Mathematics TEE S3

This course is structured around four chapters in order to introduce new concepts in mathematics, necessary for the learning of Earth and Environmental Sciences.

-Chapter 1 : Taylor and DL :Examples and Operations

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

- 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

- PT: 9 hours

The objective of this course is to develop the necessary tools 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.

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

 modeling, equations with separable variables, example: freezing/thawing of water in a lake, 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 the practical sessions and number of hours associated with each session

Tps in Python or Matlab that cover the concepts discussed in class on problems more applied to geosciences

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

Develop a solid knowledge of mathematics.

Use of scientific software to address geoscience problems using mathematical tools.