Analysis
Analysis provides the differential and variational tools used in optimization, probability, and quantitative finance.
Detailed pages
| Topic | Content |
|---|---|
Derivatives, gradient, and Hessian | Multivariate differentiation, calculation rules, linear and quadratic approximations |
| Convexity | Convex sets and functions, Jensen, Hessian, applications |
| Taylor series | Local expansions, Lagrange remainder, delta-gamma, Newton |
Ordinary differential equations | ODEs, Cauchy-Lipschitz, analytical and numerical methods |
Partial differential equations | Classification, Black-Scholes, Feynman-Kac, finite differences |