Mathematics TEE S3

This course is structured around four chapters to introduce new mathematical concepts and reminders, necessary for learning Earth and Environmental Sciences.

-Chapter 1 Taylor and DL :Examples and operations

- Chapter 2: Differential equations: modeling, equations with separable variables,^1st-order and 2nd-order constant-coefficients reminders

- Chapter 3: Functions of several variables: Partial function, contour lines, partial derivation, composition, higher-order derivatives, example: seismic wave, gradient, divergence, rotational, Laplacian (transition to other coordinate systems), extrema

- Chapter 4: Statistical concepts and interpolation: mean and standard deviation, comparison of means, least squares, Lagrange interpolation

Hourly volume :

- CM :18h

- TD: 18h

- Practical: 9h

The aim of this module is to develop the 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; Mathematics for TEE S2

• Synthetic description of the concepts covered in CM :

-Chapter 1 Taylor and DL :

Taylor and usual limited developments, sum, product, quotient

- Chapter 2: Differential equations

 modelling, equations with separable variables, example: freezing/thawing of lake water, reminders of^1st order, 2nd order with constant coefficients Example: equation of dynamics

- Chapter 3: Functions of several variables

- Partial function, contour lines, examples in cartography, partial derivation, composition, higher-order derivatives, gradient,divergence, example: topography,temperature cahmp, rotational, Laplacian (transition to other coordinate systems), extrema

- Chapter 4: Statistical concepts and interpolation :

 mean and standard deviation, comparison of means, least squares, Lagrange interpolation

• Synthetic description of TP sessions and number of hours associated with each session

Tps in Python or Matlab that take up the concepts covered in class on problems more relevant to the geosciences

Manipulate the main concepts and use common mathematical techniques useful in the geosciences.

Develop solid mathematical skills.

Use scientific software to tackle geoscience problems using mathematical tools.