Calculus for Cognitive Scientists - Higher Order Models and Their Analysis

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.

List of contents

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.

About the author

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.

Summary

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.

Product details

• Authors: James Peterson, James K Peterson, James K. Peterson
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 31.01.2016
• EAN: 9789812878755
• ISBN: 978-981-287-875-5
• No. of pages: 556
• Dimensions: 167 mm x 240 mm x 36 mm
• Weight: 988 g
• Illustrations: XXXIII, 556 p. 135 illus., 115 illus. in color.
• Series: Cognitive Science and Technology; Cognitive Science and Technology
• Subjects: Natural sciences, medicine, IT, technology > Technology > General, dictionaries; B, Artificial Intelligence, Mathematische Physik, Bildverarbeitung, Mathematische Modellierung, engineering, Computer Vision, Computer Imaging, Vision, Pattern Recognition and Graphics, Theoretical, Mathematical and Computational Physics, Mathematical physics, Computational Intelligence, Optical data processing, Mathematical modelling, Image processing, Neural networks (Computer science)