Overview
- Is suitable for self-study and also useful as a tutorial companion for introduction to differentiation and integration
- Provides the mathematical formulas and properties needed for the exercises in the appendix
- Serves as a tutorial resource in a short-term introductory course for first-year students in physics and engineering
Part of the book series: SpringerBriefs in Physics (SpringerBriefs in Physics)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book provides a comprehensive yet informal introduction to differentiating and integrating real functions with one variable. It also covers basic first-order differential equations and introduces higher-dimensional differentiation and integration.
The focus is on significant theoretical proofs, accompanied by illustrative examples for clarity. A comprehensive bibliography aids deeper understanding. The concept of a function's differential is a central theme, relating to the "differential" within integrals. The discussion of indefinite integrals (collections of antiderivatives) precedes definite integrals, naturally connecting the two. The Appendix offers essential math formulas, exercise properties, and an in-depth exploration of continuity and differentiability. Select exercise solutions are provided.
This book suits short introductory math courses for novice physics/engineering students. It equips them with vital differentialand integral calculus tools for real-world applications. It is also useful for first-year undergraduates, reinforcing advanced calculus foundations for better Physics comprehension.
Authors and Affiliations
About the author
Dr. Costas J. Papachristou is a senior faculty member at the Hellenic Naval Academy (The Naval Academy of Greece). He received a Ph.D. in Theoretical Physics from Brigham Young University, USA, and spent another year at BYU as a research faculty in Physics. At the HNA, he teaches freshman- and sophomore-level Physics. His research interests are mainly in Theoretical and Mathematical Physics (in particular, symmetry and integrability properties of classical field equations, classical electromagnetism), but he is also active in Physics Education. He is an amateur musician and a columnist for Greek newspapers and magazines.
Bibliographic Information
Book Title: Elements of Mathematical Analysis
Book Subtitle: An Informal Introduction for Physics and Engineering Students
Authors: Costas J. Papachristou
Series Title: SpringerBriefs in Physics
DOI: https://doi.org/10.1007/978-3-031-45854-5
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Softcover ISBN: 978-3-031-45853-8Published: 15 November 2023
eBook ISBN: 978-3-031-45854-5Published: 14 November 2023
Series ISSN: 2191-5423
Series E-ISSN: 2191-5431
Edition Number: 1
Number of Pages: IX, 126
Number of Illustrations: 24 b/w illustrations
Topics: Mathematical Physics, Difference and Functional Equations, Engineering Mathematics