Matrix paletteA collection of templates for entering matrices in Maple. Vector paletteA collection of buttons for entering vectors in Maple. Toview help pages, at the prompt, enter a question mark " followed by thename of the command or subject on which you want help. Do not enter anyspaces.
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For example, to refer to the help page on natural logarithms, enter"OQ. For information on different ways to get help, see The Help System onpage Using the keyboard is the most direct method, but the palettes enable you toenter a command without knowing its syntax. There are two types of input display. Use Maple Notation to display input as Maple syntax.
Maple Notation is the default. Use Standard Math Notationto display input in typeset notation as it appears in a textbook. To enter the integral in Standard Math Notation by using the palettes Display the palettes, if necessary. The Symbol, Expression, Matrix, and Vectorpalettes are displayed. Move the palettes to the side of the worksheet, ifnecessary. If required, change the input to Standard Math Notation. If there is aquestion mark? At the prompt, right-click. The context-sensitive menu isdisplayed. Choose Standard Math. On the Expression palette, click.
The integral symbol appears, andthe question mark placeholder is selected. The function sin appears, withanother placeholder. Enter [ on the keyboard , and press TAB to go to the next placeholder. Repeat step 5. Enter zero , and press TAB. On the Symbol palette, click. It is in the bottom row. Your worksheet should resemble that of Figure 1-B on page 6. To enter the integral in Maple Notation by using the palettes Note: Maple appends a semicolon to the end of the command. This signifies theend of the statement. Figure 1-C Integral input in Maple NotationNow that you know the correct notation, you could enter the expression at theprompt.
For the rest of this guide, it is assumed that you are entering expressions in Maple Notation. Thediscussion of the problem and its solution introduces you to key features of the Maple program. Do not worry too much about the mathematics. The purposeof this problem is to show you Maple ; the mathematics is secondary.
Note: When entering Maple commands, please keep in mind that they are casesensitive. She wants to take thesteepest path down, which she can find by performing the calculationsoutlined in this chapter. Start by opening a new worksheet for this problem. Apackage is a group of routines related to a particular area of mathematics. Plotting the hillBefore solving the problem, it would be helpful to get an idea of what the hilllooks like and an idea of what the answer should be.
To plot the expression Right-click the output of the expression for Macintosh, option-click. Thecontext-sensitive menu is displayed. Choose Plots, 3-D Plot, then x,y. Maple inserts the plot into theworksheet. Note: The content of context-sensitive menus varies depending on the cursorlocation or selected expression. To modify the axes ranges Right-click the plot for Macintosh, option-click , choose Axes, thenRanges. In the Axis Range dialog box:a.
Under X Axis, click the button beside the top range box. Click OK. The visualization tools in Maple enable you to see the surface from more thanone angle. To rotate the surface Click the plot to select it. Place the pointer on the plot, but not directly on the surface of the hill. Drag the plot in any direction. The surface rotates. Figure 2-A Plot of the hillWhile you could look at the surface and guess what the highest point is, youcan obtain a more precise answer by using calculus. Formore information, refer to " The ditto operators. If the step size is too large, thepath may leave the surface of the hill.
If the step size is too small, you deriveno benefit from the increased number of calculations. Use atimestep of 0. It executes the commands asthe value of a numeric variable, called an index, varies from its specifiedinitial value to its specified final value. The value of the index is incrementedafter each execution of the commands in the body of the loop. The iterationstops when the value of the index is greater than the specified final value.
Forinformation on other programming structures in Maple , refer to the Maple Introductory Programming Guide. The next commands comprise the body of the IRU loop. Remember to end theline with a colon to suppress the output. At the end of each iteration, the value of Lis increased by 1. That is, for the first iteration, the value of L is its initialvalue 1, for the second 2, and so on. For the last iteration the value of L is Maple exits at the end of the 24th iteration once L is set to 25 since 25 isoutside of the bounds of the loop.
In addition,you can plot more than one element on a single set of axes. You can then format the text by using different predefinedstyles, or you can define your own styles. In addition, you can insert formattedmathematics in your text. Adding textAdd a title to your worksheet, and add some text to describe the problem thatyou are solving. How many leaders do we need to bring to camp? As leaders, you may need to adjust this to accommodate the needs of your youth.
You must still have two deep leadership.
What time is check-in? All campers: am am on Mondays. What about meals? Troops many chose to bring their own food as well and can purchase ice from the Trading Post. Is water available at camp? Do I need to bring anything else to camp? Tent, sleeping gear A jacket and rain gear a Scout is prepared. If fires are allowed - firewood. Campers are welcome to pick up dead wood around the camp to use for firewood and use a camp saw to cut into small pieces.
Encourage your youth and leaders to be in uniform. Cooking supplies, including camp stoves, fire barrels. Other helpful items to have at camp are sunscreen, bug spray, hats for everyone, water bottles, sunglasses, a day pack to carry your items, and Scout Handbook.
Will the Trading Post be open? If so, what type of things will they have there? The trading post will be open each day during your stay at camp. We stock merit badge supplies, pocket knives, crafts, flashlights, camp shirts, camping supplies, souvenirs, various snacks, and drinks. Contact Information Questions? Contact us at help utahscouts. Scouting Scouting Ambassadors.
Stage 4: Testing the Solution How much would we have to pay in volume for a sleeker bottle? Maple's flexible graphics are well suited for sensitivity analysis. In an invisible document block, I have written a line Maple procedure called plotVolumeSensitivity that plots the optimized box volume vs. This procedure solves the NLP repeatedly for 20 different values of s and plots each solution as a blue dot.
This took Maple about 3 seconds on my 5-year-old laptop. This plot tells us that the minimum box volume and thus, our shipping costs grows very fast with the sleekness of the bottle. We will advise our client to use discretion when setting the "sleekness" requirement. Of course, there are many other tests we can and should do. Because a Maple 10 document is both interactive and easily formatted for presentation, you can use it as the medium of presentation, instead of, say, PowerPoint or LaTex.
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If you're a real Maple jockey, you can even create push-button applications for your clients to run, and embed them the applications, I mean directly into the Maple document. In the example in Figure 10, our client can simulate Stage 1 by setting a, b, c and h and clicking Draw Bottle to view the corresponding bottle. Clicking Optimize Parameters condenses Stage 3 for the client by solving the NLP on the problem data and then setting the slider bars to their optimal levels.
Draw Bottle again draws the optimal bottle. For creating such an application, there are friendly drag-and-drop palettes for placing the buttons, sliders and plot windows where you want them. But you have to know a fair amount of Maple syntax to make the buttons call the right routines on the right data when clicked. You could also place this same functionality within an applet-like application eponymously called a Maplet that the client can launch by double-clicking an icon without having to open your Maple document.
How steep is the road to learning Maple? Novices can cruise through basic derivations and plots using just the palettes three of which are shown in Figure 11 , the right-click context menus and the very handy interactive assistants, which besides the optimization assistant include dialogs for analyzing ODEs, importing and analyzing data, doing unit conversions and drawing graphics and animations. But to do more in-depth analysis in Maple, including building those nifty embedded applications, you'll have to invest a day or three learning Maple's command syntax.
This is time well spent and is no harder than learning to program Excel macros. The online help is excellent, though a beginner can find it almost too helpful: for instance, the main Help menu has 10 items, two of which are submenus that contain a further 23 items, some of which are subsubmenus. Maple 10's user interface, despite a few kinks, has made a quantum leap in this version. Ease-of-use and presentability have improved dramatically and have surpassed competitors MathCad and Mathematica along many dimensions.
This chrome exterior can weigh down performance, though. For instance, Maple 10 often took 10 or more seconds to load the procedures I wrote for this review, a task Maple 9.
The tools in Maple 10's enhanced Optimization package are powerful and user-friendly, but more of them are needed before Maple can claim to be a one-stop-shop for optimization. Missing perhaps to come in later versions are heuristics for discrete problems such as min-set-cover and TSP, and solvers for network flow problems such as min-cost flow. Also missing are quick "helping-hand" routines for examining slack variables, constructing the dual LP from the primal LP which Maple could easily do, but you'd have to write your own procedure for it and solving an LP with dual-simplex or interior-point methods.
For example, without too much effort, I wrote a Maple package for drawing weighted digraphs when I taught at Passau. One exciting possibility for extending Maple for the O. In addition to the standard heap of statistics routines, Statistics also has functionality for symbolically manipulating random variables. For instance:. ScientificErrorAnalysis to the sublime e.
Kinks and all, Maple 10 is a good investment for anyone in O. It is the only software that brings symbolics, optimization, data analysis, symbolic probability, interactive 3-D graphics, code generation, embedded application building and textbook-quality documentation, as well as the point-and-click assistants that support all of the above, all under one roof. Oh, to be a grad student again! Upgrade, volume, academic and student discounts available.
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