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.
Author(s): Thomas J. Pfaff
Publisher: Springer
Year: 2023
Language: English
Pages: 519
City: Cham
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
8.4 Project: Estimating π
9 The Derivative Graphically
9.1 Exercises
10 The Formal Derivative as a Limit
10.1 Exercises
10.2 Project: An Origin Story of the number e
11 Basic Derivative Rules
11.1 Exercises
12 Product Rule
12.1 Exercises
12.2 Project: Conceptual Product Rule Graphic
13 Quotient Rule
13.1 Exercises
14 Chain Rule
14.1 Exercises
15 Derivatives with R
15.1 Exercises
15.2 Project: Mauna Loa CO2 Projections
15.3 Project: Climate Change Projections
16 End Behavior of a Function - L'Hospital's Rule
16.1 Exercises
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
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
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
