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mathematica[1] - Using Mathematica for Calculus(If you are...

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Using Mathematica for Calculus (If you are reading this document interactively within Mathematica, then we need to do some housekeeping to make it work right. We need to make sure that all the variables we will use start out with no prior values. Please excuse the interruption.) In[121]:= Remove @ a, b, c, d, e, f, g, h, x, y D Mathematica is a software system for doing mathematical calculations. It is the Mark McGwire of calculators, much more powerful than anything you can carry in your pocket. Mathematica will perform calculations: In[122]:= Sin @ 3.4 D Out[122]= - 0.255541 simplify algebraic expressions: In[123]:= Apart A 3 x - 4 þþþþþþþþþþþþþþþþ þþþþþþþþþþþþþþþþ þþþþ x 3 + 2 x 2 - x - 2 E Out[123]= - 1 þþþþþþþþþþþþþþþþ þþþþþþþþþ 6 H - 1 + x L + 7 þþþþþþþþþþþþþþþþ þþþþþþ 2 H 1 + x L - 10 þþþþþþþþþþþþþþþþ þþþþþþ 3 H 2 + x L graph functions: In[124]:= Plot @ Sin @ x 2 D , 8 x, - 1, 3 <D -1 1 2 3 -1 -0.5 0.5 1 Out[124]= oe Graphics oe integrate and differentiate: In[125]:= ¯ x 2 sin H 2 x L cos H 3 x L ˙ x Out[125]= 1 þþþþþþþþþþ 250 H - 250 Cos @ x D + 125 x 2 Cos @ x D + 2 Cos @ 5 x D - 25 x 2 Cos @ 5 x D - 250 x Sin @ x D + 10 x Sin @ 5 x DL and solve equations. In[126]:= FindRoot[Cos[x] == 2*x, {x, 1}] Out[126]= 8 x 0.450184 <
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Mathematica will do many other mathematical operations too, most of which you have not yet learned about. As the famous entertainer, Dr. Science, says: " Mathematica knows more than you do." But that is not really true. Although Mathematica knows a lot of functions, it cannot do word problems. It cannot prove theorems or build models. It cannot create equations; it can only solve them. The hard parts of mathematics still have to be done by people, but Mathematica will help you by taking over some of the routine. The document you are looking at, either on paper or on a screen, is a Mathematica notebook , a collection of text para- graphs, mathematical calculations, and graphs. The text paragraphs can include mathematical expressions, like this: d þþþþþþþ dt sin t = cos t Whenever you use Mathematica , you will create a Mathematica notebook. Notebooks can be saved and reloaded, printed, or passed around by email. Once you leave Mathematica , your notebook is just a file like a spreadsheet or word-processing file. You could do an entire homework assignment in a Mathematica notebook, print it, and turn it in. The purpose of this lesson is to teach you to use Mathematica as a calculator. You are not going to learn how to create text paragraphs. You are just going to learn to do calculations. How to Use This Worksheet Read the text while sitting before a computer running Mathematica, and do all of the "Try it Yourself" sections. The expected time to complete this worksheet is 1-2 hours. Your teacher may ask you to work on selected subsections.
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