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Prologue | |

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Mathematica Basics | |

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Getting Started | |

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The Front End | |

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The Documentation Center | |

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Basic Calculations | |

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Parentheses, Brackets, and Braces | |

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Symbolic vs. Numerical Computation | |

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Names And Capitalization, Basic Functions | |

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Algebraic Manipulation | |

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Plotting Graphs: An Introduction to Options | |

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Variables | |

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Tips and Shortcuts | |

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Functions | |

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Defining Functions | |

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Applying Functions with @ and // | |

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Piecewise-defined Functions | |

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Equations | |

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Lists | |

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Listable Functions | |

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The Parts of a List | |

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Creating Lists | |

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Manipulating Lists | |

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Map and Apply | |

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Rules | |

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Graphics | |

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Graphics Objects and Show | |

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Graphics Primitives | |

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Graphics Directives | |

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Suppressing and Combining Graphics | |

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GraphicsRow and GraphicsGrid | |

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Animate and Manipulate | |

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Avoiding and Getting Out of Trouble | |

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A Top Ten List: Causes of Mathematica Problems | |

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What to Do When You Run into Trouble | |

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Interrupting Calculations | |

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Interpreting Mathematica Output When Things Don't Work | |

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Symbolic vs. Numerical Computation | |

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Multiple Definitions and Using the Question Mark | |

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Memory | |

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Turning a Notebook into a Report | |

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Cell Styles | |

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Page Breaks | |

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Other Tips | |

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Miscellaneous Advice | |

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The Cube Root Function | |

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Custom Initialization | |

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Limits and the Derivative | |

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Limits | |

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One-sided Limits | |

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Infinite Limits and Vertical Asymptotes | |

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Limits at ï¿½ ∞ and Horizontal Asymptotes | |

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Limits of Expressions with Symbolic Parameters | |

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The Derivative | |

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The Slope of the Tangent Line | |

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A Better Slope Approximation | |

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The Derivative | |

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Exploring the Derivative Graph | |

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Symbolic Computation of Exact Derivatives | |

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Higher-order Derivatives | |

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The Second Derivative and Concavity | |

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Exploring the Graph of the Second Derivative | |

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Applications of the Derivative | |

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Velocity, Acceleration, and Rectilinear Motion | |

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Average and Instantaneous Velocity | |

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Acceleration | |

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Simulating Motion | |

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Implicit Differentiation and Related Rates | |

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Implicit Differentiation | |

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Related Rates Problems | |

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Linear and Quadratic Approximation | |

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Linearization | |

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Quadratic Approximation | |

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Newton's Method | |

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Optimization | |

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Local Extrema | |

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The Second Derivative Test | |

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Using FindMinimum and FindMaximum | |

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Other Kinds of Critical Numbers | |

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Absolute Extrema on Closed Intervals | |

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Applied Optimization Problems | |

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Antiderivatives | |

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Special Functions | |

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Differential Equations and Initial Values | |

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Integration | |

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Limits of Sums and the Area Under a Curve | |

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Area Approximations | |

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To the Limit! | |

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The Definite Integral | |

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Integrals and Areas | |

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Animating the Convergence of Riemann Sums | |

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The Fundamental Theorem of Calculus | |

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Functions Defined by Integrals | |

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The Fundamental Theorem of Calculus | |

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Definite Integrals with Integrate | |

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Special Functions as Antiderivatives | |

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More on Initial Value Problems | |

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Numerical Integration | |

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Midpoint Rule | |

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Trapezoidal Rule | |

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Simpson's Rule | |

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Error Bounds | |

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NIntegrate | |

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Functions Given by Data | |

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Improper Integrals | |

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Applications of the Integral | |

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Area | |

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Volume | |

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Arc Length and Surface Area | |

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Moments and Centroids | |

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Differential Equations | |

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Equations and Solutions | |

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Initial Value Problems | |

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Direction Fields | |

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StreamPlot | |

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Euler's Method | |

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Exact Solutions | |

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Separable Equations | |

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Integration Between Limits: First-order Linear Equations | |

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DSolve and NDSolve | |

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Parametric and Polar Curves | |

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Parametric Curves | |

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The Cycloid | |

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Lissajous Figures | |

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Bezier Curves | |

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Arc Length | |

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Pairs of Differential Equations | |

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Direction Fields | |

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StreamPlot | |

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Euler's Method | |

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NDSolve | |

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Polar Curves | |

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Animating a Polar Plot | |

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Arc Length | |

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Plotting a "Polar Region" | |

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Area | |

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Sequences and Series | |

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Sequences | |

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Recursive Sequences: Newton's Method Revisited | |

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Series | |

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Summing an Infinite Series: Convergence | |

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Power Series | |

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Taylor Polynomials and Series | |

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The Remainder Term | |

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Projects | |

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Two Limits | |

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Computing ï¿½ as an Area | |

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Lines of Sight | |

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Color-coded Graphs | |

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Designing an Oil Drum | |

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Optimal Location of a Water Treatment Plant | |

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Newton's Method and a 1D Fractal | |

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The Vertical Path of a Rocket | |

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Otto the Daredevil | |

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Helping Mathematica Integrate | |

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The Brightest Phase of Venus | |

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The Skimpy Donut | |

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Designing a Light Bulb | |

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Approximate Antidifferentiation | |

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Percentiles of the Normal Distribution | |

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Equilibria and Centers of Gravity | |

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Draining Tanks | |

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Spruce Budworms | |

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Parachuting | |

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The Flight of a Baseball I | |

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The Flight of a Baseball II | |

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Cannonball Wars | |

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Taylor Polynomials and Differential Equations | |

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Build Your Own Cosine | |

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Index | |