Teacher(s)
Language
French
Prerequisites
Be able to manipulate algebraically and geometrically the functions of one and two variables and their derivatives.
Main themes
The course leads students to study mathematically the convergence of sequences, continuity and differentiability of functions of one and more variables, through the following topics :
- completeness of the set of real numbers and finite dimensional spaces,
- convergence of sequences: definition, examples and counter-examples, properties, method of successive approximations and application to real series,
- continuity : definition, examples and counter-examples, properties, limits and continuous extensions, global theorems,
- derivability and differentiability: definitions, examples and counter-examples, properties, higher order derivatives, Taylor expansion, free and constrained extremality conditions, implicit functions.
Learning outcomes
At the end of this learning unit, the student is able to : | |
| 1 | By the end of this activity, the student will be able to :
|
Content
Differential calculus in one and several variables :
- real numbers, vector spaces and sequences,
- continuity,
- basic topology and metric spaces,
- differentiability,
- Taylor polynomials and series,
- free and constrained optimization problems.
Teaching methods
The learning activities consist of lectures and practical sessions.
The lectures aim to introduce the fundamental concepts, to motivate them by showing examples and establishing results, to show their reciprocal links and their links with other courses in the Bachelor of Mathematical Sciences program.
The practical sessions aim at learning to choose and use methods of calculation and to construct demonstrations.
The lectures aim to introduce the fundamental concepts, to motivate them by showing examples and establishing results, to show their reciprocal links and their links with other courses in the Bachelor of Mathematical Sciences program.
The practical sessions aim at learning to choose and use methods of calculation and to construct demonstrations.
Evaluation methods
Skill acquisition will be assessed in a final exam.
Questions will require :
Questions will require :
- render material, including definitions, theorems, proofs, examples,
- select and apply methods from the course to solve problems and exercises
- adapt methods of demonstration from the course to new situations,
- synthesize and compare objects and concepts.
- the knowledge, understanding and application of the various mathematical objects and methods of the course,
- the rigor of the developments, proofs and justifications,
- the quality of the writing of the answers.
Online resources
Additional documents on Moodle.
Teaching materials
- Syllabus du cours LMAT1122 (2024-2025) disponible à la DUC
Faculty or entity
