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Constructing Difference Quotients and Derivatives.
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Summations and Integration.
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Online Plotting Tools.
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Producing Your Own Plots Using gnuplot.
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Resources Online.
Help with Integration and Differentiation
This document is intended to assist you exercises in differential and integral calculus. It provides an interface to do plotting, symbolic manipulation, and the computation of difference quotients and left and right hand sums. This document has been modified 01/27/97, hopefully to provide greater ease of use.
For many of these applications, you will have to make sure that your browser is equipped to handle gif or postscript files. If it is not, you will have to configure it so that it can process these files.
Contents
Constructing Difference Quotients and Derivatives
To evaluate the difference quotient associated with a
derivative numerically
use the interface in
Differences
To compute the derivative of a function symbolically use the interface in Derivatives-gif , Derivatives-gif11 , and Derivatives-ps where the subscript designates the type of output.
The giff11 format with xv is more flexible and allows processing of the file, however the postscript file has higher local resolution and is quicker to produce.
Summations and Integration
To compute the left and right hand sums associated with an integral, you can use the interface in Summations.
To compute the integral of a function symbolically use the links provided in Integration.
Online Plotting Tools
To plot a function, you can use the interfaces provided in plot-gif file, plot-gif11 file or, plot-postscript file.
The gif11 format with xv is more flexible and allows processing of the plot, however the postscript file has higher local resolution and is quicker to produce.
Plotting Functions Using gnuplot
To plot function such as the left and right hand sums, you can use gnuplot to plot the files on ocean. To execute gnuplot, type
in a terminal on your ocean account. The utility gnuplot will work on any machine which is running Linux. This includes ocean, pax and sushi. It does not include whale. When you get the prompt
type in the command to execute a plot. To plot a function such as cos(x) on the interval from 0 to pi, just type in
If you want to plot upper and lower sums such as produced by the software package sum.f, a file fig.com has been provided for you. To use this, type
where the file fig.com is in your local filespace on ocean where you are running gnuplot. To obtain a copy of the file fig.com , click on this. This will plot the value of the function taken over the left hand and right hand values using a step function.
Online Resources
If you are feeling ambitious, you might want to examine the large number of teaching resources on the net. These include some such as Visual Calculus which may provide addition information of the topics being studied.
