Hands-On Math

Last Revision March, 2011

Last Revision March, 2011

The topics of this chapter can be accessed by clicking their names.

Topic Name | An Image from the Topic | Brief Description |
---|---|---|

Variable Step Size | Illustrates the efficacy of employing variable step size | |

Close-Bounds to the Ratio of the Circumference of a Circle to its Diameter and to the Ratio of a Circle's Area to the Square of its Radius | Two methods are shown and compared for bounding the value of π, the motivation being that up to this point only a lower bound had been established. | |

Design a Simple Eave Trough using Optimization | Introduces the use of Polar Coordinates in comparison with Rectangular Coordinates in the context of a simple optimization | |

Approximation with Orthogonal Functions using a Macro | Carries approximation concepts a step further by employing sinusoids in approximation. Introduces the use of a Spread Sheet Macro as an effective calculation method | |

Sensitivity in Approximation - Steepest Descent | Steepest Descent, a valuable method of optimization, is described and illustrated. An example macro is provided | |

Exploring a Limit with a Spreadsheet - A Use of e | A value for the constant e is derived. A use of e is then shown in the context of the comparison of the numerical solution of a simple differential equation with its analytic solution. | |

Irregular Repayments toward Loans - Irregular Returns from Investment - Continuous Compounding - A Use of e | Returns from Investments and repayments of loans often occur at irregularly spaced intervals and in non-uniform amounts. |