TCIDATATCIArticle/ART3.LAT,dep,mathart11Scienti?c WorkPlace Demonstration DocumentRoger Hunter and Fred Richman and John Thomas and Elbert WalkerContents1Introduction32Getting Started3 2.1Where to Place the Insertion Point . . . . .3 2.2How Scienti?c WorkPlace Selects an Ex- pression . . . . . . . . . . . . . . . . . . . .3 2.3Selecting Expressions for Operations . . . .4 2.4A Keyboard Shortcut for Evaluate . . . . .4 2.5Stopping a Computation . . . . . . . . . . .4 2.6The Settings Menu . . . . . . . . . . . . . .43Working with Expressions and Functions5 3.1The Slash Operator (/). . . . . . . . . . .5 3.2Standard Mathematical Functions. . . . .6 3.3More Operations . . . . . . . . . . . . . . .7 3.4Some Special Operations and Commands.7 3.5Constants . . . . . . . . . . . . . . . . . . .8 3.6Polynomials . . . . . . . . . . . . . . . . . .8 3.7Limits . . . . . . . . . . . . . . . . . . . . .9 3.8Di?erentiation. . . . . . . . . . . . . . . .9 3.9Inde?nite Integration . . . . . . . . . . . . .9 3.10 Sequences of Operations . . . . . . . . . . .10 3.11 De?nite Integrals . . . . . . . . . . . . . . .10 3.12 Numerical Integration. . . . . . . . . . . .11 3.13 In?nite Series . . . . . . . . . . . . . . . . .11 3.14 Substituting a Value into an Expression . .114Matrices11 4.1Standard Operations . . . . . . . . . . . . .11 4.2The Matrices Submenu . . . . . . . . . . . .125Solving Systems of Equations13 5.1Solve Exact . . . . . . . . . . . . . . . . . .13 5.2Solve Numeric . . . . . . . . . . . . . . . . .14 5.3Solve Integer. . . . . . . . . . . . . . . . .14 5.4Solve Recursion . . . . . . . . . . . . . . . .146Modular Arithmetic14 6.1The Integers modulo m. . . . . . . . . . .14 6.2Matrices Modulo m . . . . . . . . . . . . . .15 6.3Polynomials Modulo m . . . . . . . . . . . .15 6.4Polynomials Modulo Polynomials. . . . .157De?nitions15 7.1New De?nition, Unde?ne, Show De?ni- tions, and Clear De?nitions . . . . . . . . .15 7.2De?nitions with Deferred Evaluation . . . .18 7.3Remembering Solutions. . . . . . . . . . .18 7.4Save De?nitions 2 ? 325 ? 3803 ? 3607, contains ? only where nec- essary. The presence of the superscript following the 3 means that ? is not necessary before the following 5. Scienti?c WorkPlace automatically chooses integer factorization.Factoring a Polynomial Placetheinsertionpoint within x5+ 7x3? 41x4y ? 41x2y + 80x3y2+ 80xy2? 52y3x2? 52y3;=?x2+ 1?(7x ? 13y)(?2y + x)2and choose Factor from the Maple menu. Scienti?c Work- Place automatically chooses polynomial factorization.Where to Place the Insertion PointScienti?c WorkPlace shows mathematics in red.When the insertion point is within mathematics, the Math/Text icon at the top of the screen displays a red M. When we say place the insertion point in the following expression“, anywhere that shows the red M is su?cient. Valid posi- tions are anywhere within, or immediately to the right of, the expression. The position immediately to the left of the expression is not valid.Expand Place the insertion point in the expression x ? 2y)2(7x ? 13y)(x2+ 1) and from the Maple menu choose xpand. You should get the polynomial in the previous example x?2y)2(7x?13y)(x2+1) = 7x5+ 7x3?41x4y?41x2y+80x3y2+80xy2?52y3x2?52y3, of course.How Scienti?c WorkPlace Selects an ExpressionWhen you place the insertion point in a mathematical ex- pression and choose an operation from the Maple menu, Scienti?c WorkPlace automatically selects either the en- tire expression, or the part containing the insertion point which is enclosed between a combination of text and binary relations, depending on the operation you chose. Here are some examples that illustrate the various possibilities.An Equation Place the insertion point anywhere within the equation x + 3x = 1 and from the Maple menu3choose Solve + Exact. In this case, Scienti?c Work- Place selected the entire expression.The solution is not equal to the original expression, so Scienti?c WorkPlace does not make it part of the original equa- tion:2x + 3x = 1, Solution is :?x =1 5?Now place the insertion point in the left hand side of the equation and from the Maple menu choose Evalu- ate.2x + 3x = 5x = 1This time, Scienti?c WorkPlace selected only the left hand side of the equation for evaluation. Notice too that since the result of the evaluation was equal to the original expression, the result was placed next to the expression, preceded by an equals sign. The in- sertion point is placed at the right end of the result so that you can select another operation to apply to the result without moving the insertion point.Selecting Expressions for OperationsIf you want to restrict the computation to a particu- lar selection, or override Scienti?c WorkPlaces automatic choice, you can use a selection. The next few examples illustrate this feature. There are two options.Operating on a Selection Use the mouse or the shift and rrow keys to select (x + y)5in the expression (x + y)5?7x ? 13y3?+ sin2x, from the Maple menu choose Expand.(x + y)