UCLA Fall 2020 

Course:  Math 132: Complex Analysis for Applications 
Website:  Lectures 1 & 2: ccle.ucla.edu/course/view/20FMATH1321 
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/20SMATH31B1 
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 (1:001:50pm): ccle.ucla.edu/course/view/20WMATH131B1
Lecture 2 (2:002:50pm): ccle.ucla.edu/course/view/20WMATH131B2 
Description:  Metric spaces and 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 Spring 2019 

Course:  Math 131BH: Honors Analysis II 
Website:  ccle.ucla.edu/course/view/19SMATH131BH1 
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 AbelDirichlet 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 StoneWeierstrass Theorem; the ArzelaAscoli 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/18FMATH1321 
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/18WMATH131B1 
Description:  Metric spaces and 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 and 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. 