James K. Peterson

Calculus for Cognitive Scientists (eBook, PDF)

Higher Order Models and Their Analysis

• Format: PDF

Produktbeschreibung

This book offers a self-study program on how mathematics, computer science and science can be profitably and seamlessly intertwined. This book focuses on two variable ODE models, both linear and nonlinear, and highlights theoretical and computational tools using MATLAB to explain their solutions. It also shows how to solve cable models using separation of variables and the Fourier Series.

Produktdetails

• Verlag: Springer Singapore
• Erscheinungstermin: 9. Februar 2016
• Englisch
• ISBN-13: 9789812878779
• Artikelnr.: 44598290

Autorenporträt

Dr. James Peterson is an Associate Professor in Mathematical Sciences and Biological Sciences at Clemson University, USA. His formal training is in mathematics but he has worked as an aerospace engineer and a software engineer also. He enjoys working on very hard problems that require multiple disciplines to make sense out of and he reads, studies and plays in cutting edge areas a lot as part of his interests.

Inhaltsangabe

Introductory Remarks.- Linear Algebra.- Numerical Methods Order One ODEs.- Multivariable Calculus.- Integration.- Complex Numbers.- Linear Second Order ODEs.- Systems.- Numerical Methods Systems of ODEs.- Predator Prey Models.- Predator Prey Models With Self Interaction.- Disease Models.- A Cancer Model.- Nonlinear Differential Equations.- An Insulin Model.- Series Solutions.- Final Thoughts.- Background Reading.

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Introduction.- Graham - Schmidt Orthogonalization.- Numerical Di erential Equations.- Biological Molecules.- Ion Movement.- Lumped and Distributed Cell Models.- Time Independent Solutions to Infinite Cables.- Time Independent Solutions to Finite and Half-Infinite Space Cables.- A Primer On Series Solutions.- Linear Partial Di erential Equations.- Simplified Dendrite - Soma - Axon Information Processing.- The Basic Hodgkin - Huxley Model.- Final Thoughts.- Background Reading.

Rezensionen

"The introductory remarks in this book address the concern that many presentations of mathematics focus so heavily on traditional content that the usefulness of mathematics in other fields can be overlooked. ... the approach is both demanding and thorough, but the brief exercise sets remain focused on providing opportunities for straightforward practice of the principles at hand. ... Summing Up: Recommended. Lower- and upper-division undergraduates." (N. W. Schillow, Choice, Vol. 54 (4), December, 2016)