MATH 696-720

Examples of Volume and Double Integrals

  1. 2D Riemann Sum


  2. 3D Riemann Sum


  3. Screen Capture


  4. Screen Capture Example 2


  5. Evaluating a Double Integral




TAMU ONLINE MATH COURSES

  • Math 409 - Advanced Calculus
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  • Math 696 - Communication and Technology in Mathematics
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email: jayneo@tamu.edu

MATH 696 Capstone Project

Using Double Integrals to Calculate the Volume of Solids

by Jayne Overgard

Texas A&M University

                 



The idea of this capstone project is to exhibit the totality of the information learned throughout this course. This web page uses html, fonts, style sheets, color, and overall design to welcome the reader. Within the web pages are various demonstrations using Maple, CamStudio video capture software, SnagIt screen capture software, Microsoft Word excerpts, Adobe pdf files, graphics, and animations. Some of the graphics were produced using Scientific Notebook and Maple. A special thank you to Texas A&M University's distance education program and Professor Allen.

The mathematical and technological portion is based on the use of double integrals to calculate the volume of solids. As a preface, I created a Maple tutorial on basic Riemann sums. This tutorial (Number1 below) incorporates Riemann graphics and one animation. Graphics and other animations are also shown in the "Graphics Corner" in the right column.

Next, we approximate the volume of solids using the Riemann sums of prisms; then we use double integrals. The new Maple aspects I learned about included RiemannSum, leftbox, rightbox, middlebox, Int(Int), int(int), and POLYGONS to create the 3D rendering of the solid.

Technologically, different links on this page will lead to different mediums used to convey the information in an interesting and intriguing manner. Number 1 below is a Maple tutorial file, then there follows a page created using Scientific Notebook (then exported to html), then another Maple tutorial containing the main mathematical topic (Number 3, Approximating and Calculating the Volume of a Solid). At the end of this main topic you will find an example of a screen capture taken from Scientific Notebook. Elsewhere in this site are examples of Microsoft word doc files, an Adobe pdf file, as well as links to graphics, animations, screen captures, and a screen cam demo (Number 6).

VOLUME OF SOLID REGIONS


GRAPHICS CORNER