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Mathematics · 210–279 · 25 concepts

University Mathematics

Reasoning-first University mathematics: 25 concepts, each with a clear explanation, a fully worked example, and self-check questions.

Practice at this level — free

Single-variable calculus

Limits & continuity Derivatives & differentiation rules Applications of derivatives Integrals & the fundamental theorem of calculus Techniques of integration Applications of integration Infinite sequences & series Power & Taylor series Parametric & polar calculus

Multivariable calculus

Multivariable functions & partial derivatives Gradients & directional derivatives Multiple integrals Vector calculus (Green's, Stokes', divergence)

Linear algebra

Vectors & vector spaces Linear transformations & matrices Determinants Eigenvalues & eigenvectors Inner product spaces & orthogonality

Differential equations

First-order differential equations Higher-order & linear differential equations Systems of differential equations Laplace transforms

Probability & statistics

Probability theory Random variables & distributions Statistical inference & estimation