Maple 9 Learning Guide - Maplesoft

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4 • Chapter 1: Introduction to MapleInteractive Problem-Solving Environment Maple allows you to undertakelarge problems and eliminates your mechanical errors. The interfaceprovides documentation of the steps involved in finding your result. Itallows you to easily modify a step or insert a new one in your solutionmethod. With minimal effort you can compute the new result.Generating Technical Documents You can create interactive structureddocuments for presentations or publication that contain mathematics inwhich you can change an equation and update the solution automatically.You also can display plots. In addition, you can structure your documentsby using tools such as outlining, styles, and hyperlinks. Outlining allowsyou to collapse sections to hide regions that contain distracting detail.Styles identify keywords, headings, and sections. Hyperlinks allow you tocreate live references that take the reader directly to pages containing relatedinformation. The interactive nature of Maple allows you to computeresults and answer questions during presentations. You can clearly andeffectively demonstrate why a seemingly acceptable solution method is inappropriate,or why a particular modification to a manufacturing processwould lead to loss or profit. Since components of worksheets are directlyassociated with the structure of the document, you can easily translateyour work to other formats, for example, HTML, RTF, and L A TEX.
2 Mathematics with Maple:The BasicsThis chapter introduces the Maple commands necessary to get youstarted. Use your computer to try the examples as you read.In This Chapter• Exact calculations• Numerical computations• Basic symbolic computations and assignment statements• Basic types of objects• Manipulation of objects and the commandsMaple Help SystemAt various points in this guide you are referred to the Maple help system.The help pages provide detailed command and topic information. Youmay choose to access these pages during a Maple session. To use the helpcommand, at the Maple prompt enter a question mark (?) followed bythe name of the command or topic for which you want more information.?command2.1 IntroductionThis section introduces the following concepts in Maple.• Semicolon (;) usage5
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 11: 1 Introduction to MapleMaple is a S
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>
Page 59 and 60: 3.1 The Maple solve Command • 51>
Page 61 and 62: 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
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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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