Download e-book for iPad: Calculus for Cognitive Scientists: Higher Order Models and by James K. Peterson

By James K. Peterson

ISBN-10: 9812878750

ISBN-13: 9789812878755

ISBN-10: 9812878777

ISBN-13: 9789812878779

This publication bargains a self-study software on how arithmetic, machine technology and technology might be profitably and seamlessly intertwined. This booklet specializes in variable ODE versions, either linear and nonlinear, and highlights theoretical and computational instruments utilizing MATLAB to provide an explanation for their suggestions. It additionally exhibits how one can remedy cable types utilizing separation of variables and the Fourier Series.

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Additional info for Calculus for Cognitive Scientists: Higher Order Models and Their Analysis

Example text

We then introduce the use of computational tools to solve the Predator–Prey model using MatLab in Sect. 11. While this model is very successful at modeling biology, the addition of self-interaction terms is not. The self-interaction models are analyzed in Chap. 11 and computational tools are discussed in Sect. 8. In Chap. 12, we show you a simple infectious disease model. The nullclines for this model are developed in Sect. 1 and our reasoning why only trajectories that start with positive initial conditions are biologically relevant are explained in Sect.

K. 1 A Roadmap to the Text In this course, we introduce enough relevant mathematics and the beginnings of useful computational tools so that you can begin to understand a fair bit about Biological Modeling. We present a selection of nonlinear biological models and slowly build you to the point where you can begin to have a feel for the model building process. We start our model discussion with the classical Predator–Prey model in Chap. 10. We try to talk about it as completely as possible and we use it as a vehicle to show how graphical analysis coupled with careful mathematical reasoning can give us great insight.

So again, the question of consistency is reasonable to ask. Here, the column vectors of AT are Y = 6 8 and Z = 18 24 We see Z = 3 Y and we have the system 6 x + 8 y = 14 = D1 3 (6 x + 8 y) = 48 = D2 This system would be consistent if the bottom equation was exactly three times the top equation. , we need −48 = 3 × 14 which is not true. So these equations are inconsistent. 1 Consider the system 2x +5y = 1 8 x + 20 y = 4 Determine if this system is consistent or inconsistent. 2 Consider the system 60 x + 80 y = 120 6 x + 8 y = 13 Determine if this system is consistent or inconsistent.

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Calculus for Cognitive Scientists: Higher Order Models and Their Analysis by James K. Peterson


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