Calculus for Cognitive Scientists: Higher Order Models and Their Analysis

✍ Scribed by James K. Peterson (auth.)

• Publisher: Springer Singapore
• Year: 2016
• Tongue: English
• Leaves: 567
• Series: Cognitive Science and Technology
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xxxiii
Front Matter....Pages 1-1
Introductory Remarks....Pages 3-7
Front Matter....Pages 9-9
Linear Algebra....Pages 11-59
Numerical Methods Order One ODEs....Pages 61-84
Multivariable Calculus....Pages 85-125
Front Matter....Pages 127-127
Integration....Pages 129-140
Complex Numbers....Pages 141-148
Linear Second Order ODEs....Pages 149-170
Systems....Pages 171-235
Numerical Methods Systems of ODEs....Pages 237-286
Front Matter....Pages 287-287
Predator–Prey Models....Pages 289-354
Predator–Prey Models with Self Interaction....Pages 355-379
Disease Models....Pages 381-399
A Cancer Model....Pages 401-431
Front Matter....Pages 433-433
Nonlinear Differential Equations....Pages 435-473
An Insulin Model....Pages 475-491
Front Matter....Pages 493-493
Series Solutions....Pages 495-513
Front Matter....Pages 515-515
Final Thoughts....Pages 517-522
Front Matter....Pages 523-523
Background Reading....Pages 525-529
Back Matter....Pages 531-556

✦ Subjects

Computational Intelligence; Theoretical, Mathematical and Computational Physics; Mathematical Models of Cognitive Processes and Neural Networks; Artificial Intelligence (incl. Robotics); Computer Imaging, Vision, Pattern Recognition and G