For A Calculus Tutorial On Triple Integrals
Created by David Alderoty © 2012
To contact the author (David Alderoty) use this
e‑mail address: David@TechForText.com, or left click
on the link below for a website communication form.
This website provides an online calculation device, in the form of a tutorial, which is presented several paragraphs below after the introductory information and instructions. The tutorial was created primarily for individuals that have studied at least three or four terms of college-level calculus, and know the basic method of solving triple integrals, but need practice to avoid errors, and to increases speed and efficiency with these calculations.
About The Tutorial Software, on This Website
This tutorial is a software-based calculation device that checks your calculations for each problem, as soon as you enter the numbers you calculated into an input box that relates to the specific problem. The results calculated by the computer are displayed after you enter the numbers you calculated, for the problem in question. However, if you want the computer to display all the calculated results, before you enter your calculations, place an X in the green input box several paragraphs below.
If you are interested, you can obtain the original Excel version of the software by downloading a zipped folder, by clicking on the link presented below. The zipped folder contains a total of four versions for Excel 2003, and 2007-2010. Two of the Excel files, with the words Formula-Study, provide direct access to the formulas and code, used to create this software. (The Excel devices require Windows and Microsoft Excel.)
STEP-BY-STEP INSTRUCTIONS FOR THIS TUTORIAL
1) This software is a tutorial designed to help you practice solving triple Integrals. To use it, enter any numbers you choose, in the two white boxes (located several paragraphs below). For calculated results, left click on the background, or anywhere outside of an input box.
2) ENTERING NUMBERS: Whenever you enter or delete a number or letter, with any of the input boxes in this software, you must first left click on the input box with the mouse, and then immediately enter or delete the number or letter.
The software generates 10 math problems with the numbers you enter, in the two white input boxes, several paragraphs below. Thus, it is best to enter single digit numbers, to avoid difficult arithmetic. *If you enter more than two digit numbers, you might have calculated results that may exceed the limits of this software, and some of the mathematical expressions.
*NOTE: the software can actually Handle calculated results up to 20 digits, without any loss of functionality. When the above is exceeded, the calculation mechanisms cannot distinguish between a correct and incorrect calculation entered by the user. However, the calculated results performed by the computer are still accurate, and are expressed in scientific notation using the letter e, such as: 1.3440585709080606e+43 or 9.754645346787656e-85.
3) PRACTICE USING DIFFERENT NUMBERS: It is usually best to practice with this tutorial several times, using a different set of numbers, until you get a score of at least 80 or 90 percent. The software calculates the score automatically. Keep in mind, each time you enter a new set of numbers, a new set of problems are generated, but the problems remain similar, except for the changes in the values of B and A, such as in As a result of this feature, the tutorial is ideal for repeat practice.
4) HOW TO SOLVE THE 10 MATH PROBLEMS: To solve the 10 math problems generated by this software, it is usually necessary to use a scientific calculator, as well as pencil and paper. When you think you have the correct calculated result, enter the number in the white input box that corresponds to the specific problem you are solving. When this is done, the software checks your calculations. If your calculations are correct the software will display a message in green type. If your calculations are incorrect you will see an error message in red type. Regardless of whether your calculations are correct or not, as soon as you enter them, the software displays the results the computer calculated, (if they are not already displayed), as shown in the following example: 2564257500 = Computer
5) CORRECT AND INCORRECT CALCULATIONS: If your calculations are correct, scroll down until you see the next problem, and solve it. If your calculations are incorrect, you can try again and/or scroll down until you see two formulas that may help you learn how to solve the problem.
6) YOUR CALCULATED RESULTS FOR THIS TUTORIAL MUST BE CARRIED OUT TO THE INDICATED NUMBER OF DECIMAL PLACES: Your calculations must be carried out to the exact number of decimal places, indicated by the software. If the software indicates that you made an error, check to see if your error relates to the above. If it does, make the required adjustments in your calculation, and proceed to the next problem. (Incidentally, the user can change a number in a small input box, which will change the required number of decimal places for all the calculations.)
Additional Information From other Websites
And Internet Videos On Triple Integrals
There many good sources on the Internet that provide instruction on mathematics, and triple integrals. Videos are especially useful in this regard. Below, I compiled a short list of websites and videos that provide instruction related to triple integrals. Some of these sources go beyond what is presented in the tutorial. You may want to do your own Internet search for additional information with www.google.com. Especially useful are video searches with www.Video.Google.com
Words on website: Triple integral examples
Words on video: triple integrals intro
Words on video: Learn About Triple Integrals - Calculus 3
Words on video: Evaluating a Triple Integral
Words on video: Learn about Triple Integrals 1
Words on video: Triple Integrals 2
Words on video: Triple Integrals 3
Words on video: Triple integrals in Cylindrical and Spherical Coordinates.
Words on video: Evaluating a Triple Integral
Words on video: How to compute triple integrals
Words on video: triple integral setup
NOTE: The above Internet links are not connected with the author this website and THE TUTORIAL PRESENTED BELOW.