Mathematics I

Objectives

1.Calculate derivatives of functions of a single variable;
2. Calculate limits using Cauchy's Rule;
3. Determine derivatives of real functions of one or more variables, defined explicitly and implicitly;
4. Apply differential calculus to locate relative extremes;
5. Determine maxima, minima and saddle points of functions of two variables;
6. Use the Lagrange Multipliers method to calculate conditioned extremes;
7. Calculate immediate indefinite integrals and rational functions (in the case of simple real roots).

Program

1. Differential Calculus

1.1Derivative of Inverse circular functions.

1.2 Relative extremes of a function, problems of optimization

1.3  Cauchy rule.

2. Function of several variables

2.1 Domain and graph.

2.2Partial derivatives of a function of several variables.

2.3Chain Rule.

2,4 Derivative of functions  defined implicitly.

2.5 Directional derivative.

2.6 Maxima and minima of a function of several variables, in some cases subject to constraints.

3. Integral calculus

3.1. Primitive and indefinite integral

3.2. Immediate primitive rules

3.3.Primitivation of rational functions (case of simple real roots)

 

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 ativities.

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

J. Stewart, Cálculo, Vol.I, 5ªEd. Thomson, São Paulo, 2005

During the semester, material supporting the course will be made available on the course's Moodle page