A Crash course in biomathematics Introduction (technical details)

INTRODUCTIONHow the zebrafish got its stripes

A crash in biomathematics

V. 1.0, L’Aquila, 2015.Jorge Guerra Pires.University of L’Aquila, Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica

Technical Details

INTRODUCTION

• Biomathematics is a quite complicate field if we want to teach it in a single picture, as so that most of the authors of classical books in biomath are not ashamed of claiming this issue. One example of that is the number of journals for biomathematics in the last decades, it seems almost impossible that in a list of 10 journals, at least one isn’t about biomathematics.

• Suppose you are given 10 problems from physics to solve. Then you are given 100 problems, making a total of 110 problems to solve, a classical summer homework given by some professors; classically people do not solve it, they make internet surveys or pay a geek for solving them, I have been paid a lot for that! But, suppose you solve them. It is likely that the physics needed to solve 10 problems or 100 did not increased considerably, they will be Newtons’ laws, Keplers’ law and so on.

• That is the magic of physics, a big knowledge is shrank in small sentences called laws, principles or theorems. When I was tutor of physics, and private professor, I noticed that the majority of people needed help on physics more than the other sciences, e.g. history and biology. The answer is simple, they wanted to handle physics the same way you handle biology, it is a mistake, impossible! Even mathematics can be handled as biology, I have seen several examples in calculus, but not physics. Why?


INTRODUCTION

J.G. Pires. University of L’Aquila, Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica

V. 1.0, L’Aquila, 2015.

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V. 1.0, L’Aquila, 2015.

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V. 1.0, L’Aquila, 2015.

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…Why? The answer is that physics is based on general laws. For instance, with the second law of Newton you can derive the wave equation, predict the trajectory of a stone/rocket, water pressure, and similar cases; I will try to bring examples from physics showing this, how a single equation that do not occupy even a half of a line can be used to make to much. Analogously, the Schrodinger, analogous to the one of Newton, supposes to describe the whole universe mathematics, “truly how God thinks”, however it is limited, being limited by Einstein’s equations; but it is still brilliant, from electron alone to orbital, the Schrödinger equation has been widely applied.


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V. 1.0, L’Aquila, 2015.

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V. 1.0, L’Aquila, 2015.

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V. 1.0, L’Aquila, 2015.

CONTENT OVERVIEW Part I: Methodological/Scientific procedures

• Useful principle/laws from physics, e.g. mass conservation;• Useful techniques for solving differential equation numerically, e.g Runger Kutta Methods;• Useful techniques and tricks for solving differential equations analytically, limited, e.g. integration factor;• Programming hints and tips, e.g. Java primes, Matlab primes; • Useful modeling strategies.

Part II: Toy models• Classical problems, e.g. prey-predator model• Problems I have faced, e.g. gene expression, pharmacokinetics and pharmacodynamics• Possible designed problems, e.g. take a physiological observation and make it happen;• Maybe more Methodological procedures/scientific

Part III: Advanced Models• Model I have faced, e.g. leptin dynamics;• Models from the literature, e.g. glucose control;• Models designed, e.g. take textbook model and make it go further.


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V. 1.0, L’Aquila, 2015.

This agenda is for the crash course, not for the Youtube channel, see the setting goals and beyong video. Further, all the videos are experimental.






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Education

A Crash course in biomathematics Introduction (technical details)