# Fiches de cours 2018-2019

## Analyse I (anglais)

Patakfalvi Zsolt

English

#### Summary

We study the fundamental concepts of analysis, calculus and the integral of real-valued functions of a real variable.

#### Content

- Reasoning , proving and arguing in mathematics

- Numbers, structures and functions

- Sequences, limit and continuity

- Series of reals

- Real-valued functions of a real variable and convergence

- Differential Calculus and the Integral

#### Keywords

real numbers, function, sequence,convergent/divergent sequence, limit, subsequence, limit of a function, continuous function, series of real numbers, convergent/divergent series, absolute convergence, derivative, class C^k, mean value theorem, Taylor's theorem, Taylor series, Riemann integral, indefinite integral, intermediate valuetheorem

#### Learning Outcomes

• The intended learning outcomes of this course are that students acquire the following capacities:
• Reason rigorously to analyse problems
• Choose appropriate analytical tools for problem solving.
• Be able to conceptualise in view of the applications of analysis.
• Apply efficiently mathematical concepts for problem solving by means of examples and exercises
• Analyze and to solve new problems.
• Master the basic tools of analysis as, for example, notions of convergence, sequences and series.
• Studying rigorously real functions we intend that students will demonstrate a deep understanding of calculus

#### Teaching methods

Ex cathedra lecture and exercises in the classroom

Written exam

#### Supervision

 Office hours No Assistants Yes Forum No Others Tutoring of exercises other measures to be defined

### Semaine de référence

LuMaMeJeVe
8-9BCH 2201 CO1
9-10
10-11  CE1100
CE1105
CO121
CO122
CO123

11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22

Cours
Exercice, TP
Projet, autre

### légende

• Semestre d'automne
• Session d'hiver
• Semestre de printemps
• Session d'été
• Cours en français
• Cours en anglais
• Cours en allemand