1. MatRIC Visualization - Simulation - Programming VSP Per Henrik Hogstad

2. Matematikk 3
Eks:
Vektorfelt / Divergens
Multiple integraler
Polarkoordinater
Matematikk 1
Derivasjon / Integrasjon
Eksisterende simuleringer 15 stk
Egenprogrammering Python / Matlab
Derivasjon
Newtons metode
Modellering
Koblede svingninger
Pendel
Taipei Elevator

3. SimReal Visualization / Simulation / Programming
Understanding Mathematics
Realistic Problem Solving
Practical Use of Mathematics
y’ = (ex)’ = ex
Air Resistance
Linear Accelerator
Multiple Integral
Heat Transfer
Mammography

4. SimReal:
Existing Visualization / Simulation ActionScript / JavaScript
Programming:
Learning Tool:
SimReal JavaScript
Jupyter
Python
Matlab
Exercises / Solutions:
SimReal

5. Divergence

7. Multiple Integrals

9. Polar Coordinates

10. Differentiation
Computing
Visualization / Simulation
Programming

11. Differentiation

12. x
Differentiation y = a

13. Newton’s Method

14. Differentiation / Integration
Position – Velocity – Acceleration
Equations of Motion
Euler’s Method

15. Free Fall
Air Resistance

17. Position - Velocity - Acceleration

18. Position - Velocity - Acceleration

19. Differentiation / Integration Vector
Position – Velocity – Acceleration
Equations of Motion
Euler’s Method

20. Differentiation - Vector

21. Differentiation / Integration - Vector

22. Differentiation / Integration - Modelling

23. SimReal - Python - Matlab

24. Algorithmic Thinking
while (t < t0)
a = g – f(v)
v = v + at
s = s + v t
move
t = t + t

25. Algorithmic Thinking
while (t < t0)
F1 = -k1x1 + k3(x2-x1) a1 = F1/m v1 = v1 + a1t x1 = x1 + v1 t
F2 = -k2x1 + k3(x2-x1) a2 = F2/m v2 = v2 + a2t x2 = x2 + v2 t
move
t = t + t

26. Programming:
Only an advanced calculator?
Mathematics:
Critical Thinking
Argumentation
Reasoning
Creativity
Realistic Problems
Algorithmic Thinking

27. Digitale Verktøy
Geogebra
Mathematica
Maple
Matlab
Python …
SimReal
Understanding Mathematics/Physics
Visualization / Simulation
Programming Browser
Open Source Code
Executable on every device
Web

28. Jupyter NTNU

30. Programming:
Only an advanced calculator?
The Department of Education:
Mathematics:
Critical Thinking
Argumentation
Reasoning
Creativity
Realistic Problems
Algorithmic Thinking
Programming

34. SimReal
Interactivity
Streaming

35. Feedback Result

36. A Common Resource Database
SimReal
A Common Resource Database
Streaming
Exercise
Video Lesson
Video Simulation
Programming
JavaScript
Python
Matlab
Practical Application
Interactive Visualization / Simulation

37. MatRIC Help Centre

38. Advanced Mathematics

41. Activity Research
Master Thesis UiA (Albania 1, Norway 2)
PhD UiA
Research Teacher Education - 2 UiA
Programming Group - 1 UiA (5 students)
Cooperation - UiA / UiO / NTNU / HiMolde
Package  Single Simulations
ActionScript  JavaScript / Python
Web
Programming
Resource Base

44. function move_particle (t,n)