Calculus One (Full Course)
Professor Leonard
Full-length recorded lectures from Professor Leonard's first-semester calculus class, covering limits, continuity, derivatives and their applications, and introductory integration. Each topic is worked example by example at classroom pace, suited to self-study alongside a textbook.
More resources on Calculus
Calculus II: Series & Sequences
Chapter of Paul Dawkins's free Calculus II notes covering sequences, infinite series, partial sums, the integral, comparison, alternating, ratio and root tests, absolute convergence, power series and Taylor series, with worked examples. Learners can decide convergence and represent functions as power series.
Paul's Online Math Notes - Calculus I
Lamar University lecture notes covering limits, derivatives, and integrals, with worked examples and graded practice problem sets. Readers finish able to compute derivatives and integrals of standard functions and apply them to optimization and related-rates problems.
Complex Variables with Applications (MIT 18.04)
Complex analytic functions and their applications: Cauchy's theorem and integral formula, Taylor and Laurent series, residues for evaluating hard integrals, harmonic functions, conformal maps, two-dimensional fluid flow, and Laplace and Fourier transforms. Provides 14 lecture note files plus problem sets and exams with solutions.
Real Analysis (MIT 18.100A)
Rigorous foundations of calculus: real numbers, convergence of sequences and series, continuity, differentiability, the Riemann integral, sequences and series of functions, uniform convergence and interchange of limits. Includes 25 lecture videos, notes, problem sets and exams, and teaches how to read and construct proofs.
Essence of Calculus
Master integration with Grant Sanderson! This calculus course unlocks the essence of integration through intuitive visuals.
Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra (MIT RES.18-008)
Third part of a 1972 lecture series, covering complex variables, ordinary differential equations and linear algebra at the sophomore level. Provides 20 lecture videos (about 11.5 hours), study guides, supplementary notes and problem sets with solutions. Assumes single and multivariable calculus.