微分方程式とデータ解析 Differential Equations and Data Analysis (Synthesis Lectures on Mathematics & Statistics) （2024）

Beltukov, Aleksei

Springer International Publishing AG（2024/12発売）

Springer International Publishing AG（2024/12発売）

• 製本 Hardcover:ハードカバー版／ページ数 190 p.
• 言語 ENG
• 商品コード 9783031622564

Full Description

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.

Contents

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.