# Mathematical Analysis I

Year
1
2023-2024
Code
01000010
Subject Area
Mathematics
Language of Instruction
Portuguese
Mode of Delivery
Face-to-face
Duration
SEMESTRIAL
ECTS Credits
6.0
Type
Compulsory
Level
1st Cycle Studies

## Recommended Prerequisites

Mathematics A from the Portuguese High School Curriculum.

## Teaching Methods

The classes are of theoretical-practical type. During a theoretical class part, teaching will be mostly expository. During an example class part,

teaching will consist of problem solving by the students under the guidance of the lecturer. A strong interaction between notions and their practical application is emphasized. In this task, the visualization and the analysis of concrete examples takes on a central role and prepares the way for the abstract definitions. Tutorial support will be available to students to help them on the tasks assigned by the lecturers.

## Learning Outcomes

The student that successfully completes this course will be able to:

i) compute the limit of a function beyond the scope of those studied in High School;

ii) derivate and integrate elementary functions;

iii) use the Fundamental Theorem of Calculus to compute areas of plane figures, volumes of solids and lengths of curves;

iv) solve a differential equation with separable variables;

v)  solve a linear differential equation of order one.

No

## Syllabus

I.   Real functions of a single variable

I.1 Elementary functions

I.2 Limits and continuity

I.3 Differentiability and applications

II. Integration

II.1 Primitives

II.2 Riemann integral and applications

II.3 Improper integrals

III. Ordinary differential equations

III.1 Equations with separable variables

III.2 Linear equations of order one.

Jorge Manuel Sentieiro Neves

## Assessment Methods

Continuous assessment
2 or more midterm exams : 100.0%

Final assessment
Exam: 100.0%

## Bibliography

[1] James Stewart: Cálculo, Volume I, Cengage Learning (tradução da 8ª edição norte-americana) 2017

[2] J. Campos Ferreira, Introdução à Análise Matemática, 11ª edição, Fundação Calouste Gulbenkian, Lisboa, 7a. Edição, (2014).

[3] J. Carvalho e Silva, Princípios de Análise Matemática Aplicada,  McGraw-Hill, (2005).

[4] Carlos Sarrico, Análise Matemática, Leitura e exercícios, 6ª edição, Colecção Trajectos Ciência n. 4, Gradiva, (2005).

[5] Zill, D. G., Equações Diferenciais com aplicações em modelagem, Thomson, S. Paulo. (2003)