Mathematics for TEE S1

This UE is divided into 4 chapters and is designed to provide abasic overview of mathematical concepts.

• Reminders: fractions, developing, factoring, remarkable identities

• Chapter1 : Equations: 1st degree equations, systems of equations, 2nd degree equations

• Chapter 2 :Derivation: definition, examples, operations, Variations and representative curves of functions
• Chapter 3: Standard functions: Exponential function, Logarithm function, Trigonometric functions
• Chapter 4: Vector calculus and scalar product

   

   

   

  Hourly volumes:

  CM: 18

  TD : 18

   

 Provide the basic tools needed to solve, reason and calculate problems based on mathematical concepts. Reminders and new mathematical notions necessary for Earth and Environmental Sciences will be introduced in this module.

Second-year mathematics program

• Synthetic description of the concepts covered in CM :

Reminders :

-Fractions, develop, factor, remarkable identities.

Chapter1 Equations

- Equations: reminders:^1st degree equations, systems of equations, example: crossing faults,

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

Chapter 2 : Dérivation

-Derivation: local point of view (rate of change, derivative number as limit, tangent to curve), global point of view (derivable function, derivative, derivative of squares, inverse cube, square root, x^n (n integer), operations on derivable functions, sum, product, inverse, quotient, derivation of compound, second derivative.

Example: calculating flow through a dam

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

Chapter 3: Standard 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, cos and sin of a real, link with the triangle, remarkable values, sin and cos functions, parity, periodicity, curves, derivatives, application to cartography.

Chapter 4: Vector calculus and scalar product

- Vector calculus and scalar product: Scalar product (proj ortho and cos), characterization of orthogonality, bilinearity and symmetry, in orthonormal basis, dev of ||u+v||², Al-Kashi, MA.MB transformation,

 vectors, translation, linear combination, line, directing vector, collinearity, plane, direction of a plane, characterization of point and vector(s), bases and reference points,

Acquire the mathematical foundations needed for earth science applications