Café Planck
Modern Education
Welcome to Café Planck
Created by Matin Bavardi & Dian Soha
Since 2010, Café Planck has stood as an open repository of mathematical and physical knowledge, representing a unique fusion of programming and scientific education. What began as a collection of educational materials has evolved into a comprehensive digital laboratory, demonstrating how programming can transform the way we learn and understand science.
Our Foundation
Built on Wolfram technology and powered by precise computational methods, Café Planck offers an extensive collection of over 30,000 pages of resources, including:
- Interactive mathematical demonstrations
- Physics simulations and visualizations
- Comprehensive course materials
- Advanced computational notebooks
- Educational programming solutions
What Sets Us Apart
- Precision-Engineered Solutions: Every demonstration and simulation is crafted with mathematical rigor and computational accuracy
- Interactive Learning: Dynamic visualizations that transform abstract concepts into tangible understanding
- Open Access: All materials are freely available, supporting our mission of democratizing scientific education
- Comprehensive Coverage: From fundamental concepts to advanced theoretical frameworks
- Professional Tools: Powered by Mathematica, offering sophisticated computations and visualizations
Resource Categories
- Mathematics (Calculus, Linear Algebra, Fourier Analysis)
- Classical Mechanics
- Quantum Mechanics
- Optics
- Special Relativity
- Computational Physics
- Advanced Visualization Techniques
Our Future
In 2020, marking a significant milestone, Café Planck’s entire collection was officially donated to PlayText Software Inc., a BC Benefit Company. This donation aligns with and supports the company’s humanitarian objectives in digital preservation and education accessibility. Our ongoing mission is to continuously update and develop these resources, making them more sophisticated and accessible to learners worldwide.
Note: To access .nb files, download the free Wolfram Player. All materials are available for public use under MIT license.
Join us in exploring the fundamental laws that govern our universe through the power of computational science and programming.
Café Planck: Transforming scientific education through programming excellence.
Table Of Contents
Mathematics
Coordinate System
Cartesian Coordinate System
Cylindrical Coordinate System
Spherical Coordinate System
Polar Coordinate System
Miscellaneous
Plane Analytic Geometry
Single variable calculus
Intervals
- Les Intervalles
Functions
- Fonction
- Injectivite
- Surjectivite
- Bijectivite
- Operation Sur Les Fonctions
- Fonction Composee
- Fonction Paire Et Impaire
- Le Sens De Variation
Limit
- Limit
- More examples of computing limits
Asymptote
- Horizontal asymptote
- Vertical asymptote
- Oblique asymptote
Derivative
- Definition
- Derivative
- Derivee Des Fonctions Elementaires
Curve
- Type 01 Download link
- Type 02 Download link
- Type 03 Download link
- Type 04 Download link
- Type 05 Download link
- Type 06 Download link
- Type 07 Download link
- Type 08 Download link
- Type 09 Download link
- Type 10 Download link
Differential
- Differential
Integral
- Definite integral
- Indefinite integral
Sequence and Series
- Sequence and Series of Numbers
- Taylor Series for Functions
- Sequence and Series of Functions
Function Visualization
- Functions of Two Variables
- Plane Curves
- Space Curves
- Parametric Surfaces
- Vector Field
- Contour Plot
- Revolution Plot 3D - I
- Revolution Plot 3D - II
- Spherical Plot 3D
- Region Plot
- Area Between Two Curves
Vector Calculus
- Vector Field
- Gradient
- Divergence
- Curl
- Laplacian
- Download link
Interactive visualization of Euclidean space
- Interactive visualization of two-dimensional Euclidean space
- Interactive visualization of three-dimensional Euclidean space
Space
- Space R2
- Space R3
- Space Rn
- Space Pn
- Space Cn
- Space C[a,b]
- Space C*[a,b]
Development of function
Inner product
- On Space Rn
- On Space Cn
- On Space Pn
- On Space C[a,b]
- On Space C*[a,b]
Norm
- On Space Rn
- On Space Cn
- On Space Pn
- On Space C[a,b]
- On Space C*[a,b]
Orthogonal Projection
- On Space Rn
- On Space Cn
- On Space Pn
- On Space C[a,b]
- On Space C*[a,b]
Orthogonalization
- On Space Rn
- On Space Cn
- On Space Pn
- On Space C[a,b]
- On Space C*[a,b]
Development of function
- On Space Rn
- On Space Cn
- On Space Pn
- On Space C[a,b]
- On Space C*[a,b]
Rodrigues’ Formula
- Jacobi polynomials
- Legendre polynomials
- Chebyshev I polynomials
- Hermite polynomials
- Laguerre polynomials
Sturm–Liouville theory
- Équation différentiel Sturm-Liouville (Part 1)
- Équation différentielle de Legendre
- Équation différentielle de Laguerre
- Équations différentielles de Hermite
- Équations différentielles de Chebyshef I
- Équation différentielle de Helmholtz
- Équations différentielles de oscillateur harmonique
- Équation de Laplace en coordonnées sphérique (Symétrie Azimutale)
Integral Transforms
- Fourier Transform
- Laplace Transform
Classical orthogonal polynomials
- Legendre Polynomials
- Hermite Polynomials
- Laguerre Polynomials
- Chebyshev Polynomials
version 1
- Fonctions de carré sommable
- Produit scalaire, normalité, orthogonalité et orthonormalité
- Bases de l’espace des fonctions de carré sommable
- Développement d’une fonction
- Théorème de Stone - Weierstrass
- La méthode de Gram-Schmidt
- Les polynômes orthogonaux classiques
- Les polynômes orthogonaux associés classiques
version 2
- Classical orthogonal polynomials
- Legendre polynomials
- Legendre polynomials in polar coordinates
- Hermite polynomials
- Laguerre polynomials
- Chebyshev I polynomials
Trigonométrie
- Circonférence trigonométrique
- Angles associés
- Les fonctions trigonométriques
- Les fonctions trigonométriques inversses
Notbooks:
- Radian and Degree conversion
- Angle and cartesian coordinate conversion
- Trigonometric circle
- Special Pairs of Angles
- Trigonometric Expand
- Trigonometric Factor
- Trigonometric Reduce
- Trigonometric equations
- Quadratic trigonometric equations
Fourier Analysis
-
Numerical Functions Download link
-
Related Functions to Fourier Analysis Download link
-
Signals Download link
-
Fourier Series Download link
-
Fourier Transforms
- Discrete Fourier Transforms (DFT)
- Fast Fourier Transform (FFT) Download link
Physics
Classical mechanics
Vectors
- Multiplication of vectors
Rectilinear motion
- Horizontal motion
- Vertical projectile motion
Curvilinear motion
- Angled projectile motion
- Curvilinear motion in polar coordinate system
- The Monkey and a gun
Harmonic motion
- Simple vertical spring-mass system
- Damped vertical spring-mass system
- Driven vertical spring-mass system
Dynamics
- Multi Mass 1
- Multi Mass 2
- Multi Mass 3
- Multi Mass 4
- Multi Mass 5
- Ramp
- Wall
- Drag
- Push
- Pulley
- Ramp and Pulley
- Elevator
Lagrangian Dynamics
- Horizontal motion
- Vertical motion
- Simple pendulum
- Simple pendulum with damping and external force
- Double pendulum
- Pendulum hanging from a spinning ring
- Horizontal mass spring system
- Vertical mass spring system
- Conical pendulum
- Spring-Pendulum system
- Pendulum on a movable support
Vibrations and waves
Basic waves formulas
- Basic waves formulas.pdf
- Basic waves formulas.pptx
Sinusoidal waveform
- Vibrations and waves
- Vertical undamped spring mass system
- Vertical damped spring mass system
- Equation Onde Classique
- Une Onde Classique
- Superposition Discrete Des Ondes
- Superposition Continue Des Ondes
Non sinusoidal waveform
- Square wave
- Triangle wave
- Sawtooth wave
Helmholtz Equation
- Helmholtz equation
- Helmholtz equation I
- Helmholtz equation II
- Helmholtz equation III
Time Equations
- Time Equations 1
- Time Equations 2
Classical wave equations
- Classical wave equations
- Taut string, Fixed at x = 0 and x = L
- Taut string, Fixed at x = 0 and free at x = L
- Taut string, Free at x = 0 and x = L
- Rectangular member
Miscellaneous
- Pulses
- Superposition of Wave Pulses
- Standing waves
Sound waves
- Sound waves
Thermodynamics
- Heat partial differential equation
Quantum mechanics
Stern-gerlach Exêriment
Wave vs Particle
Wave
- Équation d’onde classique
- Une onde classique
- Superposition discrète des ondes (Impulsion périodique)
- Superposition continue des ondes classique (Impulsion non-périodique ou Paquet d’onde)
Particle
- Équation de Schrödinger
- Superposition continue des ondes quantique (Impulsion non-périodique ou Paquet d’onde quantique)
Bases bras et kets
- Bases bras et kets
Mes Notes En Francais
- Le courant de probabilité
- Les conditions de continuité aux frontières entre les régions
- Équation de Schrödinger
- Puits de potentiel infini entre -a et a
- Puits de potentiel infini entre 0 et L
- Le potentiel en forme de marche
- La barrière de potentiel
- Le puits potentiel rectangulaire
- Équation de Hermite
- Oscillateur harmonique quantique en 1D
- Équation d’Euler-Cauchy
- Équation de Legendre
- Équation de Legendre associée
- Équation de Laplace en coordonnées sphérique
- Moment cinétique
- Les fonctions propres de l’opérateur de moment cinétique en coordonnées sphérique
- Équation de Schrödinger en 3D
- Atome d’Hydrogène
Les valeurs propres et les vecteurs propres
- Les valeurs propres et les vecteurs propres (Operateur differentiel)
- Les valeurs propres et les vecteurs propres (Operateur matriciel)
Les matrices de Pauli
- Les matrices de Pauli
Eigenvalues and eigenvectors of angular momentum operator
Version 1
- For j=1/2
- For j=1
- For j=2
Version 2
- For j=1/2
- For j=1
- For j=2
Optics
Un peu d’optique au niveau secondaire
Les miroirs
- Les miroirs convergents
- Les miroirs divergents
Les lentilles
- Les lentilles convergentes
- Les lentilles divergentes
L’oeil
- L’oeil normal
- L’oeil myope
- L’oeil presbyte
Special relativity
Under Construction
- Lorentz transformation
- Ratio of relative velocity v to the speed of light c
- Lorentz factor
- Length contraction
- Time dilation
- Composition of velocities
- Relativity of Simultaneity
- Space distance vs space-time interval
- Minkowski diagram
- Proper Time and proper length
- Metric