Calculus I

Recommended Prerequisites

High School Mathematics.

Teaching Methods

The theoretical lectures are mainly expository with a strong interaction between concepts and practical applications; as much as possible, a central role will be given to visualization and analysis of particular situations before progressive approach to more abstract notions. In practical classes the students will solve exercises under the instructor guidance and will be also encouraged to solve problems independently.  The transformation of concepts into working tools will be achieved by encouraging personal work. The formal lectures will be complemented by periods of individual attendance.

Learning Outcomes

Provide the students with basic knowledge of differential and integral calculus for real functions as well as the fundamental concepts in the study of numerical sequences and series, and sequences and series of functions. It is intended that the students acquire computational skills. It is also intended that the students acquire an understanding of the concepts that will enable them to evaluate the scope and limitations of the materials studied and their applications.

Work Placement(s)

No

Syllabus

Functions of one real variable

• Limits, continuity and derivatives

• The definite integral and its  applications

• Improper integrals

Numerical sequences and series

• Criteria for convergence

Sequences and series of  functions

• Uniform convergence (Weierstrass test)

• Power series

• Taylor’s formula and Taylor’s series

 

Head Lecturer(s)

António José Esteves Leal Duarte

Assessment Methods

Final assessment
Exam: 100.0%

Continuous Assessment
Frequency: 100.0%

Bibliography

- J. Stewart, Cálculo , 4ª ed., Vol 1 e Vol.2 , Pioneira, São Paulo, 2001.

- Earl W. Swokowski, Cálculo com geometria analítica Vol I e Vol II, São Paulo, McGraw-Hill, 1983.

- J. Campos Ferreira, Introdução à Análise Matemática, Fund. Calouste Gulbkenkian,1993.