# Analysis I

lepl1102  2021-2022  Louvain-la-Neuve

Analysis I
5.00 credits
30.0 h + 30.0 h
Q1
Teacher(s)
Language
French
Main themes
functions of a real variable, first order differential equations. Mathematical proof techniques. Modelling of simple problems, and problem solving.
Aims
 At the end of this learning unit, the student is able to : 1 At the end of the course the students will be able to Manipulate functions of a single real variable ; Use first order differential equations, linear recurrence equations and simple discrete structures in order to model and solve problems ; Apprehend and visualize a scalar function of two real variables; Calculate partial derivatives and use them to form a first-order approximation. Understand the main mathematical proof techniques ; Make a critical reading and analysis of a problem statement; Find examples and counter-examples related to a mathematical statement; Write short mathematical proofs with rigor. Modelling of simple problems, and problem solving using the methods cited above. Regarding the learning outcomes of the program of Bachelor in Engineering, this course contributes to the development and the acquisition of the following learning outcomes: LO1.1, 1.2, maybe 2.3, 2.6, 2.7, 3.2, 4.1.
Content
• Real numbers, inequalities, sequences and series
• Real functions of one variable, limits and continuity, sequences of functions
• Derivation and applications, optimization
• Taylor polynomial
• Complex numbers
• Integration and applications
• Introduction to differential equations
• Introduction to multivariable calculus: toppology, continuity, differentiability, partial derivatives and chain rule, gradient and tangent plane for scalar real functions of two variables
Teaching methods
Lectures in a large auditorium, supervised exercise (APE) and problem (APP) sessions in small groups, possibly supplemented with writing assignments and online exercises.
Evaluation methods
Evaluations are done individually in writing on the basis of the learning outcomes listed above. A test is organized during the first quadrimester, and a written exam during each session.
For the January session, the grade is awarded on the basis of the test (5 points out of 20) and the exam. During the other two sessions, the grade depends only on the exam.
Online resources
Bibliography
Teaching materials
• Calculus with Applications par Peter D. Lax et Maria Shea Terrell, Springer, 2014.
• Multivariable Calculus with Applications par Peter D. Lax et Maria Shea Terrell, Springer, 2017.
Faculty or entity

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

Title of the programme
Sigle
Credits
Prerequisites
Aims
Bachelor in Engineering : Architecture

Bachelor in Engineering 