By John Milton
This introductory textbook relies at the premise that the root of fine technological know-how is nice information. the tutorial problem addressed by means of this introductory textbook is how you can current a sampling of the big variety of mathematical instruments to be had for laboratory examine to well-motivated scholars with a mathematical heritage restricted to an introductory path in calculus.
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Extra info for Mathematics as a Laboratory Tool: Dynamics, Delays and Noise
Example text
2 The delineation between a system and its surroundings and the interactions between them is a crucial step in the scientific method. Equally important is the choice of the appropriate scale at which the problem should be considered. For example, if our interest is the kinematics of animal locomotion, it would likely not be fruitful to consider the interaction between the contractile proteins actin and myosin at the level of single atoms. On the other hand, the dynamics of the molecular motors involved in axonal transport require consideration of molecular motions.
1 Galileo Galilei (1564–1642), Italian physicist, mathematician, astronomer, and philosopher. He was an important advocate of the Copernican heliocentric theory. J. Milton and T. 1007/978-1-4614-9096-8 2, © Springer Science+Business Media New York 2014 17 18 2 The Mathematics of Change rise 4. What is the time scale of change for a dynamical system? 5. What is the general form of the solution of an nth-order linear ODE with constant coefficients? run rise x run time t1 t2 t3 t4 Fig. 1 A plot of the values of a variable x as a function of time, showing a region of negative slope (between t1 and t2 ) and a region of positive slope (between t3 and t4 ).
It can happen that the phenomena predicted by the dimensionless model occur for parameter ranges that are not reasonable for a living system. Such a demonstration would suggest that the model is not valid for the system under investigation and should encourage the modeler to seek a more robust model. 3 Input–Output Relationships In the real world, living organisms do not come with the equations that describe their actions imprinted on their bodies for all to see. Therefore, we do not begin our investigations with the assumption that a suitable mathematical model is known.