The objective of this course is to learn mathematical reasoning and rigour, the acquisition of a spirit of synthesis and the initiation to the resolution and writing of exercises within the framework of real analysis, i.e. differential and integral calculus for functions of one or more real variables.
The introduction to Mathematical Analysis is done by presenting the basic tools of differential and integral calculus. The emphasis is on learning rigour and on the initiation to the solution of exercises. Some examples taken from physics illustrate the course. The subject is subdivided into five chapters: Derivatives of numerical functions of one real variable Differentiability of functions of several real variables Integral of a function of a real variable Improper integrals
Examination: The examination will consist of two papers: an oral paper and a written paper. The questions in the written examination are exercise questions only: they are based on applications of the same kind as those proposed in the tutorials and in the course. They aim to assess the student's ability to apply the main concepts and results of the course. For the oral examination, the questions focus on theory. The emphasis is on understanding, accuracy and synthesis. This exam consists of two main questions, one typically consisting of stating a result and proving it in context, and the other consisting of several short questions on the concepts, definitions, statement of results (theorems, propositions, etc) presented in the course. The list of theorems to be known with proofs will be communicated in writing. The examination is therefore based on two learning activities, one (oral examination) on the theory and the other (written examination) on the exercises. Provided that each mark is higher than 7, both the oral and the written part each count for half of the final score. If any of the scores is less than 7, the overall score is equal to the lowest score. Precise instructions will be given in due course.
Calcul différentiel et intégral, Jacques Douchet and Bruno Zwahlen, Presses Polytechniques Romandes, Lausanne 1990. Understanding analysis Stephen, Abott, Springer New York 2002.
| Training | Study programme | Block | Credits | Mandatory |
|---|---|---|---|---|
| Bachelier en sciences mathématiques | Standard | 0 | 7 | |
| Bachelier en sciences mathématiques | Standard | 1 | 7 |