| Description |
1 online resource |
| Contents |
Intro -- Preface -- Contents -- 1 A Brief Introduction to R -- 1.1 Exercises -- 2 Describing a Graph -- 2.1 Exercises -- 3 The Function Gallery -- 3.1 Exercises -- Part I Change and the Derivative -- 4 How Fast is CO2 Increasing? -- 4.1 Exercises -- 5 The Idea of the Derivative -- 5.1 Exercises -- 6 Formulas Quantifying Change -- 6.1 Exercises -- 6.2 Project: Which Mountain to Climb? -- 7 The Microscope Equation -- 7.1 Exercises -- 8 Successive Approximations to Estimate Derivatives -- 8.1 Exercises -- 8.2 Project: Which Secant Line Approximation is Better? -- 8.3 Project: Estimating e |
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16.2 Project: Comparing Exponential and Quadratic Models ... -- Part II Applications of the Derivative -- 17 How Do We Know the Shape of a Function? -- 17.1 Exercises -- 17.2 Project: Arctic Sea Ice Analysis -- 18 Finding Extremes -- 18.1 Exercises -- 19 Optimization -- 19.1 Exercises -- 20 Derivatives of Functions of Two Variables -- 20.1 Exercises -- 21 Related Rates -- 21.1 Exercises -- 22 Surge Function -- 22.1 Exercises -- 23 Differential Equations -- Preliminaries -- 23.1 Exercises -- 24 Differential Equations -- Population Growth Models -- 24.1 Exercises |
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25 Differential Equations -- Predator Prey -- 25.1 Exercises -- 26 Differential Equations -- SIR Model -- 26.1 Exercises -- 27 Project: The Gini Coefficient-Prelude to Section III -- Part III Accumulation and the Integral -- 28 Area Under Curves -- 28.1 Exercises -- 29 The Accumulation Function -- 29.1 Exercises -- 29.2 Project: Hubbard Brook -- The Importance of a Watershed -- 30 The Fundamental Theorem of Calculus -- 30.1 Exercises -- 31 Techniques of Integration -- The u Substitution -- 31.1 Exercises -- 32 Techniques of Integration -- Integration by Parts -- 32.1 Exercises |
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Appendix A Algebra Review -- Functions and Graphs -- A.1 Exercises -- Appendix B Algebra Review -- Adding and Multiplying Fractions -- B.1 Exercises -- Appendix C Algebra Review -- Exponents -- C.1 Exercises -- Appendix D Algebra Review -- Lines -- D.1 Exercises -- Appendix E Algebra Review -- Expanding, Factoring, and Roots -- E.1 Exercises -- Appendix F Algebra Review -- Function Composition -- F.1 Exercises -- Appendix G R Glossary -- Appendix H Answers to Odd Problems -- Appendix Appendix I R Code for Figures -- Appendix References -- Index |
| Summary |
This 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 |
| Analysis |
Mathematics |
| Subject |
Calculus -- Data processing
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R (Computer program language)
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Calculus -- Data processing
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R (Computer program language)
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| Form |
Electronic book
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| ISBN |
9783031285714 |
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3031285719 |
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