03175nam a22004575i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001700153072001600170072002300186072001500209100008500224245015600309250001800465264006900483300004300552336002600595337002600621338003600647347002400683490004200707505041300749520113201162650002602294650002602320650002602346650002902372650002602401650004102427650002902468710003402497773002602531776003602557776003602593830004202629856004602671978-3-031-45854-5DE-He21320251030110832.0cr nn 008mamaa231114s2024    sz |    s    |||| 0|eng d  a97830314585457 a10.1007/978-3-031-45854-52doi 4aQC19.2-20.85 7aPHU2bicssc 7aSCI0400002bisacsh 7aPHU2thema1 aPapachristou, Costas J.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aElements of Mathematical Analysish[electronic resource] :bAn Informal Introduction for Physics and Engineering Students /cby Costas J. Papachristou.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aIX, 126 p. 24 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringerBriefs in Physics,x2191-54310 a1. 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.  aThis 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. 0aMathematical physics. 0aDifference equations. 0aFunctional equations. 0aEngineering mathematics.14aMathematical Physics.24aDifference and Functional Equations.24aEngineering Mathematics.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303145853808iPrinted edition:z9783031458552 0aSpringerBriefs in Physics,x2191-543140uhttps://doi.org/10.1007/978-3-031-45854-5