Mathematics for TEE S2

Chapter 1: Sequences: Arithmetic and geometric sequences. Calculating sums.

Chapter 2: Hyperbolic functions: definition, curves, derivatives

Chapter 3: Integral calculus: integrals, 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 common solids

Hourly volumes :

• CM: 18
• TD : 18

The aim of this module is to provide the basic tools needed to solve, reason and calculate problems based on mathematical concepts. Reminders and new mathematical notions necessary for Earth and Environmental Sciences will be introduced in this module.

UE Mathematics for TEE S1

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: calculating 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, vector normal to a line, equation of a circle, parabola of a second-degree polynomial function, section and intersections (systems, level lines), cylindrical and spherical coordinates, lengths, areas, volumes of common solids