Level of study
BAC +1
ECTS
4 credits
Component
Faculty of Science
Description
Chapter 1: Sequences: Arithmetic and geometric sequences. Calculation of sums.
Chapter 2: Hyperbolic functions: definition, curves, derivatives
Chapter 3: Integral Calculus: integral, primitives, PPI, change of variables, first order differential equations
Chapter 4: Curves and surfaces: straight line, plane, circle, parabola, cylindrical and spherical coordinates, lengths, surfaces, volumes of usual solids
Hourly volumes:
- CM : 18
- TD : 18
Objectives
The objective of this course is to provide the basic tools necessary to solve, reason and calculate based on mathematical concepts. Reminders and new mathematical notions necessary for the Earth and Environmental Sciences will be introduced in this module.
Necessary pre-requisites
UE Mathematics for TEE S1
Syllabus
Synthetic description of the concepts covered in CM:
Chapter 1: Sequences
Sequences: modes of generation, arithmetic and geometric, direction of variation. Calculation of sums.
Chapter 2: Hyperbolic Functions
-hyperbolic functions: definition, curves, derivatives
Chapter 3: Integral Calculus
- Integral calculus: integral of a continuous positive function on [a,b] as area, primitive link, primitives of reference functions, example: calculation of Earth mass, linearity, positivity, Chasles relation, mean value, PPI, example: seismograph signal, change of variables.
- 1st order linear differential equations, example: carbon 14 dating, constant variation
Chapter 4: Curves and surfaces
Parametric representation of a line, Cartesian equation of a plane, vector product, normal vector to a line, equation of a circle, parabola of a polynomial function of the second degree, section and intersections (systems, level lines), cylindrical and spherical coordinates, lengths, surfaces, volumes of usual solids