Civita symbol is also essential in curved spaces, but that is for another course.
• Note on the Surface "Area" of a D-dimensional ball, and on the Euler Γ function ( (view), (print))
  and on the Beta function and Γ(ε) for ε ˜ 0 ((view), (print))
• Rodrigues' Formula and Orthogonal Polynomials (view or print).
• Notes on Bessel functions (view), (print), giving in particular the orthonormality properties.
• On differential forms. If you have not seen differential forms before, you might want to look at my notes from 507, pages 153-4 on 1-forms and pp 167-175 on higher k-forms, or Zapolsky's notes. They are discussed in advanced calculus texts, e.g. Buck, "Advanced Calculus".
• Notes on Lie Algebras and Groups:
  • “ Lightning review of group”: (to view to print)
  • “Notes on Representations, the Adjoint rep, the Killing form, and antisymmetry of c_ij^k”: (to view to print).