Math TEE S3

This unit is organized into four chapters to review key concepts and introduce new mathematical concepts necessary for learning Earth and Environmental Sciences.

-Chapter 1 : Taylor and DL :Examples and Operations

- Chapter 2: Differential Equations: Modeling, Equations with Separable Variables,^First-Order Recurrence Equations, Second-Order Equations with Constant Coefficients

- Chapter 3: Functions of Several Variables: Partial functions , contour lines, partial derivatives, 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

Number of hours:

- CM: 6:00 p.m.

- Tutorial: 6:00 p.m.

- Lab: 9 a.m.

The objective of this course unit is to develop the tools needed to solve problems, reason, and perform calculations based on mathematical concepts. This module will cover 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 fourth grade:

-Chapter 1 : Taylor and DL :

Taylor series and common limited expansions: sum, product, quotient

- Chapter 2: Differential Equations

 Modeling, equations with separable variables, example: freezing and thawing of lake water, review of^first-order and second-order equations with constant coefficients. Example: the equation of dynamics

- Chapter 3: Functions of Several Variables

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

- Chapter 4: Basic Concepts of Statistics and Interpolation:

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

• Brief descriptions of the lab sessions and the 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

Apply key concepts and use common mathematical techniques relevant to the geosciences.

Develop a solid foundation in mathematics.

Using scientific software to address geoscience problems with the help of mathematical tools.