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Printed in Canada ISBN 1-894511-75-1 Contents Preface .................................................................................................... xiii 1 Document Mode ...................................................................................... 1 1.1 Introduction ...................................................................................... 1 1.2 In This Chapter ................................................................................ 3 1.3 Simple Mathematical Expressions ................................................... 4 Rational Expressions (Fractions) ....................................................... 5 Powers ................................................................................................ 5 Products .............................................................................................. 5 Shortcuts for Entering Mathematical Expressions ............................. 6 Other Expressions .............................................................................. 7 1.4 Evaluating Expressions .................................................................... 8 1.5 Editing Expressions and Updating Output ...................................... 9 1.6 Entering Expressions ..................................................................... 10 Palettes ............................................................................................ 10 Symbol Names ................................................................................ 16 1.7 Performing Computations ............................................................. 19 Computing with Palettes ................................................................. 20 Context Menus ................................................................................ 20 Assistants and Tutors ....................................................................... 26 1.8 Document Mode Summary ............................................................ 30 1.9 Getting Help ................................................................................... 32 2 Worksheet Mode ................................................................................... 35 2.1 In This Chapter .............................................................................. 36 2.2 Input Prompt .................................................................................. 37 Suppressing Output .......................................................................... 38 1-D Math Input ................................................................................ 38 Input Separators ............................................................................... 39 2.3 Commands .................................................................................... 40 The Maple Library ........................................................................... 40 Top-Level Commands ...................................................................... 40 Package Commands ........................................................................ 42 2.4 Palettes .......................................................................................... 44 2.5 Context Menus .............................................................................. 46 2.6 Assistants and Tutors ..................................................................... 48 iii iv · Contents Launching an Assistant or Tutor ...................................................... 48 Example: Using the Interactive Plot Builder ................................... 49 2.7 Task Templates .............................................................................. 51 Viewing Task Templates .................................................................. 51 Inserting a Task Template ................................................................ 52 Performing the Task ......................................................................... 53 2.8 Text Regions ................................................................................... 54 2.9 Names ........................................................................................... 55 Assigning to Names ........................................................................ 55 Unassigning Names ........................................................................ 57 Valid Names .................................................................................... 58 2.10 Equation Labels .......................................................................... 59 Displaying Equation Labels ............................................................. 59 Referring to a Previous Result ......................................................... 59 Execution Groups with Multiple Outputs ........................................ 61 Label Numbering Schemes ............................................................. 61 Features of Equation Labels ............................................................ 62 3 Performing Computations .................................................................... 65 3.1 In This Chapter .............................................................................. 65 3.2 Symbolic and Numeric Computation ............................................ 66 Exact Computations ........................................................................ 67 Floating-Point Computations .......................................................... 68 Converting Exact Quantities to Floating-Point Values ................... 69 Sources of Error .............................................................................. 70 3.3 Integer Operations ......................................................................... 71 Non-Base 10 Numbers and Other Number Systems ........................ 74 3.4 Solving Equations .......................................................................... 78 Solving Equations and Inequations ................................................. 78 Other Specialized Solvers ................................................................ 88 3.5 Units, Scientific Constants, and Uncertainty ................................. 96 Units ................................................................................................ 97 Scientific Constants and Element Properties ................................ 105 Uncertainty Propagation ............................................................... 111 3.6 Restricting the Domain ................................................................ 115 Real Number Domain ................................................................... 115 Assumptions on Variables ............................................................. 117 Contents · v 4 Mathematical Computations .............................................................. 123 4.1 In This Chapter ............................................................................ 125 4.2 Algebra ........................................................................................ 126 Polynomial Algebra ...................................................................... 126 4.3 Linear Algebra ............................................................................ 135 Creating Matrices and Vectors ...................................................... 135 Accessing Entries in Matrices and Vectors ................................... 144 Linear Algebra Computations ....................................................... 145 Student LinearAlgebra Package .................................................... 152 4.4 Calculus ....................................................................................... 153 Limits ............................................................................................ 153 Differentiation ............................................................................... 155 Series ............................................................................................. 161 Integration ..................................................................................... 163 Differential Equations .................................................................... 166 Calculus Packages ......................................................................... 166 4.5 Optimization ............................................................................... 168 Point-and-Click Interface .............................................................. 169 Large Optimization Problems ....................................................... 171 MPS(X) File Support .................................................................... 173 Additional Information .................................................................. 173 4.6 Statistics ...................................................................................... 173 Probability Distributions and Random Variables .......................... 173 Statistical Computations ................................................................ 175 Plotting .......................................................................................... 177 Additional Information .................................................................. 179 4.7 Teaching and Learning with Maple ............................................ 180 Student Packages and Tutors ........................................................ 181 5 Plots and Animations .......................................................................... 189 5.1 In This Chapter ............................................................................ 189 5.2 Creating Plots .............................................................................. 190 Interactive Plot Builder ................................................................. 191 Context Menu ................................................................................ 204 Dragging to a Plot Region ............................................................. 207 The plot and plot3d Commands .................................................... 208 The plots Package ......................................................................... 211 vi · Contents Multiple Plots in the Same Plot Region ......................................... 214 5.3 Customizing Plots ....................................................................... 216 Interactive Plot Builder Options ................................................... 216 Context Menu Options .................................................................. 217 The plot and plot3d Options ......................................................... 220 5.4 Analyzing Plots ........................................................................... 222 Point Probe, Rotate, Pan, and Scale Tools ..................................... 222 5.5 Creating Animations ................................................................... 223 Interactive Plot Builder ................................................................. 223 The plots[animate] Command ....................................................... 225 5.6 Playing Animations ..................................................................... 226 Animation Context Bar .................................................................. 226 5.7 Customizing Animations ............................................................. 228 Interactive Plot Builder Animation Options .................................. 228 Context Menu Options .................................................................. 228 The animate Command Options .................................................... 229 5.8 Exporting ..... ...