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Mendes France - Épinal, France

Scientific Baccalaureate

Specialization in Mathematics (+ advanced maths), Engineering Sciences, and Physics/Chemistry

Mathematics (Specialization)

Analysis

  • Numerical functions: continuity, differentiability, convexity
  • Study of limits, asymptotic developments
  • Numerical sequences: limits, monotonicity
  • Integral calculus: primitives, integrals on a segment
  • Differential equations

Algebra and Geometry

  • Orthogonality and distances in space
  • Affine transformations and isometries

Probability and Statistics

  • Discrete and continuous random variables
  • Expectation, variance and standard deviation
  • Common distributions (binomial, exponential, normal)
  • Law of large numbers theorem

Algorithms and Programming

  • Manipulation of sequences and functions
  • Simulation of random phenomena
  • Numerical approximation

Physics-Chemistry (Specialization)

Mechanics

  • Forces and interactions: fundamental principle of dynamics
  • Energy and work: conservation of mechanical energy
  • Mechanical oscillators: period, damping, resonance

Waves and Optics

  • Progressive and stationary waves
  • Diffraction and interference
  • Light spectra and applications (Doppler effect, spectroscopy)

Electricity and Electromagnetism

  • Electrical circuits (RLC, transients, RC filters)
  • Induction and Lenz-Faraday law
  • Electromagnetic waves (light, radio, microwaves)

Thermodynamics and Physical Chemistry

  • Heat and internal energy
  • Spontaneous evolution of systems: entropy and free energy
  • Chemical reactions and reaction kinetics

Advanced Mathematics (Option)

Linear Algebra and Matrices

  • Matrices and operations: sum, product, inverse
  • Eigenvalues and eigenvectors
  • Application to linear systems

Complex Numbers and Applications

  • Algebraic, trigonometric and exponential forms
  • Plane transformations: rotations, homotheties
  • Application to differential equations

Analysis

  • Numerical sequences and series (convergence, Taylor series)
  • In-depth study of functions: limited developments, generalized integrals

Probability and Statistics

  • Continuous random variables, probability density
  • Common distributions: normal law, exponential
  • Estimation and statistical tests