UCLA Winter 2018 

Course:  Math 131B: Analysis II 
Website:  TBA 
Description:  Metric spaces, pointset topology, Cauchy sequences and completeness, compact metric spaces. Continuous functions on metric spaces, continuity and connectedness, continuity and compactness. Sequences and series of functions, pointwise and uniform convergence. Uniform convergence and continuity, integration, and differentiation. Power series and real analytic functions. Inner products on periodic functions, L^2 convergence of Fourier series and Plancherel's Theorem. 
UCLA Fall 2017 

Course:  Math 115A: Linear Algebra 
Website:  ccle.ucla.edu/course/view/17FMATH115A1 
Description:  Techniques of proof, abstract vector spaces over a field, linear transformations and matrices; change of basis; determinants and eigenvector theory; diagonalizability; inner product spaces, GramSchmidt orthogonalization, and normal and selfadjoint operators. 
Course:  Math 255A: Functional Analysis 
Website:  ccle.ucla.edu/course/view/17FMATH255A1 
Description:  Hilbert spaces, Banach spaces, and fundamentals of operator theory. Topological vector spaces and weak topologies. Basics of Banach algebras and C*algebras. Spectral Theorem and functional calculus for normal operators. 
UCLA Spring 2017 

Course:  Math 131B: Analysis II 
Website:  ccle.ucla.edu/course/view/17SMATH131B2 
Description:  Metric spaces, pointset topology, Cauchy sequences and completeness, compact metric spaces. Continuous functions on metric spaces, continuity and connectedness, continuity and compactness. Sequences and series of functions, pointwise and uniform convergence. Uniform convergence and continuity, integration, and differentiation. Power series and real analytic functions. Inner products on periodic functions, L^2 convergence of Fourier series and Plancherel's Theorem. 
UCLA Winter 2017 

Course:  Math 132: Complex Analysis for Applications 
Website:  ccle.ucla.edu/course/view/17WMATH1321 
Description:  Introduction to basic formulas and calculation procedures of complex analysis of one variable relevant to applications. Topics include Cauchy/Riemann equations, Cauchy integral formula, power series expansion, contour integrals, residue calculus. 
UCLA Fall 2016 

Course:  Math 132: Complex Analysis for Applications 
Website:  ccle.ucla.edu/course/view/16FMATH1321 
Description:  Introduction to basic formulas and calculation procedures of complex analysis of one variable relevant to applications. Topics include Cauchy/Riemann equations, Cauchy integral formula, power series expansion, contour integrals, residue calculus. 
UCSD Summer Session II 2015 

Course:  Math 20E: Vector Calculus 
Website:  Archived at: www.math.ucla.edu/~hoff/Math20E/ 
Description:  Change of variable in multiple integrals, Jacobian, line integrals, Green's theorem. Vector fields, gradient fields, divergence, curl. Spherical/cylindrical coordinates. Taylor series in several variables. Surface integrals, Stoke's theorem. Conservative fields. 