Mathematics for TEE S1

This unit, organized into four chapters, is designed to provide areview and introduce basic concepts in mathematics

• Review: 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 Graphs of Functions
• Chapter 3: Common Functions: Exponential Function, Logarithmic Function, Trigonometric Functions
• Chapter 4: Vector Calculus and the Scalar Product

   

   

   

  Hourly volumes:

  CM: 18

  TD: 18

   

 To provide the foundational knowledge and 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.

10th-Grade Mathematics Curriculum

• Brief description of the concepts covered in fourth grade:

Reminders:

-fractions, expanding, factoring, notable identities.

Chapter 1 : Equations

- Equations: Review:^First-degree equations, systems of equations, example: fault intersections,

-Quadratic polynomials, roots, standard form, discriminant, solving quadratic equations, sign (without considering the complex case)

Chapter 2 : DéDerivation

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

Example: Calculating Flow Through a Dam

- Derivatives and Graphs of Functions: the relationship between the direction of change and the sign of the derivative, the derivative at an extremum, tangents to the graph

Chapter 3: Common Functions

- Exponential function: definition (“f’=f”), exp(x+y)=exp(x)exp(y), exp(x)exp(-x)=1, sign, variation, graph,

- Logarithm function: ln (recip of exp), algebraic properties, derivative, variations, limits, graph, relationship to the exponential curve,

- Trigonometric functions: the unit circle, image of a real number, cosine and sine of a real number, connection to the triangle, special values, sine and cosine functions, parity, periodicity, curves, derivatives, application to cartography

Chapter 4: Vector Calculus and the Scalar Product

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

 vectors, translation, linear combinations, line, direction vector, collinearity, plane, direction of a plane, characterization of a point and vector(s), bases and coordinate systems,

Acquire the necessary mathematical foundations for applications in the earth sciences