Documents

Lecture notes:

• Course 1 - Logic & set theory (Notes)
• Course 2 - Functions of a real variable (Notes)
• Course 3 - Continuity (Notes)

Exercise sheets:

• TD1 - Logic & set theory (Worksheet & Solutions)
• TD2 - Functions of a real variable (Worksheet & Solutions)
• TD3 - Continuity (Worksheet & Solutions)

Exams & midterms:

• Midterm 1 - Real functions & continuity (Exam & Solutions)

Exam preparations:

• Midterm 1.1 - Sets, Trigonometry, Real functions (Exam & Solutions)
• Midterm 1.2 - Real functions & continuity (Kahoot)
• Midterm 2.1 - Continuity & differentiability (Exam & Solutions)

Additional ressources:

• Review course on functions, trigonometry, limits, derivatives, and integrations (Notes)
• Usual functions and their properties (Notes)

Contents

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

2) Fundamentals of sets and functions

3) Continuous functions

• General theorems, intermediate value theorem
• Continuous image of an interval

4) Differentiable functions

• General theorems, chain rule, mean value theorem, and inverse function theorem
• Concept of $\mathcal{C}^\infty$ functions
• Basics of Taylor’s formula

5) Classical functions overview: power functions, polynomials, exponential, logarithm, trigonometric functions, and their inverses

6) Integral calculus: properties and techniques (integration by parts and change of variables)

7) First-order ordinary differential equations (non-linear, separation of variables, etc.)