5.00 credits
30.0 h + 30.0 h
Q1
Teacher(s)
Claeys Tom;
Language
French
Prerequisites
Calculation and geometric interpretation of onevariable derivatives, primitives and simple integrals.
Main themes
Using the acquired skills of differential and integral calculus from high school and from different problems, inspired in particular by physics, economics or geometry, tools, methods and mathematical intuitions will be proposed allowing in the following fields :
 Geometric description of functions of R in R² and of R² in R (tangent lines and planes, contour lines).
 Optimization of functions of two variables
 Differential equations of the first and second order
 Simple and double integrals (Cavalieri principle)
 Taylor expansion, including estimating the remainder and observing the convergence of the series
Learning sequences will be planned to allow students to reactivate and reinforce their skills on exponential and trigonometric functions, complex numbers and differential and integral calculus in one variable.
Students will be invited to ask themselves mathematical questions about the limitations of the proposed tools.
Learning outcomes
At the end of this learning unit, the student is able to :  
1  At the end of this activity, the student will be able to :

Content
 Introduction to functions
 Vectors and vectoroperations
 Functions of several variables: geometric desciption, limits, continuity, differentiability, optimisation of functions of two variables
 Multiple integrals: polar and spherical coordinates, change of variables
 Differential equations of first and linear of second order
 Taylor expansions
Teaching methods
Learning activities consist of lectures and exercise sessions, complemented by short videos on the Moodle page of the course.
The lectures aim to introduce fundamental concepts, to explain them by showing examples and by determining their results, to show their reciprocal connections and their connections with other courses in the programme for the Bachelor in Mathematics.
The exercise sessions aim to teach how to select and use methods to solve problems and calculation methods.
The lectures aim to introduce fundamental concepts, to explain them by showing examples and by determining their results, to show their reciprocal connections and their connections with other courses in the programme for the Bachelor in Mathematics.
The exercise sessions aim to teach how to select and use methods to solve problems and calculation methods.
Evaluation methods
Learning will be assessed by tests during the semester and by a final examination.
The questions will ask students to :
 judge whether a given proposition is correct or not
 reproduce the subject matter, especially definitions, theorems, methods, and examples
 select and apply methods from the course to solve problems and exercises
 adapt methods from the course to new situations
summarise and compare topics and concepts.
Assessment will focus on :
 knowledge, understanding and application of the different mathematical methods and topics from the course
 precision of calculations
 rigour of arguments, reasonings, and justifications
 quality of construction of answers.
The questions will ask students to :
 judge whether a given proposition is correct or not
 reproduce the subject matter, especially definitions, theorems, methods, and examples
 select and apply methods from the course to solve problems and exercises
 adapt methods from the course to new situations
summarise and compare topics and concepts.
Assessment will focus on :
 knowledge, understanding and application of the different mathematical methods and topics from the course
 precision of calculations
 rigour of arguments, reasonings, and justifications
 quality of construction of answers.
Online resources
Bibliography
Livre "Calculus  Early Transcendentals" par W. Briggs, L. Cochran et B. Gillet, éditeur: Pearson,
distribué par la Duc.

Book "Calculus  Early Transcendentals" by W. Briggs, L. Cochran and B. Gillet, publisher: Pearson,
distributed by the Duke.
distribué par la Duc.

Book "Calculus  Early Transcendentals" by W. Briggs, L. Cochran and B. Gillet, publisher: Pearson,
distributed by the Duke.
Teaching materials
 Calculus  Early Transcendentals, par W. Briggs, L. Cochran et B. Gillet, éditeur : Pearson
Faculty or entity
MATH