Remedial math S2

This course is based on themes involving a biological problem, for which it is essential to carry out calculations and understand or draw graphical representations (mainly curves). Motivated by these biological aspects, students are expected to acquire a minimum level of knowledge that will enable them to continue their studies in biology.

Calculus, algebra :

Enumeration, order of magnitude.

• Numerical calculations based on the principle of proportionality: conversion to a multiple or sub-multiple unit (from m to cm or km, for example), including surface or volume measurements (km²). Scale calculations.
• 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 are added) or a concentration (which are averaged). Decomposition of the numerical calculation corresponding to a dilution (identification of the quantity of substance and the quantity of container, conversion from quantities to concentrations, mixing of two solutions).
• Situation where the result and some of the parameters are known, and where a parameter used to calculate the result needs to be adjusted: notion of unknown.
• First-degree equation 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. Find f(x) knowing x and vice versa.
• From a curve, identify zones of growth, decline and optima. Pole, intersection with axes, asymptote, inflection point.
• Rate of change, secant, tangent, derivative.
• Common functions and their analytical expression: affine, quadratic, exponential and logarithmic. Know how to plot these functions (remarkable points, shape of curve between these points) or a function known numerically from a few experimental points. Combinations in simple cases (e.g. logistics). Variations and derivatives.
• Linear and exponential differential equation.
• Switch from linear to logarithmic scale and vice versa.

Recommended prerequisites*: middle school curricula

Carry out 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, etc.).

A series of biological problems will be established, leading to the development of the skills listed. Lectures will be used to fix ideas on the various skills to be developed, after they have been mobilized to solve a problem (lectures thus come after practical sessions).

Hourly volumes* :

            CM: 12h

            TD: 21h

            TP :

            Terrain :