# Daniel J Hoff

## UCLA Department of Mathematics

 UCLA Fall 2020 Course: Math 132: Complex Analysis for Applications Website: Lectures 1 & 2: ccle.ucla.edu/course/view/20F-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 Spring 2020 Course: Math 31B: Integration and Infinite Series Website: ccle.ucla.edu/course/view/20S-MATH31B-1 Description: Calculus of transcendental functions. Methods and applications of integration, including integration by parts and partial fractions. Improper integrals. Sequences and series; absolute and conditional convergence; the ratio and root tests. Power series and Taylor series.
 UCLA Winter 2020 Course: Math 131B: Analysis II Website: Lecture 1 (1:00-1:50pm): ccle.ucla.edu/course/view/20W-MATH131B-1 Lecture 2 (2:00-2:50pm): ccle.ucla.edu/course/view/20W-MATH131B-2 Description: Metric spaces and 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 Spring 2019 Course: Math 131BH: Honors Analysis II Website: ccle.ucla.edu/course/view/19S-MATH131BH-1 Description: Compactness and several characterizations in metric spaces. The Baire Category Theorem. Continuity, including connections with connectedness, compactness, and uniform continuity. Discontinuities of real functions; monotonic functions. Differentiability and rigorous treatment of the main theorems of differential calculus, including Darboux's Theorem, L'Hospital's Rule, and Taylors' Theorem. The Darboux formulation of the Riemann Integral; Riemann's formulation and their equivalence; the Lebesgue characterization of Riemann integrability. The Fundamental Theorem of Calculus and integration by parts. Improper integrals and the Cauchy and Abel-Dirichlet criteria. Sequences and series of functions; pointwise and uniform convergence with applications to continuity, integration, and differentiation; Dini's Theorem. Power series and radius of convergence. Spaces of functions; the Stone-Weierstrass Theorem; the Arzela-Ascoli Theorem. The Banach Contraction Mapping Fixed Point Principle with application to ODEs. Briefly: Inner products on periodic functions, L^2 convergence of Fourier series and Plancherel's Theorem.
 UCLA Fall 2018 Course: Math 132: Complex Analysis for Applications Website: ccle.ucla.edu/course/view/18F-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 Winter 2018 Course: Math 131B: Analysis II Website: ccle.ucla.edu/course/view/18W-MATH131B-1 Description: Metric spaces and 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 and 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.