Modules: slides, worked examples, practice links
Each module has a slide deck in the USTH style (use ← → keys or the buttons; full screen with ⛶), worked examples taken from the course problems, and links to the quizzes and the lab.
Chapter 1 · Functions, limits and continuity
M01 · Functions and their graphsLecture 1 · Tutorial 1Domain and range, parity, composition, transformations, the standard families of functions and modelling.49 practice questions on this module's topicsM02 · LimitsLectures 1–2 · Tutorial 2The limit idea, ε–δ definition, limit laws, one-sided limits, squeeze theorem, infinite limits and limits at infinity.40 practice questions on this module's topicsM03 · Continuity and the Intermediate Value TheoremLectures 2–3 · Tutorial 3 (first half)Continuity at a point and on an interval, types of discontinuity, continuous functions, the IVT.16 practice questions on this module's topics
Chapter 2 · Derivatives
M04 · The derivativeLecture 3 · Tutorial 3 (second half)Definition as a limit, tangent line, rates of change, differentiability versus continuity, higher derivatives.21 practice questions on this module's topicsM05 · Differentiation rules, implicit differentiation, related rates, linearizationLecture 4 · Tutorial 4Rules of differentiation, chain rule, implicit differentiation, related rates and linear approximation.34 practice questions on this module's topics
Chapter 3 · Applications of derivatives and antiderivatives
M06 · Extreme values, the Mean Value Theorem and the shape of a graphLecture 5 · Tutorial 5Absolute and local extrema, Rolle and the MVT, monotonicity, concavity, asymptotes and curve sketching.26 practice questions on this module's topicsM07 · Optimization, L'Hôpital's rule, Newton's method, antiderivativesLecture 6 · Tutorial 6Applied optimization, indeterminate forms, Newton's iteration and antiderivatives.25 practice questions on this module's topics
Chapter 4 · Definite integrals and their applications
M08 · The definite integral, the Fundamental Theorem and substitutionLecture 7 and the start of Lecture 8 · Tutorial 7Riemann sums, definite integral and its properties, FTC parts 1 and 2, substitution rule, average value.47 practice questions on this module's topicsM09 · Volumes, arc length and surface areaLecture 8 · Tutorial 8Volumes by cross-sections, disks, washers and shells; arc length; area of a surface of revolution.21 practice questions on this module's topics
Chapter 5 · Techniques of integration and improper integrals
M10 · Techniques of integrationLecture 9 · Tutorials 9 and 10 (first part)Integration by parts, trigonometric integrals, trigonometric substitution, partial fractions, choosing a strategy.43 practice questions on this module's topicsM11 · Improper integralsLectures 9–10a · Tutorial 10 (second part)Improper integrals of type I and II, p-integrals, the comparison theorems.17 practice questions on this module's topics
Chapter 6 · Sequences, series, power series and Taylor series
M12 · Sequences and infinite seriesLectures 10b–11 · Tutorial 11Limits of sequences, series, geometric and telescoping series, and the convergence tests.45 practice questions on this module's topicsM13 · Alternating series, power series, Taylor and Maclaurin seriesLectures 11–12 · Tutorial 12Absolute and conditional convergence, radius and interval of convergence, Taylor series and error estimates.30 practice questions on this module's topics