Here, we are talking about a very important type of modeling, showing its concept, and its applications in industry in the shape of softwares.

1. MATHEMATICAL MODELING
AND
SMULATION
Mohamed Alaa Fathalla
Mansour Nasr

2. • Why ? The need for a model
• Find ? What do we need to
describe the model
• Given ? Available data
• Assume ? Assumptions we make
• How ? The physical case
• Predict ? Equations, calculations,
Answers
• Valid ? Are the predictions accepted
• Verified ? will it be useful
• Improve ? What did I ignore !
• Use ? What will I use The model for

3. Mathematical
Modeling
what is it ?
W=Qhot - Qcold

4. Let’s do an experments,then we
will model it.
(mathematical model)

6. Mathematical
representation
Simple linear equations

7. Mathematical
representation
Non linear relation

8. Heat equation
𝜕𝑇
𝜕𝑡
= 𝑘(
𝜕𝑇2
𝜕𝑥2 +
𝜕𝑇2
𝜕𝑦2+
𝜕𝑇2
𝜕𝑧2)
Not a simple equation, the system is very complex
to be defined.

9. How to solve this
problem ?
NUMERICAL SOLUTIONS

10. Computational
Models

12. I made the model
What will I use it for!
SIMULATIONS

13. Car crash test
Insurance Institute for Highway Safety

14. Video link:
https://www.youtube.com/watch?v=oS7Nw_pV0K0

17. SOFTWARE I CAN
USE.

18. MATLAB

19. AUTODESK
http://www.autodesk.com/

20. AUTODESK
MAYA

21. MICROSOFT
HOLOLENS
Video link:
https://www.youtube.com/w
atch?v=qym11JnFQBM

22. MICROSOFT
HOLOLENS
&
AUTODESK
Video link:
https://www.youtube.com/watch?v=ywXWqNdVtjs

23. ANSYS
Higher level of accuracy.

24. Error !
Are them 100% correct

25. THE MATHEMATICS IN YOUR HEART

26. Video link:
https://www.youtube.com/watch?v=2LPboySOSvo