Calculus for Cognitive Scientists, 1st ed. 2016 Higher Order Models and Their Analysis Cognitive Science and Technology Series

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.

Well-designed self-study program on linear and nonlinear models based on both ordinary and partial differential equations

Comprehensively discusses the computational tools used to find solutions

Includes the predator-prey model, a model of diabetes detection and the cable model for excitatory neurons

Includes supplementary material: sn.pub/extras