Lycée Fermat - Classes Préparatoires

Author: RobinCamarasa

2-year undergraduate intensive course in Physics, Algebra, Mathematics Analysis and Theoretical Computer Science

Mathematics

Algebra:

  1. Set Theory
  2. Algebraic Calculations and Trigonometry
  3. Complex Numbers
  4. Real Numbers and Numerical Sequences
  5. Arithmetic
  6. Usual Algebraic Structures
  7. Polynomials and Rational Fractions
  8. Vector Spaces and Linear Applications
  9. Endomorphisms
  10. Symmetric Group

Calculus:

  1. Differential and Integral Calculus
  2. Functions of a Real Variable with Real or Complex Values
  3. Limits and Continuity
  4. Differentiability
  5. Convexity
  6. Asymptotic Analysis
  7. Integration
  8. Differential Calculus and Optimization

Probability:

  1. Probabilities on a Finite Universe, Random Variables, and Laws
  2. Expectation and Variance
  3. Discrete Random Variables

Analysis:

  1. Topology of Normed Vector Spaces
  2. Numeric and Vectorial Series
  3. Sequences and Series of Functions, Power Series
  4. Real Pre-Hilbert Spaces
  5. Discrete Summation Procedures
  6. Functions of Two Variables
  7. Integration over an Arbitrary Interval
  8. Ordinary Differential Equations
  9. Vector Functions

Physics & Chemistry

Waves and Signals

  1. Kirchhoff’s circuit laws
  2. Oscillators
  3. Linear Filtering
  4. Induction and Laplace Forces
  5. Periodic Signals
  6. Digital Electronics

Kinetics and Mechanics

  1. Description and Parameterization of Point Motion
  2. Newton’s Laws
  3. Energetic Approach to Point Motion
  4. Angular Momentum
  5. Motion in a Conservative Central Force Field
  6. Motion of a Solid
  7. Non-inertial Reference Frame
  8. Laws of Solid Friction

Optics

  1. Scalar Model of Light Waves
  2. Superposition of Light Waves
  3. Interferential Device using Wavefront Division: Young’s Double-Slit Experiment
  4. Interferential Device using Amplitude Division: Michelson Interferometer illuminated by a Spatially Extended Source

Electromagnetism

  1. Motion of Charged Particles in Electric and Magnetostatic Fields
  2. Electrostatics
  3. Magnetostatics
  4. Maxwell’s Equations
  5. Electromagnetic Field Energy
  6. Propagation and Radiation

Thermodynamics

  1. Principles of Thermodynamics
  2. Thermodynamic Machines
  3. Heat Transfers

Quantum Physics

  1. Wave Function and Schrödinger Equation
  2. Stationary States of a Particle in Piecewise Constant Potentials
  3. Non-Stationary States of a Particle in an Infinite Potential Well

Elements of Statistical Thermodynamics

  1. Boltzmann Factor
  2. System with Discrete Energy Spectra
  3. Classical Heat Capacities of Gases and Solids

Chemistry

  1. Chemical Transformations in Aqueous Solution
  2. Relationships between the Structure of Chemical Entities and Macroscopic Physical Properties
  3. Structure and Physical Properties of Solids
  4. First Principle of Thermodynamics Applied to Physicochemical Transformations
  5. Second Principle of Thermodynamics Applied to Physicochemical Transformations
  6. Thermodynamic Study of Redox Reactions
  7. Kinetic Study of Redox Reactions: Current-Potential Curve
  8. Storage and Conversion of Chemical Energy in Electrochemical Devices
  9. Corrosion

Computer science

Computer science structures

Paradigms

Logic

Other