Mathematics II

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Objectives

The complexity of economic phenomena leads to the need for their mathematical expression. The main objective of this subject is to introduce students to some of the mathematical techniques in the following topics: Integral calculus of real functions of two variables; Differential equations; Matrices and systems of linear equations and Determinants.

As specific objectives, the student is expected to calculate double integrals in regular integration domains, solve ordinary differential equations of separable variables and exact differential equations.

In Linear Algebra, the student is expected to solve systems of linear equations using the Gaussian elimination method, perform operations with matrices and calculate determinants, with some applications.

Program

1. Function of several variables

Domain and graph. Partial derivatives of a function of several variables. Chain Rule. Derivative of functions of more than one variable defined implicitly. Directional derivative. Maxima and minima of a function of several variables, in some cases subject to constraints.

2. Double integrals

Double integral: definition and properties. Calculation of double integrals in normal domains and applications.

3. Differential equations

Definition, particular and general solution. Ordinary differential equations: separable differential equation and exact differential equation.

Teaching Methodologies

The topics of this course are presented in lectures, using the blackboard and computer presentations. In practical classes, exercises are solved, stimulating the teacher / student interaction.

The course also benefits from the use of learning management platform Moodle available at the University of the Azores, increasing the performance of asynchronous activities.

Bibliography

Jean E.Weber, Matemática para economia e administração; 2ª ed , São Paulo: Harper & Row, 1986

Louis Leithold, Matemática aplicada à economia e administração, São Paulo, Editora Harbra,1988

Tom M. Apostol, Cálculo, Barcelona, Editorial Reverté, 2010

James. Stewart, Cálculo, VoII, 5ªEd. Thomson, São Paulo, 2005

Code

0104598

ECTS Credits

6

Classes

  • Teóricas - 30 hours
  • Teórico-Práticas - 30 hours

Evaluation Methodology

  • 1st Frequency: 50%
  • 2nd Frequency: 50%