Infinitesimal Analysis II

Recommended Prerequisites

Infinitesimal Analysis I.

Teaching Methods

Theoretical lectures include motivation, illustrative examples and connections with the students knowledge on Calculus. Practical classes include tutorial resolution of problems. Exercises and projects to be solved at home, either individually or  in groups, will be suggested.

Learning Outcomes

This course is an introduction to Integral Calculus, and Sequences and Series of Functions.

 

Generic competences:

Calculus capacity;

Knowledge of mathematical results;

Skills on abstraction and generalization;

Logical argumentation;

Rigorous and clear writing and oral argumentations;

Research skills;

Autonomous learning capacities;

Critical behavior;

Communication skills.

Work Placement(s)

No

Syllabus

1. Integral Calculus: primitives; Riemann integral; Fundamental Theorem of Calculus; classical theorems of integral calculus and applications; improper integrals.

2. Numerical series.

3. Sequences and series of functions: sequences of functions; series of functions; power series; Fourier series.

Head Lecturer(s)

Júlio Severino das Neves

Assessment Methods

Assessment
Approval in this course unit requires to score at least 10 (out of 20). The students that perform, along the semester, the mid-term exams, and the homework may be exempted from final examination. The sum of percentages corresponding to these two components is 100%. The other students are evaluated in final exam which is worth 100%.: 100.0%

Bibliography

J. M. Urbano, Análise Infinitesimal II - Notas do curso. Departamento de Matemática, 2005.

 

E. Lages Lima,  Curso de Análise. Vol. I. IMPA, 1995.

 

J. Stewart, Cálculo. Vol. II. Thomson Learning, 2001.