MATE-1209 Calculo III (Economía y Administración)

This course introduces topics of calculus of several variables – differentiation and integration and, mainly, the topic of optimization with or without restrictions. One of the objectives is for students to see the application of these topics on Economics. With emphasis on the use of mathematics, the techniques have applications not only in the economic context, but also in other areas such as Administration, Engineering, Physics or Biology. Students also become familiar with mathematical rigor, as many of the results and theorems are formally demonstrated. Functions of several variables. Partial derivatives, quadratic forms. Chain rule. Derivatives of implicitly defined functions. Partial elasticity. Homogenous functions. Equation systems. Implicit Function Theorem. Optimization. Maximums and minimums. Extreme Value Theorems. Local extremes. Convex sets. Concave and convex functions. Second derivative tests. Lagrange multiplier methods.