Overview
- 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 from data
- Utilizes data analysis to motivate and reinforce techniques for solving linear ODEs with constant coefficients
Part of the book series: Synthesis Lectures on Mathematics & Statistics (SLMS)
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About this book
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.
Keywords
Table of contents (10 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: Differential Equations and Data Analysis
Authors: Aleksei Beltukov
Series Title: Synthesis Lectures on Mathematics & Statistics
DOI: https://doi.org/10.1007/978-3-031-62257-1
Publisher: Springer Cham
eBook Packages: Synthesis Collection of Technology (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2025
Hardcover ISBN: 978-3-031-62256-4Published: 13 November 2024
Softcover ISBN: 978-3-031-62259-5Due: 27 November 2025
eBook ISBN: 978-3-031-62257-1Published: 12 November 2024
Series ISSN: 1938-1743
Series E-ISSN: 1938-1751
Edition Number: 1
Number of Pages: XI, 190
Number of Illustrations: 80 b/w illustrations, 1 illustrations in colour
Topics: Analysis, Fourier Analysis, Engineering Mathematics, Computational Mathematics and Numerical Analysis, Mathematical Modeling and Industrial Mathematics