Calculus for Cognitive Scientists: Derivatives, Integrals and Models

✍ Scribed by James K. Peterson (auth.)

• Publisher: Springer Singapore
• Year: 2016
• Tongue: English
• Leaves: 519
• Series: Cognitive Science and Technology
• Edition: 1
• Category: Library

✦ Synopsis

This book provides a self-study program on how mathematics, computer science and science can be usefully and seamlessly intertwined. Learning to use ideas from mathematics and computation is essential for understanding approaches to cognitive and biological science. As such the book covers calculus on one variable and two variables and works through a number of interesting first-order ODE models. It clearly uses MatLab in computational exercises where the models cannot be solved by hand, and also helps readers to understand that approximations cause errors – a fact that must always be kept in mind.

✦ Table of Contents

Front Matter....Pages i-xxxi
Front Matter....Pages 1-1
Introductory Remarks....Pages 3-22
Front Matter....Pages 23-23
Viability Selection....Pages 25-60
Limits and Basic Smoothness....Pages 61-77
Continuity and Derivatives....Pages 79-99
Sin, Cos and All That....Pages 101-111
Antiderivatives....Pages 113-120
Substitutions....Pages 121-128
Riemann Integration....Pages 129-164
The Logarithm and Its Inverse....Pages 165-177
Exponential and Logarithm Function Properties....Pages 179-204
Simple Rate Equations....Pages 205-227
Simple Protein Models....Pages 229-256
Logistics Models....Pages 257-277
Function Approximation....Pages 279-299
Extreme Values....Pages 301-313
Numerical Methods Order One ODEs....Pages 315-345
Advanced Protein Models....Pages 347-368
Front Matter....Pages 369-369
Matrices and Vectors....Pages 371-384
A Cancer Model....Pages 385-398
First Order Multivariable Calculus....Pages 399-428
Front Matter....Pages 369-369
Second Order Multivariable Calculus....Pages 429-452
Hamilton’s Rule in Evolutionary Biology....Pages 453-475
Front Matter....Pages 477-477
Final Thoughts....Pages 479-480
Front Matter....Pages 481-481
Background Reading....Pages 483-485
Back Matter....Pages 487-507

✦ Subjects

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