Below is a list of mathematics courses I have taught. Each course links to a directory archiving various course materials such as syllabi, notes, computer labs, sample exams, and daily schedules.
Course Description Banach spaces. Continuous linear transformations. Banach algebras. Hilbert Spaces. Orthonormal bases. Least-squares approximation. Compact operators and approximation. Riesz representation theorem. Applications to economics. Real-world data analysis via internet APIs, Yahoo Finance, and python.
Textbook: Functional Analysis and its Applications by Amol Sasane.
Course Description A rigorous treatment of differential calculus of one variable: sequences, limits, continuity, the derivative, the Riemann integral. Uniform convergence of functions. Metric spaces.
Textbook: Basic Analysis: Introduction to Real Analysis by Jiřı́ Lebl.
Course Description Classification of partial differential equations. Characteristics. Derivation of the classical linear second order equations. Fourier series. Separation of variables. Initial and boundary value problems.
Textbook: Partial Differential Equations for Scientists and Engineers by Stanley Farlow; Dover.
Course Description This course focuses on techniques of solving first and second order ordinary differential equations. Methods include separation of variables, variation of parameters, and the Laplace transform. Applications include linear and nonlinear models.
Textbook:
Fundamentals of Differential Equations by R. Kent Nagle , Edward B.
Saff , Arthur David Snider; Pearson.
First Course in Differential Equations with Modeling Applications by
Dennis Zill; Brooks/Cole.
Course Description Linear equations and matrices, vector spaces, subspaces, linear independence, bases, dimension, inner product spaces, linear transformations, eigenvalues and eigenvectors, orthogonal matrices and diagonalization
Textbook: Linear Algebra and its Applications by David Lay; Pearson.
Course Description This course will serve as a bridge between introductory and advanced mathematics. An introduction to the mathematical concepts and techniques of discrete mathematics: Topics include principles of logical argument, modular arithmetic and congrence classes, induction, sets, functions, relations, summations, the binomial theorem cardinality of sets.
Textbook: Mathematical Reasoning: Writing and Proof, Version 2.0 by Ted Sundstrom.
Course Description Review of vector algebra. Vector-valued functions. Divergence and curl. Multiple integrals; different coordinate systems. Line integrals, Greens Theorem, independence of path, conservative force fields. Surface integrals, Divergence Theorem, Stokes Theorem, Applications.
Textbook: Calculus for Scientists and Engineers: Early Transcendentals by Briggs, Cochran, and Gillett; Pearson.
Course Description Algebraic and geometric aspects of vectors, functions of several variables, partial derivatives, multiple integrals, vector calculus, line integrals, Green's Theorem.
Textbook: Calculus for Scientists and Engineers: Early Transcendentals by Briggs, Cochran, and Gillett; Pearson.
Course Description A study of applications of the definite integral, transcendental functions, integration techniques and infinite series.
Textbook: Calculus for Scientists and Engineers: Early Transcendentals by Briggs, Cochran, and Gillett; Pearson.
Course Description A study of limits, derivatives, continuity, differentiation and an introduction to the definite integral.
Textbook: Calculus for Scientists and Engineers: Early Transcendentals by Briggs, Cochran, and Gillett; Pearson.