Sage for Undergraduates

Description

As the open-source and free alternative to expensive software like Maple™, Mathematica®, and MATLAB®, Sage offers anyone with a web browser the ability to use cutting-edge mathematical software and share the results with others, often with stunning graphics. This book is a gentle introduction to Sage for undergraduate students during Calculus II, Multivariate Calculus, Differential Equations, Linear Algebra, Math Modeling, or Operations Research. This book assumes no background in programming, but the reader who finishes the book will have learned about 60 percent of a first semester computer science course, including much of the Python programming language. The audience is not only math majors, but also physics, engineering, environmental science, finance, chemistry, economics, data science, and computer science majors. Many of the book's examples are drawn from those fields. Filled with “challenges” for the students to test their progress, the book is also ideal for self-study. What's New in the Second Edition: In 2019, Sage transitioned from Python 2 to Python 3, which changed the syntax in several significant ways, including for the print command. All the examples in this book have been rewritten to be compatible with Python 3. Moreover, every code block longer than four lines has been placed in an archive on the book's website http://www.sage-for-undergraduates.org that is maintained by the author, so that the students won't have to retype the code! Other additions include… The number of “challenges” for the students to test their own progress in learning Sage has roughly doubled, which will be a great boon for self-study.There's approximately 150 pages of new content, including: New projects on Leontief Input-Output Analysis and on Environmental ScienceNew sections on Complex Numbers and Complex Analysis, on SageTex, and on solving problems via Monte-Carlo Simulations.The first three sections of Chapter 1 have been completely rewritten to give absolute beginners a smoother transition into Sage. Cover Title page Contents The Preface: How to Use This Book Chapter 1. Welcome to Sage! 1.1. Using Sage as a Calculator 1.2. Using Sage with Common Functions 1.3. Using Sage for Trigonometry 1.4. Using Sage to Graph 2-Dimensionally 1.5. Matrices and Sage, Part 1 1.6. Making Your Own Functions in Sage 1.7. Using Sage to Manipulate Polynomials 1.8. Using Sage to Solve Problems Symbolically 1.9. Using Sage as a Numerical Solver 1.10. Getting Help When You Need It 1.11. Using Sage to Take Derivatives 1.12. Using Sage to Calculate Integrals 1.13. Sharing the Results of Your Work 1.14. A Technicality about Functions Chapter 2. Fun Projects Using Sage 2.1. Microeconomics: Computing a Selling Price 2.2. Biology: Clogged Arteries and Poiseuille’s Law 2.3. Industrial Optimization: Shipping Taconite 2.4. Chemistry: Balancing Reactions with Matrices 2.5. Physics: Ballistic Projectiles 2.6. Cryptology: Pollard’s 𝑝-1 Attack on RSA 2.7. Mini-Project on Electric Field Vector Plots 2.8. Environmental Science: Lead and Motherboards 2.9. Macroeconomics: Leontief Input-Output Analysis Chapter 3. Advanced Plotting Techniques 3.1. Annotating Graphs for Clarity 3.2. Graphs of Some Hyperactive Functions 3.3. Polar Plotting 3.4. Graphing an Implicit Function 3.5. Contour Plots and Level Sets 3.6. Parametric 2D Plotting 3.7. Vector Field Plots 3.8. Log-Log Plots 3.9. The Removed Section Chapter 4. Advanced Features of Sage 4.1. Using Sage with Multivariable Functions and Equations 4.2. Working with Large Formulas in Sage 4.3. Derivatives and Gradients in Multivariate Calculus 4.4. Matrices and Sage, Part 2 4.5. Vector Operations 4.6. Working with the Integers and Number Theory 4.7. Some More Commands in Sage 4.8. Calculating Limits Expressly 4.9. Scatter Plots in Sage 4.10. Making Your Own Regressions in Sage 4.11. Computing in Octal? Binary? And Hexadecimal? 4.12. Can Sage Do Sudoku? 4.13. Measuring the Speed of Sage 4.14. Huge Numbers and Sage 4.15. Using Sage and \LaTeX, Part 1 4.16. Matrices and Sage, Part 3 4.17. Computing Taylor or MacLaurin Polynomials 4.18. Minimizations and Lagrange Multipliers 4.19. Infinite Sums and Series 4.20. Continued Fractions in Sage 4.21. Systems of Inequalities and Linear Programming 4.22. Differential Equations 4.23. Laplace Transforms 4.24. Vector Calculus in Sage 4.25. Using Sage and \LaTeX, Part 2 4.26. Complex Numbers and Sage Chapter 5. Programming in Sage and Python 5.1. Repetition without Boredom: The for Loop 5.2. Writing Subroutines 5.3. Loops and Newton’s Method 5.4. An Introduction to Control Flow 5.5. More Concepts in Flow Control 5.6. while Loops versus for Loops 5.7. How Arrays and Lists Work 5.8. Simulations: The Monte Carlo Method 5.9. Some Intermediate-Level Techniques 5.10. Where Do You Go from Here? Chapter 6. Building Interactive Webpages with Sage 6.1. The Six-Stage Process for Building Interacts 6.2. The Tangent-Line Interact 6.3. A Challenge: The Sine Wave Interact 6.4. Another Challenge: The Optimal Aquarium Interact 6.5. Selectors and Checkboxes 6.6. The Definite Integral Interact Appendix A. What to Do When Frustrated! Appendix B. Transitioning to SageMathCloud B.1. What Is SageMathCloud? B.2. Getting Started in SageMathCloud B.3. Other Cloud Features Appendix C. Translating Python 2 to Python 3 C.1. Changes in the Syntax of print C.2. Changes in the Behavior of range C.3. Unicode versus ASCII C.4. Unrelated but Contemporaneous Changes Acknowledgments for the Second Edition Acknowledgments for the First Edition Bibliography Index Back Cover