Free University Mathematics Courses Samples
PDFs
A complete Calculus II solutions sample featuring 18 fully worked problems on Taylor and Maclaurin series, known-series transformations, differentiation and integration of power series, intervals of convergence, Taylor polynomials, and error bounds.
A university-level Calculus III final-exam sample featuring 10 questions on vectors, partial derivatives, directional derivatives, multiple integrals, cylindrical and spherical coordinates, Lagrange multipliers, vector fields, line integrals, Green’s Theorem, and the Divergence Theorem.
Homework 5 from an eight-part university Linear Algebra assignment series. This sample includes 10 questions on linear transformations, standard matrices, rotations, reflections, projections, kernel and range, one-to-one and onto mappings, and compositions of transformations.
Videos
Calculus I – Mastering the Squeeze Theorem
Video 3 of a seven-video Calculus I series covering the Limits and Continuity chapter. This lesson explains the Squeeze Theorem through seven worked problems, including oscillating functions, constructing upper and lower bounds, evaluating limits step by step, and recognizing when the theorem can or cannot be applied.
University Probability – Expected Value and Variance
Video 10 of a complete 16-video university probability course. This lesson explains expected value as a weighted average and variance as a measure of dispersion, using probability distributions, step-by-step calculations, graphical interpretations, and practical examples to compare predictable and highly variable outcomes.