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 is to develop the skills needed to solve problems, reason, and perform calculations based on mathematical concepts. This module will cover both a review of existing mathematical concepts and the introduction of new ones 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 series and standard limited expansions: sum, product, quotient

- Chapter 2: Differential Equations

 modeling, equations with separable variables, example: freezing and thawing of a lake,^first-order and second-order equations with constant coefficients Example: the equation of dynamics

- Chapter 3: Functions of Several Variables

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

- Chapter 4: Basic Statistics and Interpolation:

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

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

Exercises in Python or MATLAB that apply the concepts covered in class to problems more relevant to the geosciences

Understand key concepts and apply common mathematical techniques used in the geosciences.

Develop a solid foundation in mathematics.

Using scientific software to address geoscience problems with mathematical tools.