Applied Mathematics
Models and computations: differential equations, approximation, matrix factorizations, Markov chains, and numerical schemes.
Differential Equations, Approximation, Numerical Linear Algebra, Markov Chains, and Numerical Methods.
Subjects
Differential Equations
First-order equations, then second-order equations and linear systems, as models rather than as pure analysis.
Explore →1 chaptersApproximation
Taylor expansions used as working approximations, with the remainder kept in view.
Explore →4 chaptersNumerical Linear Algebra
Factorizations used to compute with matrices, and the conditioning that decides whether those computations are trustworthy.
Explore →1 chaptersMarkov Chains
Finite-state Markov chains and the linear algebra of their steady states.
Explore →14 chaptersNumerical Methods
Error bounds and the stability of numerical schemes, from floating-point and root-finding through quadrature, ODE and SDE time-stepping, optimization, and Monte Carlo.
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