Toc: front-matter-2017......Page 1copyright-2017......Page 4Preface......Page 51.1 Introduction to Mathematica......Page 7 A Note Regarding Different Versions of Mathematica......Page 81.1.1 Getting Started with Mathematica......Page 9 Preview......Page 19 Five Basic Rules of Mathematica Syntax......Page 201.2 Getting Help from Mathematica......Page 21 Mathematica Help......Page 272.1.1 Numerical Calculations......Page 332.1.2 Built-In Constants......Page 352.1.3 Built-In Functions......Page 36 A Word of Caution......Page 392.2.1 Basic Algebraic Operations on Expressions......Page 412.2.2 Naming and Evaluating Expressions......Page 452.2.3 Defining and Evaluating Functions......Page 472.3.1 Functions of a Single Variable......Page 532.3.2 Parametric and Polar Plots in Two Dimensions......Page 662.3.3 Three-Dimensional and Contour Plots; Graphing Equations......Page 742.3.4 Parametric Curves and Surfaces in Space......Page 842.3.5 Miscellaneous Comments......Page 962.4.1 Exact Solutions of Equations......Page 1012.4.2 Approximate Solutions of Equations......Page 1103.1.1 Using Graphs and Tables to Predict Limits......Page 1153.1.2 Computing Limits......Page 1183.1.3 One-Sided Limits......Page 1203.1.4 Continuity......Page 1223.2.1 Definition of the Derivative......Page 1253.2.2 Calculating Derivatives......Page 1313.2.3 Implicit Differentiation......Page 1353.2.4 Tangent Lines......Page 137 Tangent Lines of Implicit Functions......Page 139 Parametric Equations and Polar Coordinates......Page 1413.2.5 The First Derivative Test and Second Derivative Test......Page 1473.2.6 Applied Max/Min Problems......Page 1553.2.7.1 Antiderivatives......Page 165 u-Substitutions......Page 1663.3.1 Area......Page 1683.3.2 The Definite Integral......Page 1743.3.4 Area......Page 180 Parametric Equations......Page 184 Polar Coordinates......Page 1853.3.5 Arc Length......Page 186 Parametric Equations......Page 187 Polar Coordinates......Page 190 Volume......Page 191 Surface Area......Page 2023.4.1 Introduction to Sequences......Page 2043.4.2 Introduction to Infinite Series......Page 2083.4.3 Convergence Tests......Page 2113.4.4 Alternating Series......Page 2153.4.5 Power Series......Page 2163.4.6 Taylor and Maclaurin Series......Page 2203.4.7 Taylor's Theorem......Page 2243.4.8 Other Series......Page 2353.5.1 Limits of Functions of Two Variables......Page 2373.5.2 Partial and Directional Derivatives......Page 239 Classifying Critical Points......Page 246 Tangent Planes......Page 249 Lagrange Multipliers......Page 2523.5.3 Iterated Integrals......Page 255 Area, Volume, and Surface Area......Page 256 Triple Iterated Integrals......Page 2624.1.1 Defining Lists......Page 2654.1.2 Plotting Lists of Points......Page 2704.2 Manipulating Lists: More on Part and Map......Page 2834.2.1 More on Graphing Lists; Graphing Lists of Points Using Graphics Primitives......Page 2924.3 Other Applications......Page 3004.3.1 Approximating Lists wi