Daniel J Hoff

UCLA Department of Mathematics




UCLA
Winter 2018
Course:

Math 131B: Analysis II
Website: TBA
Description: Metric spaces, point-set 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/17F-MATH115A-1
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, Gram-Schmidt orthogonalization, and normal and self-adjoint operators.
Course:

Math 255A: Functional Analysis
Website: ccle.ucla.edu/course/view/17F-MATH255A-1
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/17S-MATH131B-2
Description: Metric spaces, point-set 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/17W-MATH132-1
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/16F-MATH132-1
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.