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Cours scientifiques - APM_1S006_EP : Introduction to Numerical Analysis

Domaine > Mathématiques appliquées.

Descriptif

The aim of this course is to provide students with a working knowledge of basic mathematical algorithms and associated computer programming. We will cover several notions such as representation of numbers, rootfinding, polynomial approximation, numerical integration, and error analysis. A significant portion of the course will be devoted to implementation and experiments using Jupyter Notebooks with Python.

 

Grading

The grading will be based on the following elements:

  1.  Very short tests (approx. 5min) at the beginning of the second lecture of each chapter, to ensure that you remember the main notions introduced during the first lecture of the chapter. 
  2. A final exam (2h), during which you will have to complete a notebook with both theoretical answers (Markdown and Latex), code (Python), and illustrations. Authorized material during the exam: the notebooks used in the course that are provided on Moodle, as well as personnal class/lab notes.
  3.  
  4. A final exam (2h), during which you will have to complete a notebook with both theoretical answers (Markdown and Latex), code (Python), and illustrations. Authorized material during the exam: the notebooks used in the course that are provided on Moodle, as well as personnal class/lab notes.

The final grade will be computed as follows:

max(final exam, 2/3*final exam + 1/3*short tests).

Objectifs pédagogiques

Objective: Introduction to computational mathematics

  • Practical knowledge of basic (but fundamental) mathematical algorithms
  • Theoretical study: introduction to the notions of error / convergence / speed of convergence
  • Practical implementation: lab sessions using Python and Jupyter notebooks

Pour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique

Vous devez avoir validé l'équation suivante : UE FMA_1F002_EP

MAA102

Format des notes

Numérique sur 20

Littérale/grade américain

Pour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique

Vos modalités d'acquisition :

The grading will be based on the following elements:

  1. Very short tests (5-10min) at the beginning of the second lecture of each chapter, to ensure that you remember the main notions introduced during the first lecture of the chapter.
  2. A final exam (2h), during which you will have to complete a notebook with both theoretical answers (Markdown and Latex), code (Python), and illustrations. Authorized material during the exam: the notebooks used in the course that are provided on Moodle, as well as personnal class/lab notes.

The remedial exam will have the same format and rules as the final exam.

Le rattrapage est autorisé (Note de rattrapage conservée écrêtée à une note seuil de 11)
    L'UE est acquise si Note finale >= 9
    • Crédits ECTS acquis : 3 ECTS

    La note obtenue rentre dans le calcul de votre GPA.

    Programme détaillé

    Tentative schedule

    • Introduction (1 week)
    • Chapter 1: solving equations of one variable (2 weeks)
    • Chapter 2: polynomial approximation (2 weeks)
    • Chapter 3: numerical integration (2 weeks)
    • Final exam (to be scheduled)
    Veuillez patienter