Calculus II: Sequences and Series
Coursera
A Johns Hopkins course on Coursera covering sequences and series, Riemann sums, the definite integral, the Fundamental Theorem of Calculus, substitution and numerical integration. Learners finish able to approximate and compute integrals and apply them to data-driven modelling problems after a first differential calculus course.
More resources on Series & Sequences
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Khan Academy Series & Sequences
Khan Academy's Calculus 2 unit on infinite series, combining short videos with graded practice. It covers convergence and divergence tests, geometric and alternating series, power series, and Taylor and Maclaurin polynomials, so learners can decide whether a series converges and build polynomial approximations of functions.
Essence of calculus, chapter 10 (Taylor series!)
A 3Blue1Brown animated video from the Essence of Calculus series showing how Taylor polynomials are built by matching a function's derivatives at a point. Viewers come away understanding why each term appears, how approximations improve with more terms, and what radius of convergence means.
Introduction to Real Analysis
A standard undergraduate textbook building real analysis from the completeness of the reals through sequences, limits, continuity, differentiation, and the Riemann integral. Its graded exercises train students to construct epsilon-delta proofs independently.