Maple 9 Learning Guide - Maplesoft

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2 • Prefaceincludes information for new users about the help system, New User’sTour, example worksheets, and the Maplesoft Web site.• The Maple Introductory Programming Guide introduces the basicMaple programming concepts, such as expressions, data structures,looping and decision mechanisms, procedures, input and output, debugging,and the Maplet TM User Interface Customization System.• The Maple Advanced Programming Guide extends the basic Mapleprogramming concepts to more advanced topics, such as modules,input and output, numerical programming, graphics programming,and compiled code.Whereas this book highlights features of Maple, the help system is acomplete reference manual. There are also examples that you can copy,paste, and execute immediately.ConventionsThis manual uses the following typographical conventions.• courier font - Maple command, package name, and option name• bold roman font - dialog, menu, and text field• italics - new or important concept, option name in a list, and manualtitles• Note - additional information relevant to the section• Important - information that must be read and followedCustomer FeedbackMaplesoft welcomes your feedback. For suggestions and comments relatedto this and other manuals, contact doc@maplesoft.com.
1 Introduction to MapleMaple is a Symbolic Computation System or Computer Algebra System.Maple manipulates information in a symbolic or algebraic manner.You can obtain exact analytical solutions to many mathematical problems,including integrals, systems of equations, differential equations,and problems in linear algebra. Maple contains a large set of graphicsroutines for visualizing complicated mathematical information, numericalalgorithms for providing estimates and solving problems where exactsolutions do not exist, and a complete and comprehensive programminglanguage for developing custom functions and applications.Worksheet Graphical InterfaceMaple mathematical functionality is accessed through its advanced worksheetbasedgraphical interface. A worksheet is a flexible document for exploringmathematical ideas and for creating sophisticated technical reports. Youcan access the power of the Maple computation engine through a varietyof user interfaces: the standard worksheet, the command-line 1 version,the classic worksheet (not available on Macintosh r○ ), and custom-builtMaplet applications. The full Maple system is available through all ofthese interfaces. In this manual, any references to the graphical Mapleinterface refer to the standard worksheet interface. For more informationon the various interface options, refer to the ?versions help page.ModesYou can use Maple in two modes: as an interactive problem-solving environmentand as a system for generating technical documents.1 The command-line version provides optimum performance. However, the worksheetinterface is easier to use and renders typeset, editable math output and higher qualityplots.3
Page 1 and 2: Maple 9Learning GuideBased in part
Page 3 and 4: ContentsPreface 1Audience . . . . .
Page 5 and 6: Contents • vRoot Finding and Fact
Page 7: Contents • viiLast-Name Evaluatio
Page 13 and 14: 2 Mathematics with Maple:The Basics
Page 15 and 16: 2.2 Numerical Computations • 7are
Page 17 and 18: 2.2 Numerical Computations • 9Tab
Page 19 and 20: 2.2 Numerical Computations • 11Im
Page 21 and 22: 2.2 Numerical Computations • 13Th
Page 23 and 24: 2.2 Numerical Computations • 15Ma
Page 25 and 26: 2.3 Basic Symbolic Computations •
Page 27 and 28: 2.4 Assigning Expressions to Names
Page 29 and 30: 2.5 Basic Types of Maple Objects2.5
Page 31 and 32: 2.5 Basic Types of Maple Objects
Page 33 and 34: {1,2,3,a,b,c} intersect {0,1,y,a};2
Page 35 and 36: third_set := old_set minus {2, 5};2
Page 41 and 42: 2.6 Expression Manipulation • 333
Page 43 and 44: x 2 + x y + y 2(y + x) (x 2 + y 2 )
Page 45 and 46: 2.6 Expression Manipulation • 37T
Page 47 and 48: 2.6 Expression Manipulation • 39>
Page 49 and 50: 2.6 Expression Manipulation • 41C
Page 51 and 52: 3 Finding SolutionsThis chapter int
Page 53 and 54: 3.1 The Maple solve Command • 45s
Page 55 and 56: 3.1 The Maple solve Command • 47A
Page 57 and 58: 3.1 The Maple solve Command • 49>
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3.1 The Maple solve Command • 51>
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3.1 The Maple solve Command • 53f
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3.2 Solving Numerically Using the f
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3.2 Solving Numerically Using the f
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3.4 Polynomials • 59Solving Recur
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3.4 Polynomials • 61> sort(mul_va
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3.4 Polynomials • 63Table 3.1 Com
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3.5 Calculus3.5 Calculus • 65Mapl
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3.5 Calculus • 67> plot({f(x), p}
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3.5 Calculus • 69> simplify(%);x
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3.6 Solving Differential Equations
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_C1 e + _C2 e (−1) − _C3 sin(1)
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4 Maple OrganizationThis chapter in
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4.1 The Organization of Maple • 8
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CurveFitting commands that support
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4.2 The Maple Packages • 85Orthog
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4.2 The Maple Packages • 87TypeTo
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4.2 The Maple Packages • 89To vie
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4.2 The Maple Packages • 91> Limi
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4.2 The Maple Packages • 93You ca
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4.2 The Maple Packages • 95The fo
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4.2 The Maple Packages • 97To est
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4.2 The Maple Packages • 99> read
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4.2 The Maple Packages • 101The s
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5 PlottingMaple can produce several
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5.1 Graphing in Two Dimensions •
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polarplot( r-expr, angle=range )5.1
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5.2 Graphing in Three Dimensions
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5.3 Animation • 127Simultaneous u
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5.3 Animation • 129Specifying Fra
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• a,b - real constants giving the
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5.4 Annotating Plots • 133The Sph
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5.5 Composite Plots • 135> with(p
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a := plot( sin(x), x=-Pi..Pi ):5.6
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5.6 Special Types of Plots • 139T
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5.6 Special Types of Plots • 141A
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5.6 Special Types of Plots • 1431
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5.7 Manipulating Graphical Objects
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5.7 Manipulating Graphical Objects
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hedgehog := [s1, s2, c3, stelhs]:>
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5.8 Code for Color Plates • 151>
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5.10 Conclusion5.10 Conclusion •
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6 Evaluation andSimplificationExpre
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expand( (x+1)*(y^2-2*y+1) / z / (y-
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6.1 Mathematical Manipulations •
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factor( poly, RootOf(x^2-2) );6.1 M
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6.2 Assumptions • 175> assume( a
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6.2 Assumptions • 177∞Logarithm
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6.2 Assumptions • 179a:nothing kn
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6.3 Structural Manipulations • 18
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f := (x, y) → is(x < y)6.3 Struct
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term3 := 2 cos(x) 2 sin(x)6.3 Struc
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y := ln( sin( x * exp(cos(x)) ) );y
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√ z sin(z) + w6.3 Structural Mani
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6.4 Evaluation Rules • 203> eval(
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6.4 Evaluation Rules • 205proc(x:
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6.4 Evaluation Rules • 207The seq
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6.4 Evaluation Rules • 2091Import
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6.4 Evaluation Rules • 211> q :=
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6.5 Conclusion • 213> sum( ’a||
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7 Solving Calculus ProblemsThis cha
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7.1 Introductory Calculus • 217>
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7.1 Introductory Calculus • 219In
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⎡⎧ ⎛1 √⎞1⎨5 − ⎩⎢a
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7.1 Introductory Calculus • 223en
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sol := solve( {err_x=0, err_xi=0},
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7.1 Introductory Calculus • 227If
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7.1 Introductory Calculus • 229>
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7.1 Introductory Calculus • 231{0
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7.1 Introductory Calculus • 233An
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∫ 1+ sin(x) dx27.1 Introductory C
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7.1 Introductory Calculus • 237r
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7.1 Introductory Calculus • 239fy
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7.2 Ordinary Differential Equations
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{y(x) = _C1 },7.2 Ordinary Differen
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Evaluate the result at values for t
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odeplot( sol, [t, x(t)], -1..2 );7.
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You must evaluate the derivatives a
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DEplot( ode, dep-var, range, [ini-c
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DEplot( {eq1, eq2}, [x(t), y(t)], -
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f := unapply( rhs( % ), t );7.2 Ord
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eq := diff(y(t),t) = 1-y(t)*f(t);7.
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7.3 Partial Differential Equations
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8 Input and OutputMaple provides co
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8.1 Reading Files • 279For exampl
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8.2 Writing Data to a File • 281W
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ExportVector( "vectordata.txt", V )
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8.2 Writing Data to a File • 285o
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8.3 Exporting Worksheets • 287•
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8.3 Exporting Worksheets • 289ali
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8.3 Exporting Worksheets • 291\en
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8.3 Exporting Worksheets • 293Exp
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8.3 Exporting Worksheets • 295Pla
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8.3 Exporting Worksheets • 2974.
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8.5 Conclusion • 299Graphics Suit
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9 Maplet User InterfaceCustomizatio
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9.3 How to Start the Maplets Packag
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9.7 How to Activate a Maplet Applic
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Index!, 8I ( √ −1), 14π, 12~,
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Index • 309combiningpowers, 37pro
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Index • 311integer quotient, 9int
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Index • 313partial, 173fsolve, 54
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Index • 315liesymm, 83lighting sc
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Index • 317graphical, 144odeplot,
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Index • 319lighting schemes, 126l
Page 329 and 330:
Index • 321refining 2-D plots, 11
Page 331 and 332:
Index • 323by total order, 60spac
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Maple 9 Learning Guide - Maplesoft

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