University

Level 7: Intermediate University

Multivariable calculus, ODEs, linear algebra, probability

This level is part of a complete math learning path that spans from foundations to research topics. Start with the first skills and move forward when you feel confident.

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Level 7: Intermediate University

Core skills in this level

Partial derivatives

Multiple integrals

Vector calculus

Line and surface integrals

Green's, Stokes', and Divergence theorems

Gradient, divergence, curl

First-order ODEs

Second-order linear ODEs

Laplace transforms

Systems of differential equations

Partial differential equations (introduction)

Eigenvalues and eigenvectors

Diagonalization

Inner product spaces

Orthogonality

Singular value decomposition

Probability theory (axioms)

Random variables

Probability distributions

Expected value and variance

Hypothesis testing

Confidence intervals

Regression analysis