LEADER 04670nam 22007095 450 001 9910728948003321 005 20240508193008.0 010 $a3-031-28571-9 024 7 $a10.1007/978-3-031-28571-4 035 $a(MiAaPQ)EBC7255575 035 $a(Au-PeEL)EBL7255575 035 $a(OCoLC)1381709738 035 $a(DE-He213)978-3-031-28571-4 035 $a(BIP)088672560 035 $a(PPN)272271349 035 $a(CKB)26830215400041 035 $a(EXLCZ)9926830215400041 100 $a20230603d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aApplied Calculus with R /$fby Thomas J. Pfaff 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (520 pages) 311 08$aPrint version: Pfaff, Thomas J. Applied Calculus with R Cham : Springer International Publishing AG,c2023 9783031285707 320 $aIncludes bibliographical references and index. 327 $aA Brief Introduction to R -- Describing a Graph -- The Function Gallery -- I: Change and the Derivative -- How Fast is CO2 Increasing? -- The Idea of the Derivative -- Formulas Quantifying Change.-The Microscope Equation -- Successive Approximations to Estimate Derivatives -- The Derivative Graphically -- The Formal Derivative as a Limit -- Basic Derivative Rules -- Produce Rule -- Quotient Rule -- Chain Rule -- Derivatives with R -- End Behavior of a Function - L'Hospital's Rule -- II: Applications of the Derivative -- How Do We Know the Shape of a Function? -- Finding Extremes -- Optimization -- Derivatives of Functions of Two Variables -- Related Rates -- Surge Function -- Differential Equations - Preliminaries -- Differential Equations - Population Growth Models -- Differential Equations - Predator Prey -- Differential equations - SIR Model -- Project: The Gini Coefficient - Prelude to Section III -- III: Accumulation and the Integral -- Area Under Curves -- The Accumulation Function -- The Fundamental Theorem of Calculus -- Techniques of Integration - The u Substitution -- Techniques of Integration - Integration by Parts -- IV: Appendices - Algebra Review -- Algebra Review - Functions and Graphs -- Algebra Review - Adding and Multiplying Fractions -- Algebra Review - Exponents -- Algebra Review - Lines -- Algebra Review - Expanding, Factoring, and Roots -- Algebra Review - Function Composition -- Glossary -- Answers to Odd Problems -- R Code for Figures. 330 $aThis textbook integrates scientific programming with the use of R and uses it both as a tool for applied problems and to aid in learning calculus ideas. Adding R, which is free and used widely outside academia, introduces students to programming and expands the types of problems students can engage. There are no expectations that a student has any coding experience to use this text. While this is an applied calculus text including real world data sets, a student that decides to go on in mathematics should develop sufficient algebraic skills so that they can be successful in a more traditional second semester calculus course. Hopefully, the applications provide some motivation to learn techniques and theory and to take additional math courses. The book contains chapters in the appendix for algebra review as algebra skills can always be improved. Exercise sets and projects are included throughout with numerous exercises based on graphs. 606 $aMathematical statistics 606 $aComputer science$xMathematics 606 $aStochastic processes 606 $aCalculus 606 $aMathematical Statistics 606 $aMathematical Applications in Computer Science 606 $aStochastic Calculus 606 $aCàlcul$2thub 606 $aProcessament de dades$2thub 606 $aR (Llenguatge de programació)$2thub 608 $aLlibres electrònics$2thub 610 $aMathematics 615 0$aMathematical statistics. 615 0$aComputer science$xMathematics. 615 0$aStochastic processes. 615 0$aCalculus. 615 14$aMathematical Statistics. 615 24$aMathematical Applications in Computer Science. 615 24$aStochastic Calculus. 615 7$aCàlcul 615 7$aProcessament de dades 615 7$aR (Llenguatge de programació) 676 $a515.0285 700 $aPfaff$b Thomas J.$01363601 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910728948003321 996 $aApplied Calculus with R$93384455 997 $aUNINA