Remedial math S2

This UE proceeds from themes involving a biological problem, for which it is essential to carry out calculations and to understand or draw graphic representations (curves essentially). Motivated by these biological aspects, the students must acquire a minimal background allowing them to continue their studies in biology.

Calculus, algebra:

Enumeration, order of magnitude.

• Numerical calculations related to the principle of proportionality: conversion to a multiple or sub-multiple unit (from m to cm or km for example), including for surface or volume measurements (km²). Calculation of scale.
• Use a spreadsheet to perform simple operations or iterate an operation.
• Numerical application of a literal calculation.
• Simple operations on an all-numeric or all-literal calculation: addition or subtraction of a constant to an equation, multiplication or division of an equation by a constant.
• Passage d’une grandeur dans une unité à une grandeur équivalente dans une autre unité par multiplication par une constante (pression <> énergie, concentration <> osmolarité). Calcul d’une grandeur physique résultant du produit ou de la somme de plusieurs grandeurs (de type loi de Fick).
• Physical quantities corresponding to a quantity (which add up) or a concentration (which average out). Decomposition of the numerical calculation corresponding to a dilution (identification of the quantity of matter and the quantity of container, passage of the quantities to the concentrations, mixture of two solutions).
• Situation where we know the result and part of the parameters and where we have to adjust a parameter involved in the calculation of this result: notion of unknown.
• Equation of the first degree and its solution.
• System of linear equations (max. 2 unknowns) and its solution by expressing one unknown as a function of the other.

Analysis:

• Understand the representation of a phenomenon by a curve. To know how to find f(x) knowing x and vice versa.
• From a curve, identify the zones of growth, decrease, optimums. Pole, intersection with the axes, asymptote, inflection point.
• Rate of change, secant, tangent, derivative.
• Usual functions and their analytical expression: affine, quadratic, exponential and logarithm. Know how to draw these functions (remarkable points, shape of the curve between these points) or a function known numerically from some experimental points. Combinations in simple cases (ex logistic). Variations and derivatives.
• Linear and exponential differential equation.
• Passage from a linear scale to a logarithmic scale and vice versa.

Recommended prerequisites*: college programs

Realization of a typical exercise corresponding to several of the skills listed above (simple calculation in the context of a biological problem, construction or analysis of a curve...)

A series of biological problems will be established, leading to the development of the listed skills. The lectures will serve to fix the ideas on the different skills to be developed, after they have been mobilized to solve a problem (the lectures thus come after the tutorials).

Hourly volumes* :

            CM : 12h

            TD : 21h

            TP:

            Terrain: