Maple 9 Learning Guide - Maplesoft

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212 • Chapter 6: Evaluation and Simplificationc := 3> a||b||c;a23If a name does not evaluate to a single symbol, Maple does not evaluatea concatenation.> a := x;a := x> b := y+1;b := y + 1> new_name := a||b;new_name := a||(y + 1)> y := 3;y := 3> new_name;a4You can use concatenated names to assign and create expressions.> i := 1;i := 1> b||i := 0;b1 := 0You must use right single quotes.
6.5 Conclusion • 213> sum( ’a||k’ * x^k, k=0..8 );a0 + a1 x + a2 x 2 + a3 x 3 + a4 x 4 + a5 x 5 + a6 x 6 + a7 x 7+ a8 x 8If you do not use right single quotes, Maple evaluates a||k to ak.> sum( a||k * x^k, k=0..8 );ak + ak x + ak x 2 + ak x 3 + ak x 4 + ak x 5 + ak x 6 + ak x 7+ ak x 8You can also use concatenation to form title strings for plots.6.5 ConclusionIn this chapter, you have seen how to perform many kinds of expressionmanipulations, from adding two equations to selecting individual parts ofa general expression. In general, no rule specifies which form of an expressionis the simplest. The commands in this chapter allow you to convertan expression to many forms, often the ones you would consider simplest.If not, you can use side relations to specify your own simplification rules,or assumptions to specify properties of unknowns.You have also seen that Maple, in most cases, uses full evaluationof variables. Some exceptions exist, which include last-name evaluationfor certain data structures, one-level evaluation for local variables in aprocedure, and delayed evaluation for names in right single quotes.
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Maple 9Learning GuideBased in part
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ContentsPreface 1Audience . . . . .
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Contents • vRoot Finding and Fact
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Contents • viiLast-Name Evaluatio
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1 Introduction to MapleMaple is a S
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2 Mathematics with Maple:The Basics
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2.2 Numerical Computations • 7are
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2.2 Numerical Computations • 9Tab
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2.2 Numerical Computations • 11Im
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2.2 Numerical Computations • 13Th
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2.2 Numerical Computations • 15Ma
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2.3 Basic Symbolic Computations •
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2.4 Assigning Expressions to Names
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2.5 Basic Types of Maple Objects2.5
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2.5 Basic Types of Maple Objects
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{1,2,3,a,b,c} intersect {0,1,y,a};2
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third_set := old_set minus {2, 5};2
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2.6 Expression Manipulation • 333
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x 2 + x y + y 2(y + x) (x 2 + y 2 )
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2.6 Expression Manipulation • 37T
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2.6 Expression Manipulation • 39>
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2.6 Expression Manipulation • 41C
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3 Finding SolutionsThis chapter int
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3.1 The Maple solve Command • 45s
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3.1 The Maple solve Command • 47A
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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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Page 171 and 172: factor( poly, RootOf(x^2-2) );6.1 M
Page 183 and 184: 6.2 Assumptions • 175> assume( a
Page 185 and 186: 6.2 Assumptions • 177∞Logarithm
Page 187 and 188: 6.2 Assumptions • 179a:nothing kn
Page 189 and 190: 6.3 Structural Manipulations • 18
Page 195 and 196: f := (x, y) → is(x < y)6.3 Struct
Page 199 and 200: term3 := 2 cos(x) 2 sin(x)6.3 Struc
Page 205 and 206: y := ln( sin( x * exp(cos(x)) ) );y
Page 207 and 208: √ z sin(z) + w6.3 Structural Mani
Page 211 and 212: 6.4 Evaluation Rules • 203> eval(
Page 213 and 214: 6.4 Evaluation Rules • 205proc(x:
Page 215 and 216: 6.4 Evaluation Rules • 207The seq
Page 217 and 218: 6.4 Evaluation Rules • 2091Import
Page 219: 6.4 Evaluation Rules • 211> q :=
Page 223 and 224: 7 Solving Calculus ProblemsThis cha
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Page 227 and 228: 7.1 Introductory Calculus • 219In
Page 229 and 230: ⎡⎧ ⎛1 √⎞1⎨5 − ⎩⎢a
Page 231 and 232: 7.1 Introductory Calculus • 223en
Page 233 and 234: sol := solve( {err_x=0, err_xi=0},
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Page 239 and 240: 7.1 Introductory Calculus • 231{0
Page 241 and 242: 7.1 Introductory Calculus • 233An
Page 243 and 244: ∫ 1+ sin(x) dx27.1 Introductory C
Page 245 and 246: 7.1 Introductory Calculus • 237r
Page 247 and 248: 7.1 Introductory Calculus • 239fy
Page 249 and 250: 7.2 Ordinary Differential Equations
Page 251 and 252: {y(x) = _C1 },7.2 Ordinary Differen
Page 253 and 254: Evaluate the result at values for t
Page 261 and 262: odeplot( sol, [t, x(t)], -1..2 );7.
Page 265 and 266: You must evaluate the derivatives a
Page 269 and 270: DEplot( ode, dep-var, range, [ini-c
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DEplot( {eq1, eq2}, [x(t), y(t)], -
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7.2 Ordinary Differential Equations
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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
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Index • 323by total order, 60spac
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Maple 9 Learning Guide - Maplesoft

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