Mathematical Tools 1

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

- Basics of logical reasoning (connectives, quantifiers, proof by contradiction, etc.)

- Basics of sets and functions.

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

- Differentiable functions: general theorems, the chain rule, the finite increments theorem, and the reciprocal bijection theorem. The concept of a^C∞ function. An introduction to the Taylor formula.

- A compendium of classical functions: power functions, polynomials, exponential functions, logarithms, trigonometric functions, and inverse trigonometric functions.

- Integral Calculus: Properties and Techniques (Integration by Parts and Substitution)

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

Requiredprerequisites*:

High School Mathematics Curriculum.

Recommended prerequisites*:

Advanced Mathematics track.

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

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