03530nam a22005415i 4500 978-3-031-45854-5 DE-He213 20251030110832.0 cr nn 008mamaa 231114s2024 sz | s |||| 0|eng d 9783031458545 978-3-031-45854-5 10.1007/978-3-031-45854-5 doi QC19.2-20.85 PHU bicssc SCI040000 bisacsh PHU thema Papachristou, Costas J. author. aut http://id.loc.gov/vocabulary/relators/aut 67183 Elements of Mathematical Analysis [electronic resource] : An Informal Introduction for Physics and Engineering Students / by Costas J. Papachristou. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. IX, 126 p. 24 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda SpringerBriefs in Physics, 2191-5431 1. Functions -- 2. Derivative and Differential -- 3. Some Applications of Derivatives -- 4. Indefinite Integral -- 5. Definite Integral -- 6. Series -- 7. An Elementary Introduction to Differential Equations -- 8. Introduction to Differentiation in Higher Dimensions -- 9. Complex Numbers -- 10. Introduction to Complex Analysis -- Appendix -- Answers to Selected Exercises -- Selected Bibliography -- Index. 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. Mathematical physics. Difference equations. 67184 Functional equations. 67185 Engineering mathematics. 64145 Mathematical Physics. Difference and Functional Equations. 67186 Engineering Mathematics. 64145 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031458538 Printed edition: 9783031458552 SpringerBriefs in Physics, 2191-5431 67187 https://doi.org/10.1007/978-3-031-45854-5 ZDB-2-PHA ZDB-2-SXP 56547 56547