MATH 152 - Integral calculus

Apps and toys for MATH 152

Many concepts in mathematics can be illustrated by interactive computer applications and animations. In other cases, it is worthwhile to see how computers can help you with mathematical computations. Whenever appropriate I show such tools in class and I keep links to them here, so that you can refer to them later yourself.

Most tools here use either the computer algebra system Sage (via their sagecell tool for embedding in web pages) or Geogebra, which naturally embeds in webpages.

List up to now:

• Taylor: Demonstration how well Taylor polynomials approximate sin(x).
• Riemann: Approximate integrals using Riemann sums.
• Position and velocity of a car: Illustration of the Fundamental Theorem of Calculus.
• Area of a region bounded by a curve in polar coordinates
• Some animations of solids of revolution
• Animation of washer method From: http://www.mathdemos.org
• Animation of shell method From: http://www.mathdemos.org
• Graphical illustration of numerical integration methods
• Recipes for numerical integration methods
• Trochoid:Example of a parametric curve.
• Vector field plotter: plots a vector field and solution curves for you.
• Recursive sequence: Use a computer to compute the first terms of a complicated sequence--with as many digits as you like!
• Power series approximations to mathematical constants: use the power series for the exponential function and arctan to compute good approximations the e and pi.

Clock: Useful for exams