This course is about the mathematics that is most widely used in the mechanical engineering core subjects: An introduction to linear algebra and ordinary differential equations (ODEs), including general numerical approaches to solving systems of equations.

This is a direct task suitable for the early stages of learning about exponential functions. Students interpret the relevant parameters in terms of the real-world context and describe exponential growth.

Students come to see the exponential trend demonstrated through the changing temperatures measured while heating and cooling a beaker of water. This task is accomplished by first appealing to students' real-life heating and cooling experiences, and by showing an example exponential curve. After reviewing the basic principles of heat transfer, students make predictions about the heating and cooling curves of a beaker of tepid water in different environments. During a simple teacher demonstration/experiment, students gather temperature data while a beaker of tepid water cools in an ice water bath, and while it heats up in a hot water bath. They plot the data to create heating and cooling curves, which are recognized as having exponential trends, verifying Newton's result that the change in a sample's temperature is proportional to the difference between the sample's temperature and the temperature of the environment around it. Students apply and explore how their new knowledge may be applied to real-world engineering applications.

This resource was created by the Washington Office of Superintendent of Public Instruction. 

This resource was created by the Washington Office of Superintendent of Public Instruction. 

This resource was created by the Washington Office of Superintendent of Public Instruction. 

This resource was created by the Washington Office of Superintendent of Public Instruction. 

This resource was created by the Washington Office of Superintendent of Public Instruction. 

This resource was created by the Washington Office of Superintendent of Public Instruction. 

This resource was created by the Washington Office of Superintendent of Public Instruction. 

Watch this music video to help you learn about PEMDAS (Please Excuse My Dear Aunt Sally). Does this sound familiar? If not, this is an excellent device to memorize the algebraic order of operations. This video is produced by Mr. Davis Productions and plays music by Odyssey Sound Lab.

Using Avida-ED freeware, students control a few factors in an environment populated with digital organisms, and then compare how changing these factors affects population growth. They experiment by altering the environment size (similar to what is called carrying capacity, the maximum population size that an environment can normally sustain), the initial organism gestation rate, and the availability of resources. How systems function often depends on many different factors. By altering these factors one at a time, and observing the results, students are able to clearly see the effect of each one.

These instructional videos cover the Examples and Try It exercises in the OpenStax Precalculus text. Created by Brian Stonelake at Southern Oregon University.

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.