Applied Calculus with R

A 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.