Continuous Time, Discrete State Space Markov Chains (UMAP)
This module develops a model for the number of components operating in a multicomponent device. Using the number of b...
The Unit of Analysis and the Independence of Observations (UMAP)
This module addresses two problems that have received insufficient attention in the statistical literature, namely, t...
Spacecraft Attitude, Rotations and Quaternions (UMAP)
This module applies linear algebra to space flight and astrophysics. The rotational orientation of a spacecraft is ca...
The Pace of Life: An Introduction to Empirical Model-Fitting (UMAP)
In this moduel data collected by two psychologists and published in a professional science journal are used to introd...
Graphical Analysis of Some Difference Equations in Biology (UMAP)
This module shows how the behavior of the solutions to certain equations can be predicted by graphical techniques. St...
Differential Equations and Root Cellars (UMAP)
This module derives the one-dimensional heat equation, proves the uniqueness of its solutions, and finds the solution...
The t-Test for Independent Samples (UMAP)
In using this module students will gain: 1) the ability to carry out the t-test of the statistical significance of th...
One-Sided Operators in Rings (UMAP)
This module provides concrete examples (n x n matrices with n greater than or equal to 4) of one-sided identities and...
Passive Solar Heating (UMAP)
A unit that relates linear algebra through the topic of passive solar heating. A problem in solar heating is formulat...
Some Card Tricks: Algebra in Disguise (UMAP)
Many card tricks are counting problems solved by elementary algebra. Each card trick (world problem) is transformed t...
Finding the Shortest Distance on the Earth's Surface from Here to Timbuktu (UMAP)
A unit that involves pre-calculus in finding the shortest distance on the Earth's surface from here to Timbuktu. This...
Keeping Dimensions Straight (UMAP)
With this unit, the student will be able to: 1) distinguish between dimensions and units; 2) to algebraically manipul...
Layout Design and Sheet Metal Fabrication (UMAP)
A unit that involves calculus with layout design and sheet metal fabrication. In sheet metal fabrication a pattern is...
A Mathematical Model of a Universal Joint (UMAP)
In this module a universal joint is modeled to study its output pulsations. The angle of coupling that will alleviate...
Zeller's Congruence and Modular Systems (UMAP)
Section 1 introduces Zeller's congruence with motivational problems. Section 2 deals with the greatest integer functi...
The Cost Accounting Problem (UMAP)
This module that applies linear algebra to accounting. Several different techniques (including those used by accounta...
3 x 3 Rotation Matrices in Air Traffic Control (UMAP)
This module shows how orthogonal matrices are used to translate into local coordinates the airplane coordinate sent b...
Tiltup Panels: Locate the Pulleys (UMAP)
This module discusses the location of the pulleys for a cable rigging currently in use. The key differenetial equatio...
The Use of Continued Fractions in Botany (UMAP)
Students will 1) become acquainted with some of the most interseting aspects of continued fractions; 2) realize and a...
Evaluating and Analyzing Probabilistic Forecasts (UMAP)
This module presents an analysis of the quality of probabilistic forecasts, such as weather forecasting and sporting ...
Expected Loss in Keno (UMAP)
This module uses a simplified version of keno to explain the method for calculating probabilities and expected value ...
Getting in Touch with Touchy Questions (UMAP)
A unit that involves probability and statistics with questionnaires. This module explains a bias-reducing technique c...
Harmonic Motion and the Circular Functions (UMAP)
A unit that involves precalculus, harmonic motion, and circular functions. In this module an explanation of simple ha...
The Three Dimensional Trapezoid Rule (UMAP)
The Three Dimensional Trapezoid Rule is a very simple ad reasonably accurate method which can be used to approximate ...
Atmospheric Pressure in Relation to Height and Temperature (UMAP)
A unit using calculus applied to the study of atmospheric pressure in relation to height and temperature. Students ap...
The Levi-Civita Tensor and Identities in Vector Analysis (UMAP)
A unit that involves applications of vector field identities. This module allows students to gain the ability to deri...
Basic Descriptive Statistics (UMAP)
With completion of this module students will be able to: 1) use frequency distributions and histograms to summarize d...
An Application of Geometry to Economics: The .6 Rule for Industrial Costs (UMAP)
A unit that applies calculus to industrial economics. By completion of this module students will be able to examine t...
The Cobb - Douglas Production Function (UMAP)
A unit that applies calculus to economics and management science. This module develops the Cobb-Douglas Production Fu...
The Manufacturing Progress Curve (UMAP)
A unit that applies precalculus to industrial management. The purpose of this module is to teach students about learn...
Lagrange Multipliers and the Design of Multistage Rockets (UMAP)
A unit that uses Lagrange multipliers to compute the minimum total mass of an n-stage rocket capable of placing a giv...
An Application of Calculus in Economics: Oligopolistic Competition (UMAP)
In this module some of the elementary models for duopolies that utilize calculus are examined. Table of Contents: ...
Random Walks: An Introduction to Stochastic Processes (UMAP)
In this module random walks are introduced by an example of a gambling game. The associated finite difference equatio...
Unconstrained Optimization (UMAP)
This module introduces Gradient Search Procedures, with examples and applications. Students are introduced to the use...
Representing Integers as Sums or Differences of Squares (UMAP)
In this module the problem of presenting an integer as a sum or as a difference of two squares is studied. Key questi...
Dimensional Analysis (UMAP)
A unit that relates linear algebra to dimensional analysis. In using this module given a physical system and the fact...