Calculus for Cognitive Scientists Derivatives, Integrals and Models - Peterson, James K.; SpringerLink (Online service) (Singapore : Springer Nature Singapore : Imprint: Springer, 2016)
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.
Introductory Remarks -- Viability Selection -- Limits and Basic Smoothness -- Continuity and Derivatives -- Sin, Cos and All That -- Antiderivatives -- Substitutions -- Riemann Integration -- The Logarithm and Its Inverse -- Exponential and Logarithm Function Properties -- Simple Rate Equations -- Simple Protein Models -- Logistics Models -- Function Approximation -- Extreme Values -- Numerical Methods Order One ODEs -- Advanced Protein Models -- Matrices and Vectors -- A Cancer Model -- First Order Multivariable Calculus -- Second Order Multivariable Calculus -- Hamilton's Rule In Evolutionary Biology -- Final Thoughts -- Background Reading.
Keywords: Computational intelligence; Neural networks (Computer science) .; Mathematical physics; Artificial intelligence; Image processing -- Digital techniques; Computer vision; Computational Intelligence; Mathematical Models of Cognitive Processes and Neural Networks; Theoretical, Mathematical and Computational Physics; Artificial Intelligence; Computer Imaging, Vision, Pattern Recognition and Graphics