Mathematica By Example 5 Edition

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• Year: 2,017

• Pages: 569

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• Language: English

• Topic: 178

• Identifier: 978-0-12-812481-9

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• Toc: front-matter-2017......Page 1 copyright-2017......Page 4 Preface......Page 5 1.1 Introduction to Mathematica......Page 7 A Note Regarding Different Versions of Mathematica......Page 8 1.1.1 Getting Started with Mathematica......Page 9 Preview......Page 19 Five Basic Rules of Mathematica Syntax......Page 20 1.2 Getting Help from Mathematica......Page 21 Mathematica Help......Page 27 2.1.1 Numerical Calculations......Page 33 2.1.2 Built-In Constants......Page 35 2.1.3 Built-In Functions......Page 36 A Word of Caution......Page 39 2.2.1 Basic Algebraic Operations on Expressions......Page 41 2.2.2 Naming and Evaluating Expressions......Page 45 2.2.3 Defining and Evaluating Functions......Page 47 2.3.1 Functions of a Single Variable......Page 53 2.3.2 Parametric and Polar Plots in Two Dimensions......Page 66 2.3.3 Three-Dimensional and Contour Plots; Graphing Equations......Page 74 2.3.4 Parametric Curves and Surfaces in Space......Page 84 2.3.5 Miscellaneous Comments......Page 96 2.4.1 Exact Solutions of Equations......Page 101 2.4.2 Approximate Solutions of Equations......Page 110 3.1.1 Using Graphs and Tables to Predict Limits......Page 115 3.1.2 Computing Limits......Page 118 3.1.3 One-Sided Limits......Page 120 3.1.4 Continuity......Page 122 3.2.1 Definition of the Derivative......Page 125 3.2.2 Calculating Derivatives......Page 131 3.2.3 Implicit Differentiation......Page 135 3.2.4 Tangent Lines......Page 137 Tangent Lines of Implicit Functions......Page 139 Parametric Equations and Polar Coordinates......Page 141 3.2.5 The First Derivative Test and Second Derivative Test......Page 147 3.2.6 Applied Max/Min Problems......Page 155 3.2.7.1 Antiderivatives......Page 165 u-Substitutions......Page 166 3.3.1 Area......Page 168 3.3.2 The Definite Integral......Page 174 3.3.4 Area......Page 180 Parametric Equations......Page 184 Polar Coordinates......Page 185 3.3.5 Arc Length......Page 186 Parametric Equations......Page 187 Polar Coordinates......Page 190 Volume......Page 191 Surface Area......Page 202 3.4.1 Introduction to Sequences......Page 204 3.4.2 Introduction to Infinite Series......Page 208 3.4.3 Convergence Tests......Page 211 3.4.4 Alternating Series......Page 215 3.4.5 Power Series......Page 216 3.4.6 Taylor and Maclaurin Series......Page 220 3.4.7 Taylor's Theorem......Page 224 3.4.8 Other Series......Page 235 3.5.1 Limits of Functions of Two Variables......Page 237 3.5.2 Partial and Directional Derivatives......Page 239 Classifying Critical Points......Page 246 Tangent Planes......Page 249 Lagrange Multipliers......Page 252 3.5.3 Iterated Integrals......Page 255 Area, Volume, and Surface Area......Page 256 Triple Iterated Integrals......Page 262 4.1.1 Defining Lists......Page 265 4.1.2 Plotting Lists of Points......Page 270 4.2 Manipulating Lists: More on Part and Map......Page 283 4.2.1 More on Graphing Lists; Graphing Lists of Points Using Graphics Primitives......Page 292 4.3 Other Applications......Page 300 4.3.1 Approximating Lists wi