Mathematical Tools 1

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

- Basics of logical reasoning (connectors, quantifiers, reductio ad absurdum, etc.)

- Basics of sets and applications.

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

- Differentiable functions: general theorems, chain rule, finite increment theorem, and reciprocal bijection theorem. Concept of^C∞ functions. Basics of Taylor's formula.

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

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

- First-order differential equations (nonlinear, separation of variables, etc.)

Requiredprerequisites*:

High school mathematics program.

Recommended prerequisites:

Advanced Mathematics option.

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

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