Math

Pre-Algebra
Overview: operations on integers, fractions, mixed numbers and decimals; ratio, proportion and percentages; working with variable expressions; interpretation of statistical graphs; measurement and geometry; and an introduction to polynomials and graphing.
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Intermediate Algebra
Overview: Sets and the real number system, polynomial and rational expressions, exponents and radicals, word problems, systems of linear equations, and graphs.
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College Algebra Overiew: Linear and quadratic equations and inequalities; graphs of equations, including lines, circles, parabolas; composition, inverses of functions; transformations of graphs; linear and quadratic models; polynomials; exponentials, logarithms; counting; probability.
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Linear Algebra
Overview: Vectors, dot and cross products, lines and planes, projections. Vectors in n-space. Systems of Linear equations. Matrix algebra and linear transformations, inverses. Spaces and subspaces. Linear independence, basis and coordinates, dimension, rank. Determinants, Cramer's Rule. Eigenvectors, eigenvalues and diagonalization with applications. Orthonormal bases and symmetric matrices.
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Differential Equations
Overview: Separable and first-order linear equations with applications, 2nd order linear equations with constant coefficients, method of undetermined coefficients, simple harmonic motion, 2x2 and 3x3 systems of linear ODE's with constant coefficients, solution by eigenvalue/eigenvectors, nonhomogenous linear systems.
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Precalculus I
Overview: Review of high school algebra. Linear and quadratic equations and inequalities; graphs of equations, including lines, circles, parabolas; composition, inverses of functions; transformations of graphs; linear and quadratic models; equations and inequalities involving polynomials and rational functions; exponentials and logarithms, with applications.
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Precalculus II
Overview: Trigonometric functions and inverse trigonometric functions: definitions, graphs, identities, applications; real and complex zeros of polynomials; polar coordinates; DeMoivre's Theorem; conic sections; solutions of linear systems by substitution and elimination; systems of nonlinear equations and systems of inequalities; arithmetic sequences and geometric series.
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Calculus I
Overview: Tangent lines; limits and continuity; differentiation: definition, basic rules, chain rule, rules for trig, exp and log functions; implicit differentiation; rates of change, max-min, related rates problems; 2nd derivative test; curve sketching; linear approximation and differentials; L'Hospital's rule; integration: definition, antidifferentiation, area; simple substitution; volumes of solids by cross sections and shells; work; average value of a function.
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Calculus II
Overview: Integration: Fundamental Theorem of Calculus, Riemann integral; Techniques of integration, including integration by parts, simple trig substitutions, partial fractions. Basic numerical integration; improper integrals; arc length; area of surface of revolution. Separable differential equations, Euler's method, exponential growth and decay. Parametric curves and polar coordinates. Sequences, series, power series, comparison and ratio tests, Taylor series and polynomials. Vectors in three dimensions, dot product, cross product; lines, planes, cylinders, quadric surfaces; cylindrical and spherical coordinates. Functions of several variables, partial derivatives, differentials, gradient, maxima and minima.
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Multivariable Calculus
Overview: Multivariable calculus: Curves in space, arc length and curvature, velocity and acceleration. Limits and continuity, partial differentiation, local extrema, exact differentials, chain rule, directional derivative and gradient, Lagrange multipliers, 2nd derivative test. Double integration, volume and other applications, polar coordinates, triple integration, cylindrical and spherical coordinates.
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Probability and Statistics

Introduction to Statistics and Probability
Overview: Summarizing data in graphs, computation of descriptive statistics, sample spaces, classical probability theory, rules of probability, probability distributions, estimating population parameters, hypothesis testing, correlation and regression, one-way ANOVA, contingency tables, Goodness-of-Fit test.
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Spanish

Introduction An Accelerated Spanish
Overview: This course consists of 11 lessons, 9 exercises and 5 assignments and uses PowerPoint presentations and accelerated learning methodology to help the beginning or intermediate student to learn Spanish more easily and in a fun way.
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