This module serves as an introduction to the Continuous Random Variables chapter in the Elementary Statistics textbook. The original module by S. Dean and B. Illowsky has been revised; concepts removed from the original version of module are discussed in R. Bloom's module Continuous Random Variables: Properties of Continuous Probability Distributions
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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.
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 is the second installment of Single-Variable Calculus. The student will explore the mathematical applications of integration before delving into the second major topic of this course: series. The course will conclude with an introduction to differential equations. Upon successful completion of this course, students will be able to: Define and describe the indefinite integral; Compute elementary definite and indefinite integrals; Explain the relationship between the area problem and the indefinite integral; Use the midpoint, trapezoidal, and Simpson's rule to approximate the area under a curve; State the fundamental theorem of calculus; Use change of variables to compute more complicated integrals; Integrate transcendental, logarithmic, hyperbolic, and trigonometric functions; Find the area between two curves; Find the volumes of solids using ideas from geometry; Find the volumes of solids of revolution using disks, washers, and shells; Find the surface area of a solid of revolution; Compute the average value of a function; Use integrals to compute displacement, total distance traveled, moments, centers of mass, and work; Use integration by parts to compute definite integrals; Use trigonometric substitution to compute definite and indefinite integrals; Use the natural logarithm in substitutions to compute integrals; Integrate rational functions using the method of partial fractions; Compute improper integrals of both types; Graph and differentiate parametric equations; Convert between Cartesian and polar coordinates; Graph and differentiate equations in polar coordinates; Write and interpret a parameterization for a curve; Find the length of a curve described in Cartesian coordinates, described in polar coordinates, or described by a parameterization; Compute areas under curves described by polar coordinates; Define convergence and limits in the context of sequences and series; Find the limits of sequences and series; Discuss the convergence of the geometric and binomial series; Show the convergence of positive series using the comparison, integral, limit comparison, ratio, and root tests; Show the divergence of a positive series using the divergence test; Show the convergence of alternating series; Define absolute and conditional convergence; Show the absolute convergence of a series using the comparison, integral, limit comparison, ratio, and root tests; Manipulate power series algebraically; Differentiate and integrate power series; Compute Taylor and MacLaurin series; Recognize a first order differential equation; Recognize an initial value problem; Solve a first order ODE/IVP using separation of variables; Draw a slope field given an ODE; Use Euler's method to approximate solutions to basic ODE; Apply basic solution techniques for linear, first order ODE to problems involving exponential growth and decay, logistic growth, radioactive decay, compound interest, epidemiology, and Newton's Law of Cooling. (Mathematics 102; See also: Chemistry 004, Computer Science 104, Mechanical Engineering 002)