Analysis

linfo1111  2019-2020  Louvain-la-Neuve

Analysis
Note from June 29, 2020
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
7 credits
45.0 h + 37.5 h
Q1
Language
French
Prerequisites
This course assumes that the students already masters the skills in analysis (functions, derivatives and integrals) as expected at the end of secundary school.
Main themes
The course focuses on
  • understanding of mathematical tools and techniques based on a rigorous learning of concepts favored by highlighting their practical application,
  • careful handling of these tools and techniques in the framework of applications.
For most concepts, applications are selected from the other courses of the computer science program (eg economy).
 
Sets and Numbers
  • sets (intersection, union, difference)
  • Order and equivalence,
  • Interval, upper bounds, lower bounds, extremes,
  • absolute value, powers and roots
Real functions of one variable
  • injective, surjective, bijective functions,
  • algebraic operations on functions (including graphic interpretation)
  • first order functions,
  • exponential, logarithmic and trigonometric functions
  • Composition of functions and inverse functions
Limits
  • conditions to ensure that a limit exists,
  • limits to infinity
Continuous functions
  • fundamental theorems of continuous functions,
Differentiable functions
 
  • derivative at a point (including graphical interpretation)
  • The Hospital's theorem,
  • linear approximation of a function,
  • maximum and minimum,
  • encreasing of decreasing function (sign study)
  • concavity and convexity,
  • Taylor's development
Integrals
  • primitive,
  • definite integrals (including graphic interpretation)
  • undefinite integrals
Functions of two variables
  • notion and calculation of partial derivative
  • graphical interpretation of the gradient
  • interpretation and calculation of the Hessian matrix 
  • Intuitive introduction to the use of the Hessian matrix and gradient for a 2-variable function to determine critical points and their nature
  • concept and calculation of double integrals
For this last part, a mainly "tool" approach will be favored.
Aims

At the end of this learning unit, the student is able to :

1
Given the learning outcomes of the "Bachelor in Copputer science" program, this course contributes to the development, acquisition and evaluation of the following learning outcomes:
  • S1.G1
  • S2.2
Students completing successfully this course will be able to
  • Model real problems using the concepts of set, function, limit, derivative and integral;
  • Solve real problems using computational techniques for limit, derivative and integral;
  • Reason using correctly the mathematical notations and methods keeping in mind but exceeding a more intuitive understanding of the concepts;
  • Model real problems using functions of 2 variables.
 

The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
Faculty or entity


Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Aims
Bachelor in Computer Science

Master [120] in Data Science : Statistic