Calculus I

Base Knowledge

High school mathematics knowledge.

Teaching Methodologies

The curricular unit is essentially formative and seeks to articulate fundamental theoretical knowledge with the necessary developments for the curricular units of the study plan. Intuitive understanding of concepts and the ability to calculate are encouraged. The expository and interrogative method is used in the exposition of theoretical subjects and the exercises are solved in groups and individually. In interpreting the concepts and solving the exercises, the GeoGebra software and the WolframAlpha software are used.

Learning Results

Differential and integral calculus of real functions of a real variable and its applications. Introduction to differential and integral calculus with real functions of two real variables.

Topics are presented and discussed by solving exercises and using the following software: GeoGebra and WolframAlpha. Autonomous learning and rigor in the interpretation, use and description of mathematical concepts.


1. Real function of a real variable
Properties of real functions of a real variable, limit and continuity, trigonometric functions and inverse trigonometric functions, exponential function, logarithmic function and hyperbolic functions.

2. Differential calculus
Derivative, properties, derivative of the composition function and the inverse function, theorems of Rolle and Lagrange, undetermined forms and Cauchy’s rule, polynomial approximation: differentials.

3. Primitive of real functions of a real variable
Techniques for calculating the primitive function.

4. Integral calculus
Definite Integral, properties, fundamental theorem of calculus, integration by parts and by substitution, applications of the definite integral: area of a plane region, volume of a solid of revolution and length of the arc of a curve; improper integrals: Integrals at unlimited intervals.

5. A introduction to calculus with real functions of two ​​real variables
Real function of two ​​real variables, domain, range, level set and graph, first order partial derivatives, double integral in type I and type II regions, applications of the double integral.

Curricular Unit Teachers




Departamento de Física e Matemática, (2005). Quinzena de Uniformização de Conhecimentos. ISEC.

Finney, R. L., Weir, M. D., Giordano, F. R. (2003). Cálculo (de George B. Thomas). Addison Wesley.

Larson, R., Hostetler, R. P., & Edwards, B. H. (2006). Cálculo (Vol. 1). McGraw-Hill.

Rodrigues, R. (2022). Notas teóricas e exercícios de Análise Matemática. ISEC.