HAS101X - Mathematical tools for sciences and engineering
1st year B.Sc, Montpellier Faculty of Sciences, 2024
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Documents
Link to all ressources on Moodle.
Exams & midterms:
- Midterm 1 - Real functions & continuity (Exam & Solutions)
- Midterm 2 - Continuity, differentiability & integration (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)
- Midterm 2.2 - Differentiability & integration (Kahoot)
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.)
Main responsible: Clément Gallo