Calculus for Cognitive Scientists
Derivatives, Integrals and Models

Authors: James K. Peterson



Well-designed self-study program of in mathematics, cognitive and biological science, as well as computation

Includes one and two variable calculus as well as first-order models with computer solution techniques

Focuses on how to use mathematics and computation to gain insights into complicated problems

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 (24 chapters)

Front Matter
Pages i-xxxi

Introduction
Front Matter
Pages 1-1
Introductory Remarks
Pages 3-22

Using One Variable
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

Using Multiple Variables
Front Matter
Pages 369-369
Matrices and Vectors
Pages 371-384
A Cancer Model
Pages 385-398
First Order Multivariable Calculus
Pages 399-428
Second Order Multivariable Calculus
Pages 429-452
Hamilton’s Rule in Evolutionary Biology
Pages 453-475

Summing It All Up
Front Matter
Pages 477-477
Final Thoughts
Pages 479-480

Advise to the Beginner
Front Matter
Pages 481-481
Background Reading
Pages 483-485

Back Matter
Pages 487-507

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