| Course label : | Tutorials in Mathematics |
|---|---|
| Teaching departement : | MIN / Applied Mathematics and General Computing |
| Teaching manager : | Mister XAVIER BRIOIT |
| Education language : | |
| Potential ects : | 0 |
| Results grid : | |
| Code and label (hp) : | ENSCL_CPI_M3_1_1_1 - Mathématiques |
Education team
Teachers : Mister XAVIER BRIOIT
External contributors (business, research, secondary education): various temporary teachers
Summary
The second-year programme is a continuation of the first-year programme, with more in-depth curriculum on functions (plot parameter arcs and polar curves), differential equations (with non-constant coefficients), linear algebra (reduction of endomorphisms and matrices), and integration (generalised integrals). But it is also the time to explore new domains (counting, probabilities and random discrete and continuous variables), series (numerical, functions, power, Fourier), and euclidean spaces (orthogonal and symmetrical endomorphisms).
Educational goals
The order of the chapters is given for information purposes only. Chapter 1: Limited expansion Local study in 0, a, and infinity, and applications. Chapter 2: Parametric and polar curves (a) Parametric (reduction, singular points, infinite branches) (b) Polar (same as for (a)) Chapter 3: Differential equations (a) First-order linear differential equations (generalisations, superposition principle, Cauchy problem, specific solutions, variations of constants) (b) Second-order linear differential equations with constant coefficients (without second member, specific solutions, variations of constants) (c) In tutorials: change of variable, change of function, Bernoulli and Riccati equations, separable variables, etc. Chapter 4: Numerical series (a) Sequences and Sums - Review (arithmetic, geometric, arithmetic-geometric, and first-order and second-order recurrent sequences, specific sums, convergence theorems, adjacent sequences and subsequences) (b) Series (definitions, geometric and exponential series, operations on series, telescoping series, positive term series with D'Alembert, Riemann series, criteria, absolute convergent series, alternating series) Chapter 5: Geometry in space (a) Determinants, (b) Scalar product, (c) Vector product (d) Triple product (e) Planes in space (f) Lines in space (g) Distances (h) Linear systems (i) Projections and symmetries Chapter 6: Diagonalisation (a) Vector spaces (b) Linear combinations (c) Additional vector subspaces (d) Linear applications (e) Matrices (f) Projections and symmetries (g) Shift matrices (h) Diagonalisation (i) Applications Chapter 7: Generalised integral (a) Generalisations (b) Case of continuous positive functions (c) Semi-convergent and absolutely convergent integrals Chapter 8: Functions of two variables (a) Generalisations (b) Limits and continuity (c) Polar coordinates (d) Differential calculation (e) Extremum (f) Partial differential equations (g) Double integrals (h) Vector fields Chapter 9: Counting and probabilities (a) Lists and combinations (b) Finite probability space (c) Equiprobability (d) Infinite extensions Chapter 10: Random variables (a) Definitions, examples (b) Discrete random variable (c) Common laws for discrete variables (d) Continuous random variable (e) Common laws for continuous variables (uniform, exponential, normal, Cauchy) Chapter 11: Euclidean spaces (a) Scalar products and standards (b) Orthogonal endomorphisms and orthogonal matrices (c) Symmetric endomorphisms Chapter 12: Function series, power series, trigonometric series, Fourier series (a) Sequences and function series (b) Power series (c) Trigonometric series (d) Fourier series
Sustainable development goals
Knowledge control procedures
Continuous Assessment
Comments: Five tests. (Four three-hour tests and one final four-hour exam).
Online resources
Students have access to all documents distributed via a drive.
Pedagogy
90 hours of lectures 90 hours of tutorials 30 hours of tutoring
Sequencing / learning methods
| Number of hours - Lectures : | 0 |
|---|---|
| Number of hours - Tutorial : | 30 |
| Number of hours - Practical work : | 0 |
| Number of hours - Seminar : | 0 |
| Number of hours - Half-group seminar : | 0 |
| Number of student hours in TEA (Autonomous learning) : | 0 |
| Number of student hours in TNE (Non-supervised activities) : | 0 |
| Number of hours in CB (Fixed exams) : | 0 |
| Number of student hours in PER (Personal work) : | 0 |
| Number of hours - Projects : | 0 |
Prerequisites
Mastery of the first-year programme.