Teacher(s)
Language
French
Prerequisites
The mathematical background from a program of at least 4h mathematics in final year of school (upgrading, "Coup de pouce", given in the beginning of the year).
Main themes
This course has two parts:
A. Analysis of real functions (30h + 20h)
A. Analysis of real functions (30h + 20h)
- Real functions;
- Limit and continuity;
- Infinitesimal calculus, in particular: (i) differential calculus for real functions of a single real variable; (ii) Taylor polynomials
- Introduction to integral calculus for real functions of a single real variable;
- Systems of linear equations;
- Gauss-Jordan elimination method;
- Vectors, vector spaces, linear independence, bases;
- Matrixes, matrix algebra, determinants, matrixes inversion, linear independence and rank of a matrix, eigenvalues and eigen vectors
Learning outcomes
At the end of this learning unit, the student is able to : | |
| 1 |
This course must enable students to understand the mathematics encountered in economics and management, and afterwards, to acquire the capacity to manipulate the notions studied to solve problems by themselves. |
Content
In this course, two major mathematical themes are addressed: the study of the functions of a real variable (elements of infinitesimal calculus and integral calculus) and the study of systems of linear equations (elements of matrix calculus and introduction to linear algebra). These themes are approached with a view to their use in economics and management sciences.
Contents
1. Operations on fractions. General information on functions. Lines, parabolas and polynomials. Rational functions, powers and roots. Exponential function and logarithm function. Trigonometric and inverse trigonometric functions. Operations on functions.
2. Continuity. Fundamental theorems on continuity. Limits to infinity and at a point. Asymptotes. Definition and properties of the derivative. Fundamental theorems on derivatives. Growth, decrease and optimization of a function. Taylor polynomial.
3. Definition and geometric interpretation of the Riemann integral. Fundamental theorem of integral calculus. Calculation of the primitives. Improper integrals.
4. Linear systems, operations on matrices, rank and Gaussian method. Determinant and invertible matrices. Approximate solutions.
5. Linear subspaces of R^n, linear combinations, bases and dimension.
Contents
1. Operations on fractions. General information on functions. Lines, parabolas and polynomials. Rational functions, powers and roots. Exponential function and logarithm function. Trigonometric and inverse trigonometric functions. Operations on functions.
2. Continuity. Fundamental theorems on continuity. Limits to infinity and at a point. Asymptotes. Definition and properties of the derivative. Fundamental theorems on derivatives. Growth, decrease and optimization of a function. Taylor polynomial.
3. Definition and geometric interpretation of the Riemann integral. Fundamental theorem of integral calculus. Calculation of the primitives. Improper integrals.
4. Linear systems, operations on matrices, rank and Gaussian method. Determinant and invertible matrices. Approximate solutions.
5. Linear subspaces of R^n, linear combinations, bases and dimension.
Teaching methods
The lecture aims to introduce the theory from simple problems and to illustrate it by exercises solved in audience. The lecture, online syllabus, note taking and personal elaboration should help you strengthen your analysis and synthesis skills.
The TP sessions should allow you to appropriate the tools introduced in the lecture by exercises of different levels (calculation, reflection, synthesis, context, etcetera). TP sessions are also an opportunity to learn how to properly write a mathematical statement or exercise.
Both during the lecture and in the TP session, your questions are always welcome. After each supervised activity (lecture or session TP) an autonomous work of revision is necessary to be able to profit fully from the following activity.
Much of the subject matter covers the material seen in high school (particularly with regard to the study of the functions of a real variable). The basic objective is to go through the subject by identifying the essential results and techniques. The second objective is to deepen the subject by highlighting the links between the different parts, by digging the more delicate points, by questioning the reasons that motivate the theory and finally by refining the rigour and flexibility with which the studied tools and concepts are manipulated. In the linear algebra part, which goes far beyond high school achievement, your ability to abstract thinking will be solicited and strengthened.
The use, in economics and in management sciences, of the mathematical concepts presented in the course will be dealt with during some course sessions which are specifically dedicated to it.
The material presented in the course is divided into two parts: basic part (46 hours) and advanced part (14 hours). The hours devoted to the basic part and the hours devoted to the advanced part are clearly identified in the calendar available on the course Moodle site. The practical sessions are all devoted to the basic material.
The topics covered in the basic part are: numbers and functions, straight lines, parabolas, powers and polynomials, roots, exponential and logarithm, trigonometric functions, continuity, limits, derivative, extrema, variation of a function, integrals, primitives, systems of equations, operations on vectors and matrices, Gauss's method, invertible matrices, determinant and properties of the determinant.
The topics covered in the advanced part are: Taylor polynomial, fundamental theorem of calculus, improper integrals, vector subspaces, bases, dimension, approximate solutions, applications to economics and management sciences.
During week 2, all students must take a self-assessment test. Depending on the result of the test, each student will be asked to focus on the basic part or the advanced part. The self-assessment test is only formative, it is anonymous and it does not count towards the final assessment, but participation in the test is mandatory (an unjustified absence may result in non-admission to the final exam). The student can pass the final assessment by limiting himself to following the basic part of the course. The final assessment will be the same for all students (see section "method of assessment of student achievement").
The TP sessions should allow you to appropriate the tools introduced in the lecture by exercises of different levels (calculation, reflection, synthesis, context, etcetera). TP sessions are also an opportunity to learn how to properly write a mathematical statement or exercise.
Both during the lecture and in the TP session, your questions are always welcome. After each supervised activity (lecture or session TP) an autonomous work of revision is necessary to be able to profit fully from the following activity.
Much of the subject matter covers the material seen in high school (particularly with regard to the study of the functions of a real variable). The basic objective is to go through the subject by identifying the essential results and techniques. The second objective is to deepen the subject by highlighting the links between the different parts, by digging the more delicate points, by questioning the reasons that motivate the theory and finally by refining the rigour and flexibility with which the studied tools and concepts are manipulated. In the linear algebra part, which goes far beyond high school achievement, your ability to abstract thinking will be solicited and strengthened.
The use, in economics and in management sciences, of the mathematical concepts presented in the course will be dealt with during some course sessions which are specifically dedicated to it.
The material presented in the course is divided into two parts: basic part (46 hours) and advanced part (14 hours). The hours devoted to the basic part and the hours devoted to the advanced part are clearly identified in the calendar available on the course Moodle site. The practical sessions are all devoted to the basic material.
The topics covered in the basic part are: numbers and functions, straight lines, parabolas, powers and polynomials, roots, exponential and logarithm, trigonometric functions, continuity, limits, derivative, extrema, variation of a function, integrals, primitives, systems of equations, operations on vectors and matrices, Gauss's method, invertible matrices, determinant and properties of the determinant.
The topics covered in the advanced part are: Taylor polynomial, fundamental theorem of calculus, improper integrals, vector subspaces, bases, dimension, approximate solutions, applications to economics and management sciences.
During week 2, all students must take a self-assessment test. Depending on the result of the test, each student will be asked to focus on the basic part or the advanced part. The self-assessment test is only formative, it is anonymous and it does not count towards the final assessment, but participation in the test is mandatory (an unjustified absence may result in non-admission to the final exam). The student can pass the final assessment by limiting himself to following the basic part of the course. The final assessment will be the same for all students (see section "method of assessment of student achievement").
Evaluation methods
The final grade is the sum of two marks: T = the SMART week test gives a bonus between 0 and 2 points; E = Examination in session gives a score between 0 and 20 points. The final grade is T + E (if it exceeds 20 points, it is reduced to 20). If you have to represent the exam in June or September, the bonus points T remain acquired.
The test: Duration 1 hour. Calculator and gsm prohibited. The test consists of one or two exercise-type questions (closed book written). The correction will be made in audience right after the end of the test.Examination: closed book written exam lasting between 2 and 3 hours. Calculator and mobile phone prohibited. The exam consists of two or three questions including exercise-type questions and reflection questions. The answer key will be available on the Student Corner after the end of the session and before the copy consultation session.
The questions cover the core material (for 16 points) and the in-depth material (for 4 points). The questions (or parts of questions) that cover the in-depth material will be clearly identified in the exam form.
The assessment is the same for all students, regardless of whether they have followed only the core part, the in-depth part or both parts.
The test: Duration 1 hour. Calculator and gsm prohibited. The test consists of one or two exercise-type questions (closed book written). The correction will be made in audience right after the end of the test.Examination: closed book written exam lasting between 2 and 3 hours. Calculator and mobile phone prohibited. The exam consists of two or three questions including exercise-type questions and reflection questions. The answer key will be available on the Student Corner after the end of the session and before the copy consultation session.
The questions cover the core material (for 16 points) and the in-depth material (for 4 points). The questions (or parts of questions) that cover the in-depth material will be clearly identified in the exam form.
The assessment is the same for all students, regardless of whether they have followed only the core part, the in-depth part or both parts.
Other information
Attention: the schedule does not happen again the same week by week. It is therefore necessary to regularly consult the Student Corner for more details.
Beyond the prior knowledge, what matters above all is the motivation to learn and understand and the goodwill to accomplish the necessary independent work.
This teaching has two objectives:
- Allow you to be comfortable with the basic mathematical tools that will intervene in the rest of your course at the university (whether in management sciences or management engineering).
- Help you develop your capacity for analysis and synthesis.
These courses contribute to the acquisition of the following skills (see description of the Bachelor's program in management engineering):
1.1 Demonstrate intellectual independence in reasoning, take a critical and reflective look at knowledge (academic and common sense).
2.3 Master a foundation of knowledge in the field of quantitative methods, computer science and economics.
2.4 Acquire a foundation of knowledge in the field of science and technology.
3.2 Conduct clear and structured analytical reasoning by applying conceptual frameworks and scientifically based models to describe and analyze a simple but concrete problem.
8.1 Communicate information, ideas, solutions and conclusions, in a clear, structured, reasoned manner both orally and in writing, according to the target audience.
Beyond the prior knowledge, what matters above all is the motivation to learn and understand and the goodwill to accomplish the necessary independent work.
This teaching has two objectives:
- Allow you to be comfortable with the basic mathematical tools that will intervene in the rest of your course at the university (whether in management sciences or management engineering).
- Help you develop your capacity for analysis and synthesis.
These courses contribute to the acquisition of the following skills (see description of the Bachelor's program in management engineering):
1.1 Demonstrate intellectual independence in reasoning, take a critical and reflective look at knowledge (academic and common sense).
2.3 Master a foundation of knowledge in the field of quantitative methods, computer science and economics.
2.4 Acquire a foundation of knowledge in the field of science and technology.
3.2 Conduct clear and structured analytical reasoning by applying conceptual frameworks and scientifically based models to describe and analyze a simple but concrete problem.
8.1 Communicate information, ideas, solutions and conclusions, in a clear, structured, reasoned manner both orally and in writing, according to the target audience.
Online resources
The syllabus (still in the finalization phase), the course slides, the exercises with solutions for the practical work sessions and the old exam questions with detailed corrections are available on the Student Corner website. The solutions for the practical work exercises will be made available only after the practical work has taken place.
To review your prior knowledge, you can use the site https://www.auto-math.be
To review your prior knowledge, you can use the site https://www.auto-math.be
Teaching materials
- Les ressources en ligne (syllabus, slides, exercices et anciennes questions d'examen) sont les supports de cours.
Faculty or entity
