1. Mathematical methods in chemical engineer

2. Dr. Łukasz Radosiński
Room no. 112, b. C6 Tel Web: Help session: Tuesday: OW 13:30-15:30, EW 17:00-19:00 Wenesday: 15:00-17:00

3. Zasady zaliczenia
Project, to proces numerical methods applied in scientific paper, group of 5 people, positions and responsibilities, deadline 3 weeks before exams session.
Oceny:
≥50 %→3.0
≥60 %→3.5
≥70 %→4.0
≥80 %→4.5
≥90 %→5.0
≥95 %→5.5
Recalculation of data with 50 % error
Recalculation of data
Method improvement

4. About me Proffesional career:
, Research Assistant, High Energy Accelerator Research Organization KEK, Photon Factory, Tsukuba, Japonia

5. About me Proffesional career:
, Research Assistant, High Energy Accelerator Research Organization KEK, Photon Factory, Tsukuba, Japonia
, Consultant, Toyoink, Tsukuba, Japonia,

6. About me Proffesional career:
, Research Assistant, High Energy Accelerator Research Organization KEK, Photon Factory, Tsukuba, Japonia
, Consultant, Toyoink, Tsukuba, Japonia,
, Assistant Professor, Chemical Phsysics Institute, PWr.
Project Manager
2011-, Associate Professor, Group of Bioprocess and Biomedical Engineering.
Project Manager, team leader
Other:
- Bussiness brokarage, market region Europe-Asia.

7. Scope of the module Important:
To learn how to combine advanced mathematical methods with experimantal data.
Experimental data post-processing.
To learn how to use computational methods to solve analytical problems.
Important:
Only selected methods. 15 h is not enough!

8. Scope of the module
To combine calculus algebra, differentia equations, statistics and computer technology.
What are the most popular and useful mathematical methods in industry, business and science.
To increase possibilities of getting good job.

9. Does knowledge of mathematics increse your chance of getting a job?
Depends what job!
Driving licence B cat.
Does driven has to know about vehicle’s mechanics? No!
Salary around PLN

10. Does knowledge of mathematics increse your chance of getting a job?
Depends what job!
Driving licence D cat.
Does driven has to know about vehicle’s mechanics? Limited knowledge, identification of mailfaction, basic repairs.
Salary app PLN brutto

11. Does knowledge of mathematics increse your chance of getting a job?
Depends what job!
Superlicence
Does driven has to know about vehicle’s mechanics? YES! Direct inclusion in the design and exploatation process.
Salary app. 22 mln Euro brutto (S. Vettel 2014)

12. Does knowledge of mathematics increse your chance of getting a job?
Depends what job!
Limited usage of mathematical methods, week based summaries, line optimisation,
Salary app.1800 netto PLN
Process engineer
YES, extensive use of analitcal and post processing methods
Salary > 5000 PLN
Senior engineer R&D

13. Does knowledge of mathematics increse your chance of getting a job?
Depends what job!
YES, system integration, every team has numerical or IT specialists, know what your team is capable of
Salary > 7000 PLN
Manager
Insurance analyst
Data mininig, statistics
Salary > CHR annual

15. What will we use to perform computations?
Microsoft Excel
MATLAB

17. USE UNIVERSITY .
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18. When registered:

21. Wait for your reservation to start and click monitor button to start virtual machine.
In the first login window as login enter: platon\wcss-yourlogin and password for Platon website.
Second login window is for login: Administrator, to read your password click the gold key It shows above the table.

22. Differential equations Linear regression Nonlinear regression
Linear equations
Nonlinear equations
Differential equations
Linear regression
Nonlinear regression
Introductionary statistics
Fitting model

23. Differential equations Linear regression Nonlinear regression
Linear equations
Nonlinear equations
Differential equations
Linear regression
Nonlinear regression
Introductionary statistics
Fitting model

24. Differential equations Linear regression Nonlinear regression
Linear equations
Nonlinear equations
Differential equations
Linear regression
Nonlinear regression
Introductionary statistics
Fitting model

25. Differential equations Linear regression Nonlinear regression
Linear equations
Nonlinear equations
Differential equations
Linear regression
Nonlinear regression
Introductionary statistics
Fitting model

26. Differential equations Linear regression Nonlinear regression
Linear equations
Nonlinear equations
Differential equations
Linear regression
Nonlinear regression
Introductionary statistics
Fitting model

27. Differential equations Linear regression Nonlinear regression
Linear equations
Nonlinear equations
Differential equations
Linear regression
Nonlinear regression
Introductionary statistics
Fitting model

28. Differential equations Linear regression Nonlinear regression
Linear equations
Nonlinear equations
Differential equations
Linear regression
Nonlinear regression
Introductionary statistics
Fitting model

29. Differential equations Linear regression Nonlinear regression
Linear equations
Nonlinear equations
Differential equations
Linear regression
Nonlinear regression
Introductionary statistics
Fitting model
Równania liniowe
Równania nieliniowe
Równania różniczkowe
Regresja liniowa
Regresja nieliniowa
Wstęp do statystyki
Dopasowanie modelu

30. Fourier series

31. Model
Dealing with engineering problems often requiers to use mathematical model in order to interpolate or extrapolate values of interests
Although deriving mathematical model might be a challange ever greater one might its analysis,
Typical approach is to exchange one complex mathematical formula by a series of simple functions: e.g. series expansion
Complex function  collection of simple functions
𝑙𝑛 arctanh 𝑥  𝑥, 𝑥 2 , 𝑥 3 , 𝑥 4 ,…

32. Many natural and engineering phenomena occurs in periodic manner:
weather, radio signal, molecular vibrations, mechanical devices, image.
What is more interesting is that those phenomena interfere together creating very complex but periodic phenomena
In order to deal with such signals it is needed to develope a procedure to investigate what are those fundamental periodic components of out complicated phenomena  to simplify it

33. Example El Nino

35. Enso data after applying smoothing filter twice

36. Enso data cosine series fit
𝑦= 𝑎 0 + 𝑎 1 cos 2𝜋 𝑥 𝑐 𝑏 1 sin 2𝜋𝑥 𝑐 1
𝑎 2 cos 2𝜋 𝑥 𝑐 𝑏 2 sin 2𝜋𝑥 𝑐 2 +
𝑎 3 cos 2𝜋 𝑥 𝑐 𝑏 1 sin 2𝜋𝑥 𝑐 3
𝑐 1 =11.94
𝑐 2 =22.03
𝑐 3 =43.58