2.2 Table summary of topics to study

2.2.1 Math 121A

ch.	title	topics	Exam
1	series	infinite series, power series,def. of covergence, tests for convergence,	1
		test for alternating series, power series, binomial series
2	complex numbers	finding circle of convergence (limit test), Euler formula	1
		power and roots of complex numbers, log, inverse log
4	partial differentiation	total diffenertials, chain rule, implicit differentiation	1
		partial diff for max and minumum, Lagrange muktipliers,
		change of variables Leibniz rule for differnetiation of integrals
14	complex functions	Def. of analytic fn, Cauchy-Riemann conditions, laplace equation,	1
		contour integrals, Laurent series, Residue theorm, methods
		of finding residues, pole type, evaluating integrals by
		residue, Mapping, conformal
7	Fourier series	expansion of function in sin and cosin, complex form, how to find	2
		coeff, Dirichlet conditions, different intervals, even/odd, Parseval’s

15	Laplace/Fourier transforms	Laplce transform, table, how to use Laplace to solve	F
		ODE, Methods of finding inverse laplace, partial fraction, convolution,
		sum of residues, Fourier transform, sin/consine transforms, Direc Delta
		Green method to solve ODE using impluse
9	Calculus of variations	Euler equation solving, Setting up Lagrange equations, KE, PE	F
		Solving Euler with constrainsts

2.2.2 Math 121B

ch.	title	topics	Exam
11	Special functions	Gamma, Debta, Error function	1
12	Series solution to ODE	Legendre, Bessel, orthogonality	1
13	PDE	separation of variables, Laplace (steady state),	2
		Heat (diffusion), Wave equation. Laplce in different coordinates,
		Laplacian, Wave in different coord.Poission equation
16	Probability	Baye’s formula, how to find probability, methods	final
		of counting, Random variable concept, mean, Var, SD,
		distributions (Binomial, Gauss, Poisson)