Mathematics TEE S3

This EU is structured around four chapters in order to introduce reminders and new concepts in mathematics that are necessary for learning Earth and Environmental Sciences.

-Chapter 1 : Taylor and DL :Examples and Operations

- Chapter 2: Differential equations: modeling, separable equations,^first-order reminders, second-order equations with constant coefficients

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

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

Hours per week:

- CM: 6 p.m.

- Tutorial: 6 p.m.

- Practical work: 9 hours

The objective of this course unit is to develop the tools necessary to solve problems, reason, and perform calculations based on mathematical concepts. This module will introduce both a review of existing concepts and new mathematical concepts necessary for Earth and Environmental Sciences.

EU: Mathematics for TEE S1; Mathematics for TEE S2

• Brief 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, separable variable equations, example: freezing/thawing of lake water,^first-order reminders, second-order reminders 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 field, rotational, Laplacian (transition to other coordinate systems), extrema

- Chapter 4: Statistics and interpolation concepts:

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

• Brief description of practical sessions and number of hours associated with each session

Tps in Python or Matlab that revisit the concepts covered in class on problems more applicable to geosciences

Handle key concepts and use common mathematical techniques useful in geosciences.

Develop a solid understanding of mathematics.

Using scientific software to address geoscience problems using mathematical tools.