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Titlebook: Differential Equations and Data Analysis; Aleksei Beltukov Textbook 2025 The Editor(s) (if applicable) and The Author(s), under exclusive

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书目名称Differential Equations and Data Analysis
编辑Aleksei Beltukov
视频video
概述Focuses on linear ODEs with constant coefficients, data analysis, and engineering design.Discuss the process of translating physical laws into the language of ODEs and estimation of model parameters f
丛书名称Synthesis Lectures on Mathematics & Statistics
图书封面Titlebook: Differential Equations and Data Analysis;  Aleksei Beltukov Textbook 2025 The Editor(s) (if applicable) and The Author(s), under exclusive
描述.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..
出版日期Textbook 2025
关键词Ordinary Differential Equations; Modeling with Differential Equations; Modeling with ODEs; Applied Diff
版次1
doihttps://doi.org/10.1007/978-3-031-62257-1
isbn_softcover978-3-031-62259-5
isbn_ebook978-3-031-62257-1Series ISSN 1938-1743 Series E-ISSN 1938-1751
issn_series 1938-1743
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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https://doi.org/10.1007/978-1-349-00867-4atmospheric pressure, the exponential fits are very good. Linearization brings out unexpected similarity between convective cooling and RC-circuits which is called the electro-thermal analogy. More importantly, it justifies our narrow focus on linear ODE with constant coefficients.
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,Linearized ODE and Exponential Laws,atmospheric pressure, the exponential fits are very good. Linearization brings out unexpected similarity between convective cooling and RC-circuits which is called the electro-thermal analogy. More importantly, it justifies our narrow focus on linear ODE with constant coefficients.
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Discrete Fourier Transform,strated by its use for filtering out noise, comparing spectra of different data sets, and predicting periodic events, such as solar activity. The most important use of DFT, as far as the subject-matter of this book is concerned, is approximation of solutions of linear nonhomogeneous ODE with constant coefficients.
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Fourier Series,st order scalar linear ODE with constant coefficients. We will now show that the exact solution can be easily found as a Fourier series. Finding Fourier series solutions of higher order ODE and matrix-vector systems is just as simple.
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