## Continuity of functions of one and several variables

### Teaching unit

### Description

Approach to the concept of function and study of elementary functions.

### Objectives

Acquire and use mathematical language fluently, both orally and in writing, and rigorous formalization and structuring of a real problem in the form of mathematical problem.

To know how to compose functions and derive composite functions by chain rule.

Correctly handle the literature and information sources available to strengthen and expand knowledge and increase torque capacity to pose and solve mathematical so many problems that may arise and relate to the subject.

Use various technological tools (such as computer software) that facilitate solving math problems and understand the limitations of such tools.

Knowledge and skill in handling major real functions of real variable linear, quadratic, polynomial, rational, trigonometric, exponential, logarithmic. Being able to use them as a tool to solve a large variety of problems.

Calculate domains and limits of functions of one and several variables. Understand and interpret the concept of continuity of functions of one or several variables.

Correctly interpret graphic representations of functions and their level curves.

### Subjects

#### Lecture topics

- Concept of real function of a one real variable: domain, range.
- Elementary functions.
- Applications to the economy of linear and quadratic functions.
- Functions of several variables: domain, composite function, level curves.
- Limits of functions of one or several variables.
- Continuity of functions of one or several variables.

#### Laboratory topics

- Identification of the elementary functions and their properties.
- Continuity of real functions of one and several variables.
- Stepped functions
- Function graphing.