HAS101X - Mathematical tools for sciences and engineering
1st year B.Sc, Montpellier Faculty of Sciences, 2024
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)
Exam preparations:
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.)