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EXAMPLE 1 Add 2 and 3.
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Notice that the kernel has assigned In[1] to the input expression and Out[1] to the output. This enables you to keep track of the order in which the kernel evaluates instructions. These labels are important because the order of evaluation does not always correspond to the physical position of the instruction within the notebook. In this book, however, we shall not include In and Out labels in our examples. In working out the examples and problems in this book, you may find that your answers do not agree with the answers given in the text. This may occur if you have defined a symbol to have a specific value. For example, if x has been defined as 3, all occurrences of x will be replaced by 3. You should clear the symbol (see Section 1.5) and try the problem again. All examples and problems assume that symbols have been cleared prior to execution. You can work on several different notebooks in a single Mathematica session. However, if you are using only one kernel, changes to symbols in one notebook will affect identical symbols in all notebooks. There are times when you may wish to evaluate only part of an expression. To do this, select the portion of the expression you wish to evaluate. Then press [CTRL] + [SHIFT] + [ENTER] on a PC or [COMMAND] + [RETURN] on a Mac.
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EXAMPLE 2 Suppose we wish only to perform the multiplication in the expression 2 3 + 5.
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First select 2 * 3: 2 *3 + 5 Then press [CTRL] + [SHIFT] + [ENTER] (PC) or [COMMAND] + [RETURN] (Mac). 6+5 A semicolon (;) at the end of a Mathematica command will suppress output. This is useful in long sequences of calculations when only the final answer is important.
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EXAMPLE 3 Suppose we wish to define a = 1, b = 2, c = 3 and then display their sum. Here are two ways to write
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this problem. a=1 b=2 c=3 a+b+c 1 2 3 6 a = 1; b = 2; c = 3; a+b+c 6
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Occasionally you may introduce an instruction that takes an excessively long time to execute, or you may inadvertently create an infinite loop. To abort a calculation, go to Evaluation Abort Evaluation. Alternatively, you may press [ALT] + [ . ] to abort ([COMMAND] + [ . ] on the Macintosh). On the rare occasion when this does not work, you will have to terminate the kernel by going to Evaluation Quit Kernel Local. However, by doing so, you will lose all your defined symbols and values. Your Mathematica notebook will not be lost, however, so they can easily be restored. As with all computer software, there are times when Mathematica will crash completely. The only remedy is to close Mathematica and reload it. On rare occasions, you may have to reboot your computer. In either event, your notebook changes will be lost. It is therefore extremely important to back up your notebook often! Finally, there may be times when you wish to include comments within your Mathematica commands. Anything written within (* and *)is ignored by the Mathematica kernel.
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EXAMPLE 4
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12 + (* these words will be ignored by the kernel *) 3 15
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Getting Acquainted
SOLVED PROBLEMS
1.1 Multiply 12 by 17 and then add 9.
SOLUTION
12 * 17 + 9 213
1.2 Multiply the 12 by 17 in Problem 1.1, but do not add the 9.
SOLUTION
Select 12 * 17 with the mouse.
* 17 + 9
Press [CTRL] + [SHIFT] + [ENTER] 204 + 9
[COMMAND] + [RETURN] on a Mac.
1.3 The following program is an infinite loop. Execute it and then abort the evaluation. x = 1; While[x > 0, x = x + 1]
SOLUTION
x = 1; While[x > 0, x = x + 1] [ALT] + . $Aborted
1.4 Multiply 17.2 by 16.3 and then add 4.7.
SOLUTION
17.2 * 16.3 + 4.7 285.06
1.5 Multiply 17.2 by the sum of 16.3 and 4.7.
SOLUTION
17.2 * (16.3 + 4.7) 361.2
1.6 Compute the sum of 2 x + 3, 5 x + 9, and 4 x + 2.
SOLUTION
(2 x + 3) + (5 x + 9) + (4 x + 2) 14 + 11 x
Mathematica Quirks
Mathematica is case sensitive. For example, Integrate and integrate are different. All Mathematica-defined symbols, commands and functions begin with a capital letter. Some symbols, such as FindRoot, use more than one capital letter. To avoid conflicts, it is a good idea for all user-defined symbols to begin with a lowercase letter. Different brackets are used for different purposes.
Square brackets are used for function arguments: Sin[x] not Sin(x).
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