Mathematics for TEE S1

This course, structured in four chapters, aims to providereminders and basic concepts in mathematics.

• Reminders: fractions, expanding, factoring, notable identities

• Chapter 1 : Equations: first-degree equations , systems of equations, second-degree equations

• Chapter 2 :Derivatives: definition , examples, operations, variations, and representative curves of functions
• Chapter 3: Common Functions: Exponential Function, Logarithmic Function, Trigonometric Functions
• Chapter 4: Vector Calculus and Scalar Product

   

   

   

  Hourly volumes:

  CM: 18

  TD: 18

   

 Provide the basic tools needed to solve problems, reason, and perform calculations based on mathematical concepts. This module will introduce reminders and new mathematical concepts necessary for Earth and Environmental Sciences.

High school mathematics curriculum

• Brief description of the concepts covered in CM:

Reminders:

-fractions, expand, factorize, remarkable identities.

Chapter 1 : Equations

- Equations: reminders:^First-degree equations, systems of equations, example: fault crossings,

-Second degree polynomial function, roots, canonical form, discriminant, solving second degree equations, sign (without complexes)

Chapter 2 : Dérivation

-Derivation: local perspective (rate of change, derivative as a limit, tangent to the curve), global perspective (differentiable function, derivative, derivative of squares, inverse cube, square root, x^n (n integer), operations on differentiable functions, sum, product, inverse, quotient, derivation of the composite, second derivative

Example: Calculating flow rate through a dam

- Variations and representative curves of functions: relationship between direction of variation and sign of the derivative, derivative at an extremum, tangents to the curve

Chapter 3: Common Functions

- Exponential function: definition ("f'=f"), exp(x+y)=exp(x)exp(y), exp(x)exp(-x)=1, sign, variation, curve,

- Logarithm function: ln (recip of exp), algebraic properties, derivative, variations, limits, curve, link with exponential curve,

- Trigonometric functions: trigonometric circle, image of a real number, cosine and sine of a real number, link with triangles, notable values, sine and cosine functions, parity, periodicity, curves, derivatives, application to cartography

Chapter 4: Vector Calculus and Scalar Product

- Vector calculus and scalar product: Scalar product (orthogonal projection and cosine), characterization of orthogonality, bilinearity, and symmetry, in orthonormal basis, derivative of ||u+v||², Al-Kashi, MA.MB transformation.

 vectors, translation, linear combinations, line, direction vector, collinearity, plane, direction of a plane, characterization of points and vectors, bases and reference frames,

Acquire the necessary mathematical foundations for applications in earth sciences.