In this video, we use direction fields (drawn as quiver plots) to illustrate the numerical integration of differential equations. We include a heuristic example of how one might try to adapt step size by comparing different orders of approximation.

In the first video, we present a biological circuit topology from Ma, Trusina, El-Samad, Lim, and Tang, "Defining network topologies that can achieve biochemical adaptation," Cell, 138: 760-773 (2009). This topology supports adaptation, which is not the absence of change in response to stimulation/stress, but, instead, the ability to produce delayed compensation for those changes. In the second video, we summarize the method of almost linear stability analysis used to solve for the dynamics of this example system.

To describe how oscillations are supported in systems of differential equations, we present a classic "Romeo and Juliet" picture of two-dimensional oscillations, and we analyze how trajectories change as nullclines are arranged at different angles in the phase plane. In addition to models based on traditional systems of differential equations, dynamical systems with time delays and dynamical systems with stochastic fluctuation (i.e. stochastic resonance) can also support oscillations.

In the five parts of this video, we define the derivative and then build a cribsheet of rules for expressing the slopes of simple functions and combinations of functions. These include the power rule, the chain rule, the product and quotient rules, and the rules for differentiating sinusoidal functions.

The first video segment presents a canonical mathematical example from quantitative biology, in which mRNA is transcribed from a gene sequence, and protein is translated from mRNA. The second segment uses eigenvector-eigenvalue analysis to sketch the trajectories of the system in a phase portrait. Finally, the third segment generalizes the linear stability analysis used to study this example.

Paul Andersen explains how diffraction can be affected by the size of the wavelength. When waves pass through an opening or move around an obstacle a shadow region is created. The size of the shadow zone will decrease as the wavelength matches the size of the obstacle or opening.

Discover Physics is a conceptual physics textbook intended for students in a nonmathematical one-semester general-education course.

With a simple demonstration activity, students are introduced to the concept of friction as a force that impedes motion when two surfaces are in contact. Then, in the Associated Activity (Sliding and Stuttering), they work in teams to use a spring scale to drag an object such as a ceramic coffee cup along a table top or the floor. The spring scale allows them to measure the frictional force that exists between the moving cup and the surface it slides on. By modifying the bottom surface of the cup, students can find out what kinds of surfaces generate more or less friction. They also discover that both static and kinetic friction are involved when an object initially at rest is caused to slide across a surface.

Using the same method for measuring friction that was used in the previous lesson (Discovering Friction), students design and conduct experiments to determine if the amount of area over which an object contacts a surface it is moving across affects the amount of friction encountered.

Student groups are provided with a generic car base on which to design a device/enclosure to protect an egg on or in the car as it rolls down a ramp at increasing slopes. During this in-depth physics/science/technology activity, student teams design, build and test their creations to meet the design challenge, and are expected to perform basic mathematical calculations using collected data, including a summative cost to benefit ratio.

Paul Andersen explains how the perceived frequency of a source depends on the motion of both the source and the observer. As a source approaches an observer the frequency will increase and as it moves away it will decrease. The same will occur for a moving observer.

The resource "The Doppler Effect" is included in the Physics Fundamentals topic of the EICC Engineering Techology Simulations resource series. This series is segment of a Department of Labor grant awarded to the Eastern Iowa Community Colleges (EICC) of Clinton, Muscatine, and Scott.

Douglas College custom textbook for first year college physics. Physics 1107 based on Open Stax College Physics. Algebra based, designed primarily for biology and earth science majors.

Douglas College custom textbook for first year college physics. Physics 1108 based on Open Stax College Physics. Algebra based, designed primarily for biology majors transferring to Simon Fraser University.

This is a custom textbook for Physics 1207 Introductory General Physics II at Douglas College. This is the second semester of a non-calculus based course intended primarily for life science majors. It focuses on electricity, magnetism, optics and modern physics. This textbook is based on Open Stax College Physics.

Students use a compass and a permanent magnet to trace the magnetic field lines produced by the magnet. By positioning the compass in enough spots around the magnet, the overall magnet field will be evident from the collection of arrows representing the direction of the compass needle. In activities 3 and 4 of this unit, students will use this information to design a way to solve the grand challenge of separating metal for a recycling company.

The course provides the technological background of treatment processes applied for production of drinking water. Treatment processes are demonstrated with laboratory experiments.