Physics 4321 / 7305 Syllabus - Fall 2009

Fourier series: vector dot-product analogy; orthogonality and closure;
                expansions (even, odd, neither); Fourier transforms.
                
Generalized Functions / Distributions: delta function, theta step Heavyside
                function, and their derivatives and Laplace transforms;
                applications to electric charge distributions.

Ordinary Differential Equations: order, linearity, homogeneity; 
                examples simple harmonic oscillator, damped SHO,
                damped driven SHO, resonance, Green functions.

Coordinate Systems; Scale functions; Divergence, Gradient, Curl, Laplacian.

Partial Differential Equations: Separation of variables, Cartesian
                coordinates in 1, 2, and 3 dimensions, Cylindrical
                Polar coordinates, Spherical Polar coordinates,
                example Laplace's Equation, Green functions.

Group Theory:   Discrete groups: cyclic groups Zn; dihedral groups Dn; symmetric groups Sn; alternating groups An.
                Group multiplication tables. Representations. Sporadic groups.
                Lie groups: SO(2); SO(3); SO(n); SU(n); Sp(2n).

Complex Analysis: Roots of Unity, Cauchy-Riemann equations, analyticity, contour integrals,
                  residues, Laurent expansion

Chaos: Sensitive Dependence on Initial Conditions Nonlinearity, Fractals, Hausdorf Dimension, 
               Lyapunov Exponents, Hennon Map, Logistic Map, 
               Cantor Dust, Sierpinski Gasket, Menger Sponge, Mandelbrot Set, Julia Set,
               Chua's Circuit, Period 3 Implies Chaos

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