Calculus for Cognitive Scientists

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.

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

Autorentext
Dr. James Peterson is an Associate Professor in Mathematical Sciences and Biological Sciences at Clemson University, USA. His formal training is in mathematics but he has worked as an aerospace engineer and a software engineer also. He enjoys working on very hard problems that require multiple disciplines to make sense out of and he reads, studies and plays in cutting edge areas a lot as part of his interests.

Inhalt

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.