Syllabus Grade 1-12

Course Material starting with Basics and continuing with  Model Workshop and Game Workshop following progression from simple to more complex with key examples, is listed as follows:

Counting in Binary and Decimal Form:
  1. Constructing the Natural Numbers  see Creation  compare Worldometer
  2. Binary Representation of Natural Numbers
  3. Binary Numbers: Illustration1  +  Illustration2
  4. Reading Binary Representation
  5. Binary Addition. Compare with 2048 Game.
  6. Binary Abacus1
  7. Binary Abacus2
  8. Abacus Adding Machine
  9. Binary Scale
  10. Binary Multiplication
  11. Binary Subtraction
  12. Natural Numbers: Base 3
  13. Natural Numbers: Any Base
  14. Binary Division
  15. Pocket Calculator
  16. Construction of Rational Numbers
Geometry – Motion
  1. Screen Geometry
  2. Motion-Change: x = x + v*dt
  3. Motion on Screen   Rabbit Motion
  4. Draw Line
  5. Newtonian Mechanics: Angry Birds Basic  (with image)
  6. Newtonian Mechanics
Elementary Functions
  1. Polynomials
  2. Exponential Function exp(t)
  3. Natural Logarithm log(t)
  4. Harmonic Series
  5. Trigonometric Functions cos(t) and sin(t) (Lissajous Figures) (Variant 2d) (Variant 3d)
  6. Polar Coordinates
  7. Complex Numbers
Solving Equations:
  1. Solving f(x)=0 by Bisection
  2. Solving f(x)=0 by Time Stepping x = x + f(x)*dt
  3. Solving x=g(x) by Fixed Point Iteration
  4. Solving f(x) = 0 by Newton’s Method
Calculus
  1. Calculus: Compute x = integral f(t)dt by Time Stepping dx=f(t)*dt
  2. Time Stepping: Smart, Dumb and Midpoint Euler
  3. Integral: Midpoint Euler vs Forward/Endpoint Euler
  4. L2 Projection on Continuous Piecewise Linears
  5. Piecewise Linear Approximation/Interpolation see Illustration
  6. Finite Element Method FEM 1d  (Compare with DigiMat Pro)
  7. FEM 2d -Laplace u = f = 1 (with f = delta function)
Modeling
  1. Examples from Model Workshop.