Analysis (03_XBANA)
- Coefficient : 3
- Hourly Volume: 75h (including 36h supervised)
- CTD : 36h supervised (and 6h unsupervised)
- Out-of-schedule personal work : 33h
AATs Lists
Description
Elementary tools for processing the functions of several variables (excluding integration seen in S4), used in physics disciplines
- Basic Properties of Multiple Variable Functions
- Basics about curves and surfaces
- Representation of functions of 2 variables
- Regularity properties of functions (continuity, differentiability, etc.)
- Differentiability
- linear partial differential equations
- 1st order
- 2nd order
- Conditions to the limits
- Extrema of functions of several variables
- Twice differentiable functions
- Local and global extrema
- Extrema related
Learning Outcomes AAv (AAv)
AAv1 [heures: 15, B2,B3] : At the end of this course, each student is able to determine the parametric and Cartesian equations of a family of curves using the correspondence between geometric properties and their analytical counterparts. Conversely, it is capable of recognizing and representing a simple surface described by equations.
AAv2 [heures: 15, B2,B3] : At the end of this course, each student is able to prove the continuity or non-continuity of a function of 2 or 3 variables, calculate first and second partial derivatives in particularly in situations of function composition and variable change.
AAv3 [heures: 15, B2,B3] : At the end of this course, each student is able to carry out, independently, the research and classification of critical points (and possible extrema) according to the sign of the determinant of Hessiana. It will be able to suggest avenues in the case not determined by the classification.
AAv4 [heures: 15, B2,B3] : At the end of this teaching, in relation to physics situations such as the study of vibrating strings or the evolution of the temperature of a bar, each student is able to solve elementary differential equations (1st and 2nd order linear), to apply or propose a change of variable to reduce to the simple case, to particularize the solutions verifying boundary conditions.
AAv5 [heures: 15, B2,B3] : At the end of this course, each student knows how to determine, through calculation, the law of a function of a VA or a pair of VAs as well as the marginal laws which result from it and apply it to probability calculations.
Assessment methods
One long assessment and the average of several short assessments
Key Words
Functions of several variables, partial derivatives, extrema
Prerequisites
The analysis program for the S1 and S2 semesters