Maple 11 User Manual

Maple User Manual......Page 1
Contents......Page 3
Preface......Page 13
1.1  Introduction......Page 17
1.2  In This Chapter......Page 19
1.3  Simple Mathematical Expressions......Page 20
Products......Page 21
Shortcuts for Entering Mathematical Expressions......Page 22
Other Expressions......Page 23
1.4  Evaluating Expressions......Page 24
1.5  Editing Expressions and Updating Output......Page 25
1.6  Entering Expressions......Page 26
Palettes......Page 27
Using Palettes......Page 28
Defining a Mathematical Function......Page 30
Handwriting Palette......Page 31
Symbol Names......Page 32
Using Symbol Names......Page 33
Example: Indefinite Integral......Page 34
1.7  Performing Computations......Page 35
Context Menus......Page 36
Approximating the Value of an Expression......Page 38
Using Units......Page 40
Tutors......Page 42
Using a Context Menu to Launch the Plot Builder......Page 44
1.8  Document Mode Summary......Page 46
1.9  Getting Help......Page 48
2  Worksheet Mode......Page 51
2.1  In This Chapter......Page 52
2.2  Input Prompt......Page 53
1-D Math Input......Page 54
2.3  Commands......Page 55
Top-Level Commands......Page 56
Package Commands......Page 57
2.4  Palettes......Page 60
2.5  Context Menus......Page 62
Launching an Assistant or Tutor......Page 64
Example: Using the Interactive Plot Builder......Page 65
Viewing Task Templates......Page 67
Inserting a Task Template......Page 68
Performing the Task......Page 69
2.8  Text Regions......Page 70
Assigning to Names......Page 71
Mathematical Functions......Page 72
Unassigning Names......Page 73
Valid Names......Page 74
Referring to a Previous Result......Page 75
Label Numbering Schemes......Page 77
Features of Equation Labels......Page 78
3.1  In This Chapter......Page 81
3.2  Symbolic and Numeric Computation......Page 82
Exact Computations......Page 83
Floating-Point Computations......Page 84
Converting Exact Quantities to Floating-Point Values......Page 85
Sources of Error......Page 86
3.3  Integer Operations......Page 87
Non-Base 10 Numbers......Page 90
Finite Rings and Fields......Page 91
3.4  Solving Equations......Page 93
Solving Equations and Inequations......Page 94
Symbolically Solving Equations and Inequations......Page 96
Numerically Solving Equations......Page 99
Working with Solutions......Page 102
Ordinary Differential Equations (ODEs)......Page 104
Partial Differential Equations (PDEs)......Page 108
Integer Equations......Page 109
Solving Linear Systems......Page 110
3.5  Units, Scientific Constants, and Uncertainty......Page 111
Overview of Units......Page 112
Conversions......Page 113
Applying Units to an Expression......Page 115
Performing Computations with Units......Page 117
Changing the Current System of Units......Page 118
Extensibility......Page 119
List of Scientific Constants......Page 120
Element Properties......Page 121
Accessing an Element or Isotope Property Definition......Page 122
Value, Units, and Uncertainty......Page 123
Units......Page 124
Performing Computations......Page 125
Uncertainty Propagation......Page 126
Quantities with Uncertainty......Page 127
Performing Computations with Quantities with Uncertainty......Page 128
Additional Information......Page 129
Real Number Domain......Page 130
The assume Command......Page 132
The assuming Command......Page 134
4  Mathematical Computations......Page 137
4.1  In This Chapter......Page 139
Arithmetic......Page 140
Sorting Terms......Page 142
Coefficients and Degrees......Page 146
Factorization......Page 147
Other Commands......Page 148
Creating Matrices......Page 149
Editing and Viewing Large Matrices and Vectors......Page 152
Creating Matrices and Vectors for Large Problems......Page 155
Accessing Entries in Matrices and Vectors......Page 158
Matrix Arithmetic......Page 159
Point-and-Click Interaction......Page 162
LinearAlgebra Package Commands......Page 164
Student LinearAlgebra Package......Page 166
Limits......Page 167
The limit Command......Page 168
Differentiation......Page 169
The diff Command......Page 171
Differentiating an Operator......Page 172
Directional Derivative......Page 173
Series......Page 175
Integration......Page 177
The int Command......Page 178
Numeric Integration......Page 179
VectorCalculus Package......Page 180
4.5  Optimization......Page 182
Point-and-Click Interface......Page 183
Large Optimization Problems......Page 185
Probability Distributions and Random Variables......Page 187
Adding Custom Distributions......Page 188
Example 1......Page 189
Example 2......Page 190
Plotting......Page 191
Additional Information......Page 193
4.7  Teaching and Learning with Maple......Page 194
Student Packages and Tutors......Page 195
5.1  In This Chapter......Page 203
5.2  Creating Plots......Page 204
Interactive Plot Builder......Page 205
Example 1 - Display a plot of a single variable expression......Page 208
Example 2 - Display a plot of multiple expressions of 1 variable......Page 209
Example 3 - Display a plot of a multi-variable expression......Page 211
Example 4 - Display a conformal plot......Page 213
Example 5 - Display a plot in polar coordinates......Page 215
Example 6 - Interactive Plotting......Page 216
Context Menu......Page 219
Dragging to a Plot Region......Page 222
Example 1 - Display a plot of a single variable expression......Page 223
Example 6 - Interactive Plotting......Page 224
Display a 3-D Plot......Page 225
The pointplot Command......Page 226
The matrixplot Command......Page 227
List of Expressions......Page 229
The display Command......Page 230
Interactive Plot Builder Options......Page 231
Context Menu Options......Page 232
2-D Plot Options......Page 233
3-D Plot Options......Page 234
The plot and plot3d Options......Page 235
5.5  Creating Animations......Page 238
Interactive Plot Builder......Page 239
The plots[animate] Command......Page 240
Animate a 2-D plot......Page 241
Animation Context Bar......Page 242
Context Menu Options......Page 244
The animate Command Options......Page 245
5.9  Code for Color Plates......Page 246
6  Creating Mathematical Documents......Page 247
6.1  In This Chapter......Page 248
Quick Character Formatting......Page 249
Quick Paragraph Formatting......Page 251
Copy and Paste......Page 252
Using the Insert Menu to Add Sections......Page 253
Indentation and the Tab Key......Page 254
Applying Character Styles......Page 255
Creating Character Styles......Page 256
Modifying Character Styles......Page 257
Applying Paragraph Styles......Page 258
Creating Paragraph Styles......Page 259
Modifying Paragraph Styles......Page 260
Creating and Applying Style Sets......Page 261
Reverting to a Style Set......Page 262
Document Blocks......Page 263
Applying Document Blocks: General Process......Page 264
Working in Document Mode......Page 265
Expand an Execution Group within a Document Block......Page 266
Inline Document......Page 267
Creating a Table......Page 268
Inserting Rows and Columns......Page 269
Modifying the Physical Dimensions of a Table......Page 270
Alignment Options......Page 271
Controlling the Visibility of Cell Content......Page 272
Execution Order Dependency......Page 273
Table of Values......Page 274
Formatting Table Headers......Page 275
2-D Math and Plots......Page 276
Table of Mathematical Expressions......Page 277
Formatting Lists Using the Context Bar......Page 278
Formatting Lists Using the Paragraph Style Dialog......Page 279
Inserting, Renaming, and Deleting a Bookmark......Page 280
Inserting Images......Page 281
Show or Hide Worksheet Content......Page 282
Command Output Versus Insertion......Page 283
Adding Graphical Interface Components......Page 284
Removing Graphical Interface Components......Page 285
Example Component Properties......Page 286
Creating a Question......Page 287
6.5  Auto-Execute......Page 288
Security Levels......Page 289
Insert a Canvas......Page 290
Canvas Style......Page 291
6.7  Spell Checking......Page 292
Selecting a Suggestion......Page 293
User Dictionary......Page 294
6.8  Hyperlinks......Page 295
Linking to an Email Address......Page 296
Linking to a Maplet Application......Page 297
Linking to a Document......Page 298
6.9  Worksheet Compatibility......Page 299
7.2  Creating and Using Data Structures......Page 301
Accessing Elements......Page 302
Using Sets......Page 303
Using Lists......Page 304
Creating and Using Arrays......Page 305
Tables......Page 306
Matrices and Vectors......Page 307
Defining a Function......Page 308
Distinction between Functional Operators and Other Expressions......Page 309
Multivariate and Vector Functions......Page 310
Using Operators......Page 311
Using Strings......Page 313
Expression Types......Page 314
Testing the Type of Subexpressions......Page 315
Testing for a Subexpression......Page 316
Left and Right-Hand Side......Page 317
Numerator and Denominator......Page 318
Indeterminates......Page 319
Simplifying......Page 320
Factoring......Page 321
Combining......Page 322
Converting......Page 323
Normalizing......Page 325
Substituting a Value for a Subexpression......Page 326
Numerical Approximation......Page 329
Evaluating Complex Expressions......Page 330
Evaluating Boolean Expressions......Page 331
Levels of Evaluation......Page 332
Delaying Evaluation......Page 333
Using an Assigned Name as a Variable or Keyword......Page 334
Unassigning a Name Using Unevaluation Quotes......Page 335
8.1  In This Chapter......Page 337
Syntax......Page 338
else Clause......Page 339
elif Clauses......Page 340
Repetition (for Statement)......Page 341
Syntax......Page 342
Examples......Page 343
Syntax......Page 344
while Loop......Page 345
Example......Page 346
General Loop Statements......Page 347
Additional Information......Page 348
Creating a Sequence......Page 349
Adding and Multiplying Expressions......Page 350
Selecting Expression Operands......Page 351
Mapping a Binary Command over Two Lists or Vectors......Page 352
Additional Information......Page 353
Defining and Running Simple Procedures......Page 354
Procedure Return Values......Page 355
Displaying Maple Library Procedure Definitions......Page 356
Modules......Page 358
9.2  Simple Maplet......Page 359
Maplet File......Page 360
9.4  Authoring Maplets......Page 361
Maplet Builder......Page 362
Design a Maplet Using the Maplet Builder......Page 364
Define the number of rows in the Maplet......Page 365
Add a plot region to row 1......Page 366
Add columns to row 2......Page 367
Add a label to row 2......Page 368
Add a text region to row 2......Page 369
Add a button to row 2......Page 370
Maplets Package......Page 372
Example 1 - Design a Maplet Using the Maplets Package......Page 373
Example 2 - Accessing User-Defined Procedures......Page 375
User-Defined Procedure and Maplet Code......Page 376
Maplet File......Page 378
Saving Data to a File......Page 379
Saving Expressions to a File......Page 381
Import Data Assistant......Page 382
Reading Expressions from a File......Page 383
LaTeX......Page 385
Plain Text......Page 386
Summary of Translation......Page 387
Overview of MapleNet......Page 388
Exporting Assignments to Maple T.A.......Page 389
External Calling......Page 390
Microsoft Excel Add-In......Page 391
OpenMaple......Page 392
Index......Page 395