Mathematical Methods 2

Mathematical Methods for Economics II

I. Linear algebra 

Vector spaces: algebraic and geometric properties, scalar products, norms, orthogonality; linear transformations; systems of linear equations: properties of their solution sets; determinants: characterization, properties and applications.

II. Functions of several real variables 

Geometric representations: graphs and level curves; differentiable functions: characterizations, properties with respect to various operations and applications; second order derivatives: properties and applications; the implicit function theorem, and application to comparative statics problems; homogeneous and homothetic functions: characterizations and applications.

III. Multi-variable optimization 

Convex sets; geometric properties of functions: convex functions, their characterizations, properties and applications; further geometric properties of functions: quasiconvex functions, their characterizations, properties and applications; unconstrained optimization: geometric characterizations, characterizations using calculus and applications; constrained optimization with equality constraints: geometric characterizations, Lagrange characterization using calculus and applications; properties of value function: envelope theorem and applications.

IV. Differential Equations 

First-order differential equations, qualitative theory and stability

Textbook: K. Sydsaeter and P. Hammond: Mathematics for Economic Analysis.
Plus Notes and Tutes