Lycée Fermat - Classes Préparatoires
Author: RobinCamarasa
2-year undergraduate intensive course in Physics, Algebra, Mathematics Analysis and Theoretical Computer Science
Mathematics
Algebra:
- Set Theory
- Algebraic Calculations and Trigonometry
- Complex Numbers
- Real Numbers and Numerical Sequences
- Arithmetic
- Usual Algebraic Structures
- Polynomials and Rational Fractions
- Vector Spaces and Linear Applications
- Endomorphisms
- Symmetric Group
Calculus:
- Differential and Integral Calculus
- Functions of a Real Variable with Real or Complex Values
- Limits and Continuity
- Differentiability
- Convexity
- Asymptotic Analysis
- Integration
- Differential Calculus and Optimization
Probability:
- Probabilities on a Finite Universe, Random Variables, and Laws
- Expectation and Variance
- Discrete Random Variables
Analysis:
- Topology of Normed Vector Spaces
- Numeric and Vectorial Series
- Sequences and Series of Functions, Power Series
- Real Pre-Hilbert Spaces
- Discrete Summation Procedures
- Functions of Two Variables
- Integration over an Arbitrary Interval
- Ordinary Differential Equations
- Vector Functions
Physics & Chemistry
Waves and Signals
- Kirchhoff’s circuit laws
- Oscillators
- Linear Filtering
- Induction and Laplace Forces
- Periodic Signals
- Digital Electronics
Kinetics and Mechanics
- Description and Parameterization of Point Motion
- Newton’s Laws
- Energetic Approach to Point Motion
- Angular Momentum
- Motion in a Conservative Central Force Field
- Motion of a Solid
- Non-inertial Reference Frame
- Laws of Solid Friction
Optics
- Scalar Model of Light Waves
- Superposition of Light Waves
- Interferential Device using Wavefront Division: Young’s Double-Slit Experiment
- Interferential Device using Amplitude Division: Michelson Interferometer illuminated by a Spatially Extended Source
Electromagnetism
- Motion of Charged Particles in Electric and Magnetostatic Fields
- Electrostatics
- Magnetostatics
- Maxwell’s Equations
- Electromagnetic Field Energy
- Propagation and Radiation
Thermodynamics
- Principles of Thermodynamics
- Thermodynamic Machines
- Heat Transfers
Quantum Physics
- Wave Function and Schrödinger Equation
- Stationary States of a Particle in Piecewise Constant Potentials
- Non-Stationary States of a Particle in an Infinite Potential Well
Elements of Statistical Thermodynamics
- Boltzmann Factor
- System with Discrete Energy Spectra
- Classical Heat Capacities of Gases and Solids
Chemistry
- Chemical Transformations in Aqueous Solution
- Relationships between the Structure of Chemical Entities and Macroscopic Physical Properties
- Structure and Physical Properties of Solids
- First Principle of Thermodynamics Applied to Physicochemical Transformations
- Second Principle of Thermodynamics Applied to Physicochemical Transformations
- Thermodynamic Study of Redox Reactions
- Kinetic Study of Redox Reactions: Current-Potential Curve
- Storage and Conversion of Chemical Energy in Electrochemical Devices
- Corrosion
Computer science
Computer science structures
- Number Representation
- Data Structures
- Immutable Recursive Types and Trees
- Applications of Trees
- Basics of Graphs and Shortest Paths
- Advanced Graphs
- Languages and Automata
Paradigms
- Recursive Programming
- Introduction to Functional Programming
- Dynamic Programming
Logic
- Syntax and Semantics of Propositional Logic
- Natural Deduction for Propositional Logic
Other
- Databases
- Complexity analysis