Maple 9 Learning Guide - Maplesoft

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22 • Chapter 2: Mathematics with Maple: The BasicsOther properties of sequences will become apparent as you progressthrough this manual. Sequences extend the capabilities of many basicMaple operations. For example, concatenation is a basic name-formingoperation. The concatenation operator in Maple is “||”. You can usethe operator in the following manner.> a||b;abWhen applying concatenation to a sequence, the operation affects eachelement. For example, if S is a sequence, then you can prepend the namea to each element in S by concatenating a and S.> S := 1, 2, 3, 4;S := 1, 2, 3, 4> a||S;a1 , a2 , a3 , a4You can also perform multiple assignments using expression sequences.For example> f,g,h := 3, 6, 1;f, g, h := 3, 6, 1> f;3> h;1
2.5 Basic Types of Maple Objects • 23ListsYou create a list by enclosing any number of Maple objects (separatedby commas) in square brackets.> data_list := [1, 2, 3, 4, 5];data_list := [1, 2, 3, 4, 5]> polynomials := [x^2+3, x^2+3*x-1, 2*x];polynomials := [x 2 + 3, x 2 + 3 x − 1, 2 x]> participants := [Kathy, Frank, Rene, Niklaus, Liz];participants := [Kathy, Frank, Rene, Niklaus, Liz]Thus, a list is an expression sequence enclosed in square brackets.Order Maple preserves the order and repetition of elements in a list.Thus, [a,b,c], [b,c,a], and [a,a,b,c,a] are all different.> [a,b,c], [b,c,a], [a,a,b,c,a];[a, b, c], [b, c, a], [a, a, b, c, a]Because order is preserved, you can extract a particular element from alist without searching for it.> letters := [a,b,c];letters := [a, b, c]> letters[2];bUse the nops command to determine the number of elements in a list.> nops(letters);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 11 and 12: 1 Introduction to MapleMaple is a S
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: 2.5 Basic Types of Maple Objects2.5
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 37 and 38: 2.5 Basic Types of Maple Objects
Page 39 and 40: 2.5 Basic Types of Maple Objects
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
Page 63 and 64: 3.2 Solving Numerically Using the f
Page 65 and 66: 3.2 Solving Numerically Using the f
Page 67 and 68: 3.4 Polynomials • 59Solving Recur
Page 69 and 70: 3.4 Polynomials • 61> sort(mul_va
Page 71 and 72: 3.4 Polynomials • 63Table 3.1 Com
Page 73 and 74: 3.5 Calculus3.5 Calculus • 65Mapl
Page 75 and 76: 3.5 Calculus • 67> plot({f(x), p}
Page 77 and 78: 3.5 Calculus • 69> simplify(%);x
Page 79 and 80: 3.6 Solving Differential Equations
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3.6 Solving Differential Equations
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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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