1 A Section A BRIEF TOUR. 1.1 Subsection Subsection 2

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Melvin Gallagher
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1 A BRIEF TOUR Maple V is a complete mathematical problem-solving environment that supports a wide variety of mathematical operations such as numerical analysis, symbolic algebra, and graphics. This worksheet takes you on a very brief tour introducing some very basic interactions with Maple. For a more comprehensive introduction you may consult many other excellent sources such as books (e.g. Introduction to Maple by Andre Heck), web documents (see the links in my Maple page), the help file of Maple (click on the menu help and choose introduction). Worksheets are organized into sections. A section is identified by a box with a [+] or [-] sign embedded in it: To expand a section, click the [+] button with your mouse and it will change to a [-]. Try this now. To collapse a section, click the [-] and it will change to a [+]. Try this now. 1 A Section This is the content enclosed in the section What you have just expanded is an example of a section. Worksheets can be organized into a hierarchy of sections, with subsections within sections. Below are examples of subsections for this section. Expand and collapse them: 1.1 Subsection 1 This is a short paragraph within a subsection Subsection 1.1 A subsection Subsection 1.2 This is another subsection. 1.2 Subsection This is another subsection. and its content A worksheet is built by execution groups 1

2 2 Execution Group Execution groupsare the fundamental computation elements in the worksheet. Their primary purpose is to combine one or more Maple commandsand their results into a single reexecutable unit. You can easily recognize an execution group by a large square bracket immediately to the left of the command prompt. > solve( a*x^2 = 4, {x} ); When you place the cursor on any command line in an execution group and press [Enter], all commands in that group are executed in sequence and the results are displayed at the end of the execution group. The cursor is automatically advanced to the first command line in the next execution group. In addition to Maple commands and their results, an execution group can contain descriptive paragraphs. Examples The following execution group contains a paragraph, a Maple command line with one command, and the command result. A Maple command and the computed result. > expand((a + b)^3); New Maple worksheets begin with a single execution group containing an empty command line (as shown below). New execution groups can also be created by inserting an execution group (using the Insert menu). The results produced by a Maple command may be numeric, symbolic or graphical. 3 Enter Maple commands Empty command lines can be created by inserting an execution group (using the Insert menu). You can execute commands by typing them at a Maple prompt and pressing [Enter]. If you end a command line by a semicolon ; and then hit [Enter], Maple will execute the command and display the result. > 3+7; 10 If you end a command line by a colon : and then hit [Enter], Maple will execute the command but won t display the result. This is useful in intermediate calculations where you don t want certain messy results to appear in your worksheet. > 3+7: You can enter more than commands in an execution group. When you hit [Enter] the commands in the execution group will be executed and their results will be displayed in the order they were entered. > 1+2; 3+4; a+b; 3 2

3 7 a + b 4 Enter an expression You can enter powers, roots, polynomials, sine and cosine, and all kind of functions into Maple. Here are some simple examples A simple monomial > 3*x^2; 3 x 2 A polynomial > -2*x^100-4*x^3+150; 2 x x > 3*x*z^2 +x^2*y + 3*t; 3 x z 2 + x 2 y + 3 t Root (there are two ways to do this) > root(x+2,3); root[3](x^2+2); (x + 2) (1/3) (x 2 + 2) (1/3) Sine and Cosine and square root > sin(3*x) + cos^2(x) + sqrt(x-3); sin(3 x) + cos 2 + x 3 You can denote (or store) an expression for later references > p:=x^2-3*x+2; p := x 2 3 x + 2 Now use the reference p in other commands. > sqrt(p); x2 3 x Evaluate an expression Use the command eval to evaluate an expression at some value of a parameter in the expression. > eval(x^2-3*x+2,x=-2); 12 In the same way, we can use the command subs > subs(x=-2, > x^2-3*x+2); 12 > eval(sqrt(x^2-3*x+2),x=-2); 12 3

4 To get the numerical value of the above result we can use the command evalf (% stands for the most recent output) > evalf(%); Enter an equation/inequality As you may expect, use = for equations and <,>,<=,>= for less, greater, less or equal, greater or equal in inequalities. Here are some examples. An equation > x^3-2*x=-2*x^2+5*x-100; x 3 2 x = 2 x x 100 An inequality (with absolute value in it) > abs(x^3-2*x) < 4*x-2; x 3 2 x < 4 x 2 > abs(x+1)<=abs(2*x^2-3) + 4*x; x x x > 2*x-a <= 3*x^2-6; 2 x a 3 x 2 6 > rhs(x^2+1 = 2*x+2); lhs(x^2+1 = 2*x+2); 2 x + 2 x You can store an equation/inequality in a variable for later references. Use the assigment command := > eqn1 := sin(x)-x^2 = 5*x; INEQ1:= 3*x+2 <= 4*x +5; eqn1 := sin(x) x 2 = 5 x INEQ1 := 3 x x + 5 > rhs(ineq1); lhs(eqn1); 4 x + 5 sin(x) x 2 7 Graphics The following command generates a plot of a function y = x 2 2 x with x in the interval [-3,3]. > plot( x^2-2*x, x = -3..3); 4

5 We can also specify the y-range of the plot (compare with the above) > plot( x^2-2*x, x = -3..3, y=-2..5); We can also plot two or more functions in the same plot with different colors and styles > plot([sin(x), x-x^3/6], x=0..2, color=[red,blue], style=[point,line]); 5

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1 Maple Introduction. 1.1 Getting Started. 1.2 Maple Commands

1 Maple Introduction. 1.1 Getting Started. 1.2 Maple Commands 1 Maple Introduction 1.1 Getting Started The software package Maple is an example of a Computer Algebra System (CAS for short), meaning that it is capable of dealing with problems in symbolic form. This