Mathematics for TEE S1

This UE is structured in 4 chapters and aims at givingreminders and elementary notions in mathematics

• Reminders: fractions, develop, factor, remarkable identities

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

• Chapter 2 :Derivation: definition, examples, operations, Variations and representative curves of functions
• Chapter 3: Common Functions: Exponential function, Logarithm function, Trigonometric functions
• Chapter 4: Vector Calculus and Scalar Product

   

   

   

  Hourly volumes:

  CM : 18

  TD : 18

   

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

Second grade math program

• Synthetic description of the concepts covered in CM:

Reminders :

-fractions, develop, factor, remarkable identities.

Chapter 1 Equations

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

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

Chapter 2 : Dérivation

-Derivation: local point of view (rate of change, derivative number as limit, tangent to the 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 the compound, second derivative

Example: calculation of flow through a dam

- Variations and representative curves of functions: link between direction of variation and sign of the derivative, derivative number 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, 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, transformation of MA.MB,

 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 necessary mathematical foundations for applications in the earth sciences