Analysis·Course
Mathematical Analysis
Mathematical analysis: limits, derivatives, integrals, series, multivariable functions, and applications in economics and physics
8
Modules
24
Articles
~2 h
Reading
IV
CLOs
§ 01 — 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 →
§ 02 — Learning outcomes
4 outcomes.
CLO I
Limits and Continuity
Compute limits of functions and examine continuity.
CLO II
Differential Calculus
Find derivatives, apply differentiation rules, and investigate functions.
CLO III
Integral Calculus
Compute definite and indefinite integrals and apply integrals to problems in geometry and physics.
CLO IV
Series and Multivariable Functions
Examine the convergence of series and find partial derivatives and extrema.
§ 03 — Practices