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R is the amazing, free, open-access software package for scientific graphs and calculations used by scientists worldwide. The R Student Companion is a student-oriented manual describing how to use R in high school and college science and mathematics courses. Written for beginners in scientific computation, the book assumes the reader has just some high school algebra and has no computer programming background. The author presents applications drawn from all sciences and social sciences and includes the most often used features of R in an appendix.
In addition, each chapter provides a set of computational challenges: exercises in R calculations that are designed to be performed alone or in groups. Several of the chapters explore algebra concepts that are highly useful in scientific applications, such as quadratic equations, systems of linear equations, trigonometric functions, and exponential functions. Each chapter provides an instructional review of the algebra concept, followed by a hands-on guide to performing calculations and graphing in R.
R is intuitive, even fun. Fantastic, publication-quality graphs of data, equations, or both can be produced with little effort. By integrating mathematical computation and scientific illustration early in a student's development, R use can enhance one's understanding of even the most difficult scientific concepts. While R has gained a strong reputation as a package for statistical analysis, The R Student Companion approaches R more completely as a comprehensive tool for scientific computing and graphing.
Introduction: Getting Started with R
R Tutorial
Vectors
Graphs
Real-World Example
Final Remarks
Computational Challenges
References
R Scripts
Creating and Saving an R Script
Running an R Script
Finding Errors in an R Script
Sharpening Up Your Scripts with Comments
Real-World Example
Final Remarks
Computational Challenges
Reference
Functions
Creating New Functions in R
More about User-Defined R Functions
Real-World Example
Final Remarks
Computational Challenges
Afternotes (Short Remarks on Topics for Further Study)
References
Basic Graphs
Real-World Example
Graphs of One Variable
Graphs of Two Variables
Final Remarks
Computational Challenges
Afternotes
Data Input and Output
Data Frames in R
Final Remarks
Computational Challenges
Afternotes
Loops
Writing a "For-Loop"
Checking the Loop
OK, Mr. Fibonacci…So What?
Real-World Example
Final Remarks
Computational Challenges
References
Logic and Control
Logical Comparison Operators and Logical Vectors
Boolean Operations
Missing Data
More about Indexes
Conditional Statements
Real-World Example
Final Remarks
Computational Challenges
Afternotes
Reference
Quadratic Functions
Real-World Example
Final Remarks
Computational Challenges
References
Trigonometric Functions
Right Triangles
Trigonometric Functions
Right Triangles, Circles, and Radians
Properties of Trigonometric Functions
Polar Coordinates
Triangulation of Distances
Real-World Examples
Final Remarks
Computational Challenges
Afternotes
Exponential and Logarithmic Functions
Achieving Real Power
The Special Number e
The Number e in Applications
The Exponential Function
Exponential Growth
Logarithmic Functions
Logarithmic Scales
Real-World Examples
Final Remarks
Computational and Algebraic Challenges
References
Matrix Arithmetic
Another Way to Multiply Vectors
Matrix Multiplication
Matrix Addition and Subtraction
Reading a Data File into a Matrix
Real-World Example
Final Remarks
Computational Challenges
Afterwords
References
Systems of Linear Equations
Matrix Representation
Matrix Inverse
Inverse Matrices and System Solutions in R
Real-World Examples
Final Remarks
Computational Challenges
Afternotes
References
Advanced Graphs
Two-Dimensional Plots
Options for Styles of Symbols, Lines, Axes
Other Customizations
Multiple Panels
Three-Dimensional Plots
Color
Final Remarks
Computational Challenges
Reference
Probability and Simulation
Random Variables
Probability
Probability Distributions of Counts
Probability Distributions of Measurements
Real-World Example
Computational Challenges
Afternotes
References
Fitting Models to Data
Fitting a Quadratic Model
Multiple Predictor Variables
Nonlinear Statistical Models
Final Remarks
Computational Challenges
Afternotes
References
Conclusion—It Doesn’t Take a Rocket Scientist
Real Solar System Example
The Problem
The Concept
Changes in Velocities
Move the Earth
Getting Organized
Outline of R Script for Calculating the Trajectory of Earth
The R Script
Computational Challenges
Afternotes
Appendix A: Installing R
Appendix B: Getting Help
Appendix C: Common R Expressions
Index
Brian Dennis is a professor with a joint appointment in the Department of Fish and Wildlife Sciences and the Department of Statistical Sciences at the University of Idaho. He received a master's degree in statistics and a Ph.D. in ecology from The Pennsylvania State University. He has authored over 70 scientific articles on applications of statistics and mathematical modeling in ecology and natural resource management. He has been enthusiastically using R in his scientific work and teaching R in his courses for a decade.
