Analysis·Course
Mathematical Analysis
Mathematical analysis: limits, derivatives, integrals, series, multivariable functions, and applications in economics and physics
Part of the Mathematics track — finish it for a verifiable diploma →
§ 01 — Orientation
New here?
What you'll be able to do, who this is for, how long it takes, and where to begin.
By the end, you will be able to
- 01Work rigorously with limits and continuity.
- 02Differentiate and understand what a derivative means.
- 03Integrate and apply the fundamental theorem.
- 04Handle series and functions of several variables.
- 05Prove analysis results, not just compute them.
Who this is for
How long it takes
- Quick orientationSkim the opening module and the cheatsheet to get the shape of it.~2 h
- Full read-throughRead every article once, in order.~2 h
- Mastery pathRead, take the quizzes, and space out your reviews.~2 weeks
- APA
Stoa. (2026). Mathematical Analysis [Online course]. Stoa. https://stoa.school/course/math-analysis
- MLA
Stoa. “Mathematical Analysis.” Stoa, 2026, https://stoa.school/course/math-analysis.
- Chicago
Stoa. “Mathematical Analysis.” Stoa. Accessed September 1, 2026. https://stoa.school/course/math-analysis.
§ 02 — Curriculum
8 modules.
Each module is a small unit. Most read in sequence — but a determined reader can begin anywhere.
- M ISets and Limits of SequencesAxioms of the real numbers, set theory, limits of numerical sequences3 articles
18 minBegin → - M IISingle-Variable Functions: Limit and ContinuityFunction limits, continuity, Weierstrass and Bolzano theorems3 articles
18 minBegin → - M IIIDerivative and DifferentialDifferentiability, differentiation rules, Taylor’s formula3 articles
18 minBegin → - M IVThe Riemann IntegralDefinite integral, Newton–Leibniz theorem, integration techniques3 articles
18 minBegin → - M VSeriesNumerical and functional series, convergence tests, power series3 articles
18 minBegin → - M VIMultivariable FunctionsDifferentiation, multiple integrals, extrema of multivariable functions3 articles
18 minBegin → - M VIIVector AnalysisLine and surface integrals, Green’s, Stokes’, and Gauss’s formulas3 articles
18 minBegin → - M VIIIMeasure Theory and the Lebesgue IntegralLebesgue measure, Lebesgue integral, limit transition theorems3 articles
18 minBegin →
§ 03 — Learning outcomes
4 outcomes.
Compute limits of functions and examine continuity.
Find derivatives, apply differentiation rules, and investigate functions.
Compute definite and indefinite integrals and apply integrals to problems in geometry and physics.
Examine the convergence of series and find partial derivatives and extrema.
§ 04 — Practices