Mathematics for TEE S2

Chapter 1: Sequences: Arithmetic and geometric sequences. Calculating sums.

Chapter 2: Hyperbolic functions: definition, curves, derivatives

Chapter 3: Integral calculus: integrals, primitives, IPP, change of variables, first-order differential equations

Chapter 4: Curves and surfaces: straight lines , planes, circles, parabolas, cylindrical and spherical coordinates, lengths, areas, volumes of common solids

Hourly volumes:

• CM: 18
• TD: 18

The objective of this course unit is to provide the basic tools needed 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

Brief description of the concepts covered in CM:

Chapter 1: Consequences

Sequences: methods of generation, arithmetic and geometric, direction of variation. Calculation of sums.

Chapter 2: Hyperbolic Functions

-hyperbolic functions: definition, curves, derivatives

Chapter 3: Integral Calculus

• Integral calculus: integral of a continuous positive function on [a,b] as area, primitive link, primitives of reference functions, example: calculation of Earth's mass, linearity, positivity, Chasles' relation, average value, IPP, example: seismograph signal, change of variables.
• ^First-order linear differential equations, example: carbon-14 dating, constant variation

Chapter 4: Curves and Surfaces

Parametric representation of a line, Cartesian equation of a plane, vector product, vector normal to a line, equation of a circle, parabola of a second-degree polynomial function, section and intersections (systems, contour lines), cylindrical and spherical coordinates, lengths, areas, volumes of common solids.