Blackboard

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.

A

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)

B

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

C

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»

D

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

E

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

F

F1 . Uniform grid search

F2 . Bisection method

F3 . Fibbonacci method

F4 . Golden ratio method

F5 . Obtaining the minimum for parabolic interpolation

F6 . Parabolic method

G

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

Contact info

If you have a suggestion or a question, please write Oleksandr Kaleniuk, Ph. D., Senior lecturer at DTE / IATE / ISKPI.