Maple Worksheets: Getting Started Tips for getting started: Maple commands and variables are case sensitive and order of command execution is important! Commands can be executed individually by pressing "Enter" at each command. Organize executable commands by placing them after Maple prompts ("[>"). Use Shift+Enter to create a new line at the same prompt without executing the command. Use the "!!!" button to execute all commands in your worksheet in order, "!" will execute only selected commands. You can insert plain text that is not executed as a command, and you can format this text as you would with a word processor. You can press Esc or Ctrl+Space to pull up a list of symbols and commands that complete what you just typed.

Clearing Variables At the start of every worksheet, it's a good idea to clear all variables using "restart," otherwise you may get unexpected results! LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRic= Loading Additional Packages You may also want to use some additional Maple packages, load these using "with." Some tools for creating various plots LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRJnBsb3RzRidGL0YyL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIjtGJ0Y9LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjI3Nzc3NzhlbUYn Packages useful for Linear Algebra (colon hides output) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRLkxpbmVhckFsZ2VicmFGJ0YvRjIvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiOkYnRj0vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkUvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVA== Packages for working with Differential Equations LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRKERFVG9vbHNGJ0YvRjIvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiOkYnRj0vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkUvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVA== JSFH

Comments You can create a comment that will not be executed by inserting plain text between your Maple prompts (as I have been doing.) You can also insert a comment using "#" 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 Variables Values are assigned to variables with ":=" not with "=", which is reserved for equations. Notice how Maple handles LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= in the following: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJyZzZG90O0YnRi8vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRy1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRictRjM2LVEiO0YnRi9GNi9GOkZQRjtGPUY/RkFGQ0ZFL0ZJUSwwLjI3Nzc3NzhlbUYn 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJyZzZG90O0YnRi8vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRy1JI21pR0YkNiVRInlGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRictRjM2LVEiO0YnRi9GNi9GOkZQRjtGPUY/RkFGQ0ZFL0ZJUSwwLjI3Nzc3NzhlbUYn This can be useful if we want to assign an equation to a variable name 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJyZzZG90O0YnRi8vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRy1JI21pR0YkNiVRInpGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRictRjM2LVEiO0YnRi9GNi9GOkZQRjtGPUY/RkFGQ0ZFL0ZJUSwwLjI3Nzc3NzhlbUYn You need to be very careful when defining variables. If you are having problems executing commands in your worksheet, check your variable assignments! Terminating Statements Semicolons and colons are used as statement separators in Maple, use these to terminate your statements. Use a semicolon at the end of each statement to display the output once the command is executed. A colon at the end of the statement will execute the command, but will not display the output. 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRic=

Maple has many procedures defined to do various tasks. Procedures will require that you specify certain parameters (some may be optional) which are explained in Maple help, usually along with some examples. The 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 procedure takes an equation (or equations) and solves for the specified variable(s). This can also be used to solve inequalities and systems of equations. 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 Functions Mathematical functions are treated as a special type of procedure in Maple, using arrow notation ("->"). For instance, to define 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 as a function: 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 Now we can evaluate 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at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JFEiMkYnRjRGNEY0RjQ=: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUkjbW5HRiQ2JFEiMUYnL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUY7NiRRIjJGJ0Y+Rj4tRkE2LVEiO0YnRj5GREZHRklGS0ZNRk9GUUZTL0ZXUSwwLjI3Nzc3NzhlbUYn Procedures Procedures can extend to more than just mathematical functions, the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEmc29sdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYjUSFGJy9GM1Enbm9ybWFsRidGPUY9 procedure used above can take an expression or list as a parameter. Defining our function above as a procedure is slightly more complicated, since we need to specify the input type: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUkjbW5HRiQ2JFEiMUYnL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUY7NiRRIjJGJ0Y+Rj4tRkE2LVEiO0YnRj5GREZHRklGS0ZNRk9GUUZTL0ZXUSwwLjI3Nzc3NzhlbUYn

JSFH

Palettes Maple supports many operators, symbols and expressions. The most common of these are available in palettes, so that you can select them without knowing the correct syntax for the procedure and read them in a more familiar format. The following statements use the Expression palette and the equivalent procedure: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkmbXNxcnRHRiQ2Iy1GIzYjLUkjbW5HRiQ2JFEiNEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIjtGJ0Y0LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRk0vJSZkZXB0aEdGVi8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GODYtUSJ+RidGNEY7L0Y/Rj1GQUZDRkVGR0ZJRksvRk9GTS1JI21pR0YkNiVRJXNxcnRGJy8lJ2l0YWxpY0dGPUY0LUkobWZlbmNlZEdGJDYkRi5GNEY3 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUklbXN1YkdGJDYlLUkjbW9HRiQ2LVEkbG9nRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZ1bnNldEYnLyUqc2VwYXJhdG9yR0Y3LyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkYtSSNtbkdGJDYkUSMxMEYnRjIvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUZKNiRRJDEwMEYnRjJGMi1GLzYtUSI7RidGMi9GNlEmZmFsc2VGJy9GOVEldHJ1ZUYnL0Y7RmZuL0Y9RmZuL0Y/RmZuL0ZBRmZuL0ZDRmZuRkQvRkhRLDAuMjc3Nzc3OGVtRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGRi8lJmRlcHRoR0Zlby8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GLzYtUSJ+RidGMkZlbi9GOUZmbkZpbkZqbkZbb0Zcb0Zdb0ZERkctSSNtaUdGJDYlRjEvJSdpdGFsaWNHRmZuRjItRlE2Ji1GIzYjRklGMi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZQRlg= 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 Right Click Right clicking on an expression will give you a context menu to perform operations without knowing the correct procedure. Notice that some of the following operations result in complex procedures! Right clicking on the following expression allows us to evaluate for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjJGJ0Y5Rjk=: 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 or solve for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=: 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JSFH or differentiate implicitly with respect to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=: 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 or plot: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEqc21hcnRwbG90RicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNictRiM2Ji1GLDYmUSJhRidGL0YyRjUtSSNtb0dGJDYuUSIsRidGMi9GNlEnbm9ybWFsRicvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GQTYuUSJ+RidGMkZERkYvRklGNEZKRkxGTkZQRlJGVC9GWEZWLUYsNiZRImJGJ0YvRjJGNUYyRkQvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRictRjk2JS1GIzYxRlpGPS1GQTYuUSIrRidGMkZERkZGZ25GSkZMRk5GUEZSL0ZVUSwwLjIyMjIyMjJlbUYnL0ZYRmpvLUkjbW5HRiQ2JVEiMkYnRjJGRC1GQTYuUSIqRidGMkZERkZGZ25GSkZMRk5GUEZSL0ZVUSwwLjE2NjY2NjdlbUYnL0ZYRmRwRmluRmZvLUZdcDYlUSIzRidGMkZERlotRkE2LlEiPUYnRjJGREZGRmduRkpGTEZORlBGUi9GVVEsMC4yNzc3Nzc4ZW1GJy9GWEZdcUZaRmluLUZBNi5RIl5GJ0YyRkRGRkZnbkZKRkxGTkZQRlIvRlVRLDAuMTExMTExMWVtRicvRlhGY3FGXHBGWkYyRkQ=

More Examples From here on, I will assume some familiarity with calculus and linear algebra topics. If something looks unfamiliar, try searching for it in help!

We'll work with the following functions for these problems: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZALUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GUy1GLDYlUSJ4RidGL0YyLUY2Ni1RKCZzcmFycjtGJ0Y5RjtGPkZARkJGREZGRkhGUkZULUkjbW5HRiQ2JFEiNEYnRjlGTy1JJW1zdXBHRiQ2JUZVLUYjNiMtRmZuNiRRIjNGJ0Y5LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GaG8tRmZuNiRRIjVGJ0Y5Rk8tRmpuNiVGVS1GIzYjLUZmbjYkUSIyRidGOUZhby1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIRmdvRmlvRlUtRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSEZnb0Zpby1GZm42JFEiNkYnRjktRjY2LVEiO0YnRjlGOy9GP0YxRkBGQkZERkZGSEZSRk0tSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGUy8lJmRlcHRoR0ZmcS8lKmxpbmVicmVha0dRKG5ld2xpbmVGJ0ZPLUYsNiVRImdGJ0YvRjJGNUZPLUkobWZlbmNlZEdGJDYkLUYjNiVGVS1GNjYtUSIsRidGOUY7RmBxRkBGQkZERkZGSEZSL0ZOUSwwLjMzMzMzMzNlbUYnLUYsNiVRInlGJ0YvRjJGOUZYRlUtRjY2LVEnJnNkb3Q7RidGOUY7Rj5GQEZCRkRGRkZIRlJGVC1Gam42JS1GNjYtUS8mRXhwb25lbnRpYWxFO0YnRjlGO0Y+RkBGQkZERkZGSEZSL0ZOUSwwLjExMTExMTFlbUYnLUYjNiNGW3NGYW9GZ3AtSSZtZnJhY0dGJDYoLUZmbjYkUSIxRidGOUZocy8lLmxpbmV0aGlja25lc3NHRl90LyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmR0LyUpYmV2ZWxsZWRHRj1GXXE= Limits To evaluate limits we can use the expression palette: 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 or we can use the equivalent command limit(function, point, direction): 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 Differentiation Maple has several procedures for differentiation, the expression palette contains some familiar notation: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkmbWZyYWNHRiQ2KC1GIzYjLUklbXN1cEdGJDYlLUkjbW9HRiQ2LVEwJkRpZmZlcmVudGlhbEQ7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZ1bnNldEYnLyUqc2VwYXJhdG9yR0Y8LyUpc3RyZXRjaHlHRjwvJSpzeW1tZXRyaWNHRjwvJShsYXJnZW9wR0Y8LyUubW92YWJsZWxpbWl0c0dGPC8lJ2FjY2VudEdGPC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkstRiM2Iy1JI21uR0YkNiRRIjJGJ0Y3LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GIzYlRjMtRjQ2LVEifkYnRjcvRjtRJmZhbHNlRicvRj5GZ24vRkBGZ24vRkJGZ24vRkRGZ24vRkZGZ24vRkhGZ25GSUZMLUYxNiUtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjhRJ2l0YWxpY0YnRk5GVC8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXnAvJSliZXZlbGxlZEdGZ25GWS1GYW82JVEiZkYnRmRvRmdvLUkobWZlbmNlZEdGJDYkLUYjNiNGYG9GNy1GNDYtUSI7RidGN0Zmbi9GPkZmb0ZpbkZqbkZbb0Zcb0Zdb0ZJL0ZNUSwwLjI3Nzc3NzhlbUYn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkmbWZyYWNHRiQ2KC1JI21vR0YkNi1RKyZQYXJ0aWFsRDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJnVuc2V0RicvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRi1GIzYlLUYvNi1GMUYyL0Y2USZmYWxzZUYnL0Y5Rk4vRjtGTi9GPUZOL0Y/Rk4vRkFGTi9GQ0ZORkRGRy1GLzYtUSJ+RidGMkZNRk9GUEZRRlJGU0ZURkRGRy1JI21pR0YkNiVRInlGJy8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRicvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmBvLyUpYmV2ZWxsZWRHRk5GVS1GWTYlUSJnRidGZm5GaW4tSShtZmVuY2VkR0YkNiQtRiM2JS1GWTYlUSJ4RidGZm5GaW4tRi82LVEiLEYnRjJGTS9GOUZobkZQRlFGUkZTRlRGRC9GSFEsMC4zMzMzMzMzZW1GJ0ZYRjItRi82LVEiO0YnRjJGTUZjcEZQRlFGUkZTRlRGRC9GSFEsMC4yNzc3Nzc4ZW1GJw== These are equivalent to the diff(expression, variables) command: 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 Another procedure that can be used is the differential operator D[argument indices](function)(evaulation point). This is slightly different from the diff() operator, as it can evaluate derivatives at a point, but cannot handle expressions that are not functions: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiREYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSJmRicvRjBRJXRydWVGJy9GM1EnaXRhbGljRidGMi1GNjYkLUYjNiMtRiw2JVEieEYnRj1GP0YyLUkjbW9HRiQ2LVEiO0YnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJw== 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiREYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSJmRicvRjBRJXRydWVGJy9GM1EnaXRhbGljRidGMi1GNjYkLUYjNiMtSSNtbkdGJDYkUSIwRidGMkYyLUkjbW9HRiQ2LVEiO0YnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJw== 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 Integration Integration is also easily accomplished using the expression palette: 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 Of course there is an equivalent command, int(expression, variables): 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 Additional Topics Maple also has commands for many other specific calculus topics, here are a few that might be useful (look up syntax in the help menu!): taylor outputs a Taylor series expansion dsolve is a solver for ordinary differential equations inttrans[laplace] performs a Laplace transform BesselI, BesselJ, BesselK and BesselY can be used to call the various Bessel functions LegendreP and LegendreQ can be used to call the Legendre functions

JSFH

Remember to load the LinearAlgebra package! Notice all of the different commands this will allow us to use, many of which can be very tedious to perform by hand for large matrices: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRic= QyQtSSV3aXRoRzYiNiNJLkxpbmVhckFsZ2VicmFHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiUiIiI= Matrices We won't get very far before we need to input a matrix of some sort. We can use the Matrix() command to generate some matrices quickly, but it is often simpler to use the Matrix palette. Double click on a large matrix to see and edit its entries: QyQ+SSJBRzYiLUknTWF0cml4R0YlNiUiIiNGKTckNyQiIiJGKTckRikiIiUhIiI= QyQ+SSJCRzYiLUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMvSSQlaWRHRiUiKi8pKj5fIiEiIg== QyQ+SSNDMUc2Ii1JJ01hdHJpeEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjL0kkJWlkR0YlIipvKSo+XyIhIiI= QyQ+SSNDMkc2Ii1JLVJhbmRvbU1hdHJpeEdGJTYlIiQrIi9JKmdlbmVyYXRvckdGJTsiIiEiIiovSS5vdXRwdXRvcHRpb25zR0YlNyMvSSZzaGFwZUdGJUkqaGVybWl0aWFuR0YlIiIi Vectors Vectors can be defined using angled brackets (< >): Qyg+SSN2MUc2Ii1JJDwsPkdGJTYlIiIiISIiRilGKT5JI3YyR0YlLUYnNiVGKUYpRilGKT5JI3YzR0YlLUYnNiUiIiMiIiFGKUYp Matrix Arithmetic Matrices can be easily added and subtracted, but there are two kinds of multiplication. We can multiply a matrix by a scalar using *, the product of two matrices is not commutative and uses a period: QyQsJkkiQUc2IiIiIkkiQkdGJUYmRiY= QyQsJkkiQUc2IiIiIkkiQkdGJSEiIkYm QyQsJEkiQUc2IiIiJiIiIg== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RJyZzZG90O0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZMLUYsNiVRIkJGJ0YvRjItRjY2LVEiO0YnRjlGOy9GP0YxRkBGQkZERkZGSEZKL0ZOUSwwLjI3Nzc3NzhlbUYn QyQtSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0c2JEYmSShfc3lzbGliR0YpNiRJIkFHRilJIkJHRikiIiI= QyQtSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0c2JEYmSShfc3lzbGliR0YpNiRJIkJHRilJIkFHRikiIiI= Useful Functions We can use commands to manipulate matrices quickly (see the output of with(LinearAlgebra) above). Here are a few examples: QyQtSSxEZXRlcm1pbmFudEc2IjYjSSJBR0YlIiIi QyQtSSxFaWdlbnZhbHVlc0c2IjYjSSJBR0YlIiIi QyQtSS1FaWdlbnZlY3RvcnNHNiI2I0kiQUdGJSIiIg== QyQtSTBMVURlY29tcG9zaXRpb25HNiI2I0kiQUdGJSIiIg== QyQtSTBRUkRlY29tcG9zaXRpb25HNiI2I0kiQUdGJSIiIg== QyQtSSxHcmFtU2NobWlkdEc2IjYjPCVJI3YxR0YlSSN2MkdGJUkjdjNHRiUiIiI= QyQtSSxHcmFtU2NobWlkdEc2IjYkPCVJI3YxR0YlSSN2MkdGJUkjdjNHRiVJK25vcm1hbGl6ZWRHRiUiIiI=

51¸£ÀûÉç Mathematics Department, Allison Chapin 2010 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=