Professor access
Student access
login
*
Password
*
(*) mandatory fields
Password forgotten
Create a new account
Level upgrading platform
Toggle navigation
Home
Maths
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Physics
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Forum
Table of contents
Maths
Home
Maths
Chapter 1
Analysis Basics
Introduction
Learning programme
Continuous applications
Exercise 1
Exercise 2
Exercise 3
Finite limits
Infinite limits
Exercise 4
Exercise 5
Differentiable applications
Exercise 6
Exercise 7
Exercise 8
Taylor-expansion
Exercise 9
Exercise 10
Exercise 11
Exercie 12
Comparison relations and compared growths
Numeric sequences
Exercie 13
Exercie 14
Exercie 15
Multiple choice quiz
Aditionnal exercises
Exercie 16
Exercie 17
Exercie 18
Exercie 19
Exercie 20
Chapter 2
Algebra bases
Introduction
Learning program
The field of complex numbers
Trigonometric form of complex numbers
Exercise 1
Exercise 2
Exercise 3
Exponential form of complex numbers
Exercise 4
Exercise 5
Second degree equation
Exercise 6
Ring of polynomials
Euclidian division of polynomials
Exercise 7
Roots of a polynomial
Exercise 8
Exercise 9
Vector spaces
Linear combinations, linearly independant famillies, generating famillies, bases, dimension
Vector spaces of finite dimension
Exercise 10
Exercise 11
Exercise 12
Exercise 13
Aditionnal exercises
Exercise14
Exercise 15
Exercise 16
Exercice 17
Exercise 18
Exercise 19
Exercise 20
Multi choice quiz
Chapter 3
Linear algebra
Introduction
Learning program
Vector subspaces
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Linear applications
Exercise 5
Exercise 6
Matrix of a linear application in a basis, change of basis formula
Exercise 7
Exercise 8
Determinants
Exercise 9
Quiz
Aditionnal exercises
Exercise 10
Exercise 11
Exercise 12
Exercise 13
Exercise 14
Exercise 15
Exercise 16
Chapter 4
Integration
Introduction
Learning program
Riemann's Integral
Exercise 1
Exercise 2
Generalised integrals
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Quiz
Aditionnal exercises
Exercise 9
Exercise 10
Exercise 11
Exercise 12
Exercise 13
Exercise 14
Chapter 5
Normed vector spaces
Introduction
Learning program
Normed vector spaces
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Sequences in a normed vector space
Special sets and special points in a normed vector space
Exercise 6
Exercise 7
Exercise 8
Limits
Continuous applications
Exercise 9
Exercise 10
Exercise 11
Quiz
Aditionnal exercises
Exercise 12
Exercise 13
Exercise 14
Exercise 15
Exercise 16
Chapter 6
Sequences of functions
Introduction
Learning program
Definitions, examples
Exercise 1
Exercise 2
Continuity, differentiability
Exercise 3
Exercise 4
Dominated Convergence Theorem
Exercise 8
Exercise 9
Parameter-Dependant Integrals
Exercise 11
Exercise 12
lessons
Definitions, examples
Continuity, differentiability
Dominated Convergence Theorem
Parameter-Dependant Integrals
Multiple choice quiz
exercises
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Exercise 1
Exercise 10
Exercise 11
Exercise 12
Exercise 13
Exercise 14
Chapter 7
Number series and functions series
Introduction
Learning program
Module 7 Number series and functions series
Exercise 1
Exercise 2
Exercise 3
Study of positive term series
Exercise 4
Alternating series
Exercise 5
Exercise 6
Function series, pointwise convergence
Exercise 7
Uniform convergence
Exercise 9
Normal convergence
Exercise 10
Exercise 11
QCM
Aditionnal exercises
Exercise 12
Exercise 13
Exercise 14
Exercise 15
Exercise 16
Exercise 17
Chapter 8
Reduction of endomorphisms
Introduction
Learning program
Reduction of endomorphisms
Exercise 1
Exercise 2
Eigenvalues and eigenvectors
Exercise 3
Exercise 4
Characteristic polynomial
Exercise 5
Diagonalization of an endomorphism or a matrix
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Exercise 10
Exercise 11
Exercise 12
Trigonalization
QCM
Aditionnal exercises
Exercise 13
Exercise 14
Exercise 15
Exercise 16
Exercise 17
Exercise 18
Exercise 19
Exercise 20
Chapter 9
Power series
Introduction
Learning program
Radius of convergence
Exercise 1
Exercise 2
Fundamental properties
Exercise 3
Exercise 4
Sums and products of power series
Exercise 5
Exercise 6
Development in power series of a function
Development as a power series of usual functions
Exercise 8
Exercise 9
Exercise 10
Exercise 11
QCM
Aditionnal exercises
Exercise 12
Exercise 13
Exercise 14
Exercise 15
Exercise 16
Exercise 17
Chapter 10
Euclidian algebra
Introduction
Learning program
Euclidian algebra
Orthogonality
Exercise 1
Exercise 2
Exercise 3
Orthogonal automorphisms, orthogonal matrices
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Diagonalization of symmetric endomorphisms
Exercise 8
Exercise 9
Exercise 10
QCM
Aditionnal exercises
Exercise 11
Exercise 12
Exercise 13
Exercise 14
Exercise 15
Exercise 16
Exercise 17
Chapter 11
Differential equations
Introduction
Learning program
Equations différentielles
Exercise 1
Exercise 2
Differential equation of the second order
Resolution of the homogeneous equation
Exercise 3
Exercise 4
Equations that can be reduced to a linear equation
Exercise 5
Exercise 6
QCM
Aditionnal exercises
Exercise 7
Exercise 8
Exercise 9
Exercise 10
Chapter 12
Probability
Introduction
Learning program
Probability spaces
Exercise 1
Conditionality and independance
Exercise 2
Exercise 3
Exercise 4
Random variables
Expected value of a random variable
Variance and standard deviation
Exercise 5
Exercise 6
Exercise 7
Generating series of a random variable with natural integer values
Asymptotic results
Exercise 8
Exercise 9
Exercise 10
QCM
Aditionnal exercises
Exercise 11
Exercise 12
Exercise 13
Exercise 14
Exercise 15
Exercise 16