This is the Blackboard — a collection of interactive visuals on basic maths, numerical methods, and mathematical programming.
The visuals are stackable, you can write your own sequence using the "sequence" parameter. For instance: https://okaleniuk.codeberg.page/blackboard/A5.html?sequence=A5A7B2B5B9 is a 5-pages long sequence about splines.
There is a primitive sequence constructor, too: https://okaleniuk.codeberg.page/blackboard/sequence_constructor.html
A1 . Derivative
A2 . Derivatives of some functions
A3 . Differential analysis–synthesis
A4 . Power series
A5 . Polynomial interpolation
A6 . Cubic polynomial with governable derivatives
A7 . Runge's phenomenon
A8 . Chebyshov nodes
A9 . Piecewise smooth function (primitive spline)
AA . Lagrange interpolating polynomial
AB . Lagrange interpolant formulas
AC . Lagrange basis polynomial
AD . Weighted basis polynomial
AE . Least squares approximation
AF . Vandermonde matrix
AG . Rational interpolation
B1 . Parametric curve (cubic)
B2 . Naïve cubic spline
B3 . Quadratic spline with non-continuous derivatives
B4 . Animation with a quadratic spline
B5 . NURBS is an acronym
B6 . Degree of the basis functions
B7 . Non-uniformity (knot vectors)
B8 . Rationality (weights)
B9 . NURBS circle
BA . Bezier curves
BB . Rational Bezier curves
BC . Bezier curve is a polynomial parametric curve
C1 . Cartesian coordinate system and homogeneous coordinates
C2 . What's «too far» in homogeneous coordinates?
C3 . Translation
C4 . Rotation
C5 . Scaling
C6 . Affine transformation
C7 . Projective transformation
C8 . Formulas in Cartesian coordinates
C9 . Matrix multiplication in homogeneous coordinates
CA . Matrices make transformations «stackable»
D1 . Ways to describe a linear system
D2 . Overspecified systems
D3 . Iterative solver
D4 . Direct solver
D5 . The complexity of the direct solution
D6 . Gaussian elimination
D7 . How to chose a solver?
D8 . Gauss-Seidel
E1 . Complex numbers sum
E2 . Complex number scalar multiplication
E3 . Complex numbers multiplication
E4 . Conformal transformation
E5 . Bilinear transformation
E6 . Bi-quadratic transformation
E7 . Cubic-linear transformation
E8 . A practical example
F1 . Uniform grid search
F2 . Bisection method
F3 . Fibbonacci method
F4 . Golden ratio method
F5 . Obtaining the minimum for parabolic interpolation
F6 . Parabolic method
G1 . Coordinate descent
G2 . Hooke-Jeeves pattern search
G3 . Rosenbrock's method
G4 . Powell's method
G5 . Nedler-Mead's method (simplex search)
G6 . Gradient descent
G7 . Steepest descent
G8 . Coordinate descent (another Gauss-Seidel)
G9 . Levenberg-Marquardt
GA . Newton's (second order)
GB . Fletcher-Reeves'
GC . Davidon-Fletcher-Powell's
GD . Broyden–Fletcher–Goldfarb–Shanno's
H1 . Penalty method
H2 . Barier method
I1 . 6-bit integer number
I2 . 6-bit fixed point number
I3 . 6-bit floating-point number
I4 . Representation error of the 6-bit float
I5 . The error of the floating point sum
I6 . Kahan summation algorithm
I7 . Cubic equation error quiz
I8 . Cubic equation error cube
I9 . Error estimations with intervals
IA . Interval comparison
IB . Interval addition
IC . Interval multiplication
ID . Rational interval arithmetics
IE . Real comparison
IF . NaN can contain error codes
J1 . Rieman integral
J2 . Numerical integration
J3 . Euler's method for the ODE Cauchy problem
K1 . Sine function
K2 . Sine mnemonic
K3 . Cosine function
K4 . Cosine mnemonic
K5 . Sin and cos application: rotation
K6 . Sin and cos application: smooth movement
K7 . Sin and cos application: closed curves
K8 . Tangent function
K9 . Arctangent function
KA . Arctangent scale
L1 . Uniform grid solver
L2 . Bisection solver
L3 . Secant solver (regula falsi)
L4 . Improved regula falsi (Illinois method)
If you have found a bug, please report it at the Codeberg project page.
If you have a suggestion or a question, please write Oleksandr Kaleniuk,