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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 � ∞ 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 � 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 | |