Calculus for Cognitive Scientists Higher Order Models and Their Analysis - Peterson, James K.; SpringerLink (Online service) (Singapore : Springer Nature Singapore : Imprint: Springer, 2016)
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.
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.
Keywords: Computational intelligence; Mathematical physics; Neural networks (Computer science) .; Artificial intelligence; Image processing -- Digital techniques; Computer vision; Computational Intelligence; Theoretical, Mathematical and Computational Physics; Mathematical Models of Cognitive Processes and Neural Networks; Artificial Intelligence; Computer Imaging, Vision, Pattern Recognition and Graphics