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Code 1302
Course Calculus II
Semester First and Second
ECTS Credit Units 7,5
Course taught in English Yes
Available for Exchange Students Yes
Requirements Mandatory Precedence:
1301. Calculus I
Regents Patrícia Xufre
Pedro Chaves
Course Aim The course develops the fundamental tools of differential calculus in ℝⁿ, that enable the mathematical formulation and study of models in Economics, Business and Finance.
Program content
  1. Spaceℝⁿ
    Topological notions.
  2. Functions fromℝⁿintoℝm
    Examples in Economics/Business; domain; level curves; limits and continuity.
  3. Differentiation inℝⁿ
    Partial derivatives; differentiation; Taylor’s theorem; derivative of the composite function; homogeneous functions and Euler’s theorem.
  4. Inverse function theorem and Implicit function theorem.
  5. Optimization
    Free optimization; optimization with equality constraints; optimization with inequality constraints; Karush-Kuhn-Tucker conditions. Sufficiency and Necessity theorems. Envelope theorem.