Overall objectives:

O1 - The student must have basic concepts of real functions of one or more real variables.
O2 - The student should be able to apply concepts and solve differential calculus exercises in IR.
O3 - The student should be able to apply concepts and solve calculus problems in IR^n, in particular optimization problems with restrictions and without restrictions.

Syllabus:

C1 - Generalities on real valued functions of one real variable: elementary functions and composition of functions, domain and range; composite function, inverse function and implicit function; limits and continuity; Weierstrass theorem; Bolzano?s theorem.
C2 - Differential calculus in IR: derivative of a function at a point, geometric interpretation; derivation rules; the derivative of a composite function (chain rule); the derivative of the inverse function; derivatives of functions defined implicitly and parametrically; Cauchy rule; graphs of functions: curve sketching.
C3 - Differential calculus in IR^n: Notions and generalities about on real valued functions of two or more real variables; domain and range, contour lines and its geometric representation; limits and continuity; Partial derivation of 1st order, gradient vector; higher order derivatives, Young-Schwarz theorem, Hessian matrix; practical rules for the calculation of unconstrained extreme points; constrained optimization: the Lagrange multipliers method; Karush-Kuhn-Tucker optimization conditions.

Literature/Sources:

Renshaw Geoff , 2009 , "Maths for Economics", Second Edition , Oxford University Press
Piskounov N. , 1986 , Cálculo Diferencial e Integral, Vol. I e II , Lopes da Silva Editora
Pires, Gabriel E. , 2012 , Cálculo Diferencial e Integral em Rn , IST Press
Jacques, Ian , 1996 , Mathematics for Economists and Business, 2nd Ed , Harlow: Addison Wesley
Apostol, Tom M. , 1985 , Cálculo, Vol. I e II , Reverté
Mateus, Abel e Mateus, Margarida , 2002 , Microeconomia: Exercícios e Estudos de Casos , Verbo

Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
Lectures, problem solving and discussion sessions with resolution of exercise sheets. Self-study, research, problem solving. The evaluation consists of two mandatory tests. The final grade is obtained by arithmetic mean of both test results. At the time of appeal, the student can recover the grade of only one of the frequencies (weight 50%) or, alternatively, the complete exam (weight 100%), that is, can recover the whole matter