• ECTS

    5 credits

  • Component

    Faculty of Science

Description

This course is an introduction to analysis (functions of one real variable) for first-year PCSI students.

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Objectives

- Rudiments of logical reasoning (connectors, quantifiers, reasoning by the absurd...)

- Rudiments on sets and applications.

- Continuous functions: general theorems, intermediate value theorem, continuous image of an interval.

- Derivable functions: general theorems, chain-rule, finite increase theorem and reciprocal bijection theorem. Notion of C∞ function. Rudiments of Taylor's formula.

- Bestiary of classical functions: power, polynomials, exponential, logarithm, trigonometric and reciprocal trigonometric functions.

- Integral calculus: properties and techniques (integration by parts and change of variable)

- Differential equations of order 1 (non-linear, separation of variables...)

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Teaching hours

  • Outils Mathématiques 1 - CMLecture22,5h
  • Outils Mathématiques 1 - TDTutorial22,5h

Necessary prerequisites

Prerequisites*:

High school mathematics program.

 

Recommended prerequisites*:

expert mathematics option.

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Knowledge control

2 continuous tests (written) + 1 final exam (written).

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Further information

Content manager: laurent.guieu@umontpellier.fr

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