Torrence B., Torrence E. The Student’s Introduction to Mathematica and the Wolfram Language

3rd Edition. — Cambridge University Press, 2019. — 550 p. — ISBN: 978-1-108-40636-9. (Interactive table of contents).The unique feature of this compact student's introduction to Mathematica and the Wolfram Language(TM) is that the order of the material closely follows a standard mathematics curriculum. As a result, it provides a brief introduction to those aspects of the Mathematica software program most useful to students. Used as a supplementary text, it will help bridge the gap between Mathematica and the mathematics in the course, and will serve as an excellent tutorial for former students. There have been significant changes to Mathematica since the second edition, and all chapters have now been updated to account for new features in the software, including natural language queries and the vast stores of real-world data that are now integrated through the cloud. This third edition also includes many new exercises and a chapter on 3D printing that showcases the new computational geometry capabilities that will equip readers to print in 3D.Getting Started.
Launching Mathematica.
The Basic Technique for Using Mathematica.
The First Computation.
Commands for Basic Arithmetic.
Input and Output.
The Basic Math Assistant Palette.
Decimal In, Decimal Out.
Use Parentheses to Group Terms.
Three Well-Known Constants.
Mathematica Commands from Palettes.
Let Mathematica Do Your Typing.
Free-Form Input.
Computing with Real Data.
Saving Your Work and Quitting Mathematica.
Frequently Asked Questions About Mathematical Syntax.
Working with Mathematica.
Opening Saved Notebooks.
Adding Text to Notebooks.
Printing.
Creating Presentations.
Sharing a Notebook.
Mathematical Kernel.
Tips for Working Effectively.
Working with Entities and Units.
Getting Help from Mathematica.
Troubleshooting.
Functions and Their Graphs.
Defining a Function.
Plotting a Function.
Using Mathematical Plot Options.
Investigating Functions with Manipulate.
Producing a Table of Values.
Working with Piecewise Defined Functions.
Plotting Implicitly Defined Functions.
Combining Graphics.
Enhancing Your Graphics.
Working with Data.
Managing Data: An Introduction to Lists.
Importing Data.
Working with Difference Equations.
Algebra.
Factoring and Expanding Polynomials.
Finding Roots of Polynomials with Solve and NSolve.
Solving Equations and Inequalities with Reduce.
Understanding Complex Output.
Working with Rational Functions.
Working with Other Expressions.
Solving General Equations with FindRoot.
Solving Difference Equations with RSolve.
Solving Systems of Equations and Inequalities.
Calculus.
Computing Limits.
Working with Difference Quotients.
The Derivative.
Visualizing Derivatives.
Higher-Order Derivatives.
Maxima and Minima.
Inflection Points.
Implicit Differentiation.
Differential Equations.
Integration.
Definite and Improper Integrals.
Numerical Integration.
Surfaces of Revolution.
Sequences and Series.
Multivariable Calculus.
Vectors.
Real-Valued Functions of Two or More Variables.
Parametric Curves and Surfaces.
Other Coordinate Systems.
Vector Fields.
Line Integrals and Surface Integrals.
Linear Algebra.
Matrices.
Performing Gaussian Elimination.
Matrix Operations.
Minors and Cofactors.
Working with Large Matrices.
Solving Systems of Linear Equations.
Vector Spaces.
Eigenvalues and Eigenvectors.
Visualizing Linear Transformations.
Programming.
FullForm: What the Kernel Sees.
Numbers.
Map and Function.
Control Structures and Looping.
Scoping Constructs: With and Module.
Iterations: Nest and Fold.
Patterns.
3D Printing.
3D Printing Basics.
MeshRegions.
MeshRegions from the Wolfram Knowledgebase.
Mesh Assembly, Modification, and Diagnostics.
Extrusion.
Printing a Solid of Revolution.
Printing a 3D Terrain Map.