Bilinear forms, quadratic forms, inner product, norm, unitary space.
Linear isometry and orthogonal matrices. Gram-Schmidt procedure.
Orthogonal projection, properties. Geometric interpretation of least squares procedure.
Convex sets, convex functions, Jensen's inequality.
Multi-facet convex sets. Vertices.
Cones and convex cones.
Multi-facet convex cones. Dual cones and Farkas' lemma.
Complete metric space. Contractions and Banach fixed point theorem. Applications.
Differential equations. Economic and geometrical interpretations. Basics, e.g. initial condition, integral curve. Existence theorem.
Non-linear first order equations with separable variables.
Linear differential equations with constant coefficients. Solutions techniques.
Higher order differential equations. Non-homogeneous differential equations and test functions.
Stability of a solution. Stability of stationary points.
Difference equations.
Applications to economic modeling.
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