Differential Equations and Data Analysis

This book is focused on modeling with linear differential equations with constant coefficients.  The author starts with the elementary natural growth equation and ends with the heat equation on the real line.  The emphasis is on linear algebra, Fourier theory, and specifically data analysis, which is given a very prominent role and is often the book's main driving force.  All aspects of modeling with linear differential equations are illustrated by analyzing real and simulated data in MATLAB®.  These modeling case studies are of particular interest to students who anticipate having to use differential equations in their fields.  The book is self-contained and is appropriate as a supplement for a first course in differential equations whose prerequisites include proficiency in multivariate calculus and MATLAB literacy.

The Cooling of a Light Bulb.- Usain Bolt’s Record.- The RC circuit.- Ion Channels.- Cart on a Track.- RLC circuit Resonance.- Tides.- RLC circuit Driven by a Square Wave.- A Train of Carts.- A Quarter Car Model.- Vibration Absorber.- Design of a Low Pass Filter.- Programming a Thermostat.- Balancing a Pendulum.

Aleksei Beltukov, Ph.D., is an Associate Professor in the Department of Mathematics at the University of the Pacific in California.  He received his B.S. in chemical engineering from Mendeleyev University in Moscow, Russia and Ph.D. in mathematics from Tufts University.  Dr. Beltukov’s research interests include inverse problems, harmonic analysis, differential equations, and data analysis.