This 14-minute video lesson explains how the product of the transforms of two functions relates to their convolution. [Differential Equations playlist: Lesson 44 of 45]

This 10-minute video lesson looks at using the method of undetermined coefficients to solve nonhomogeneous linear differential equations. [Differential Equations playlist: Lesson 22 of 45]

This 11-minute video lesson gives another example using undetermined coefficients. [Differential Equations playlist: Lesson 23 of 45]

This 8-minute video lesson gives another example where the nonhomogeneous part is a polynomial. [Differential Equations playlist: Lesson 24 of 45]

This 6-minute video lesson concludes the series on undetermined coefficients by putting it all together. [Differential Equations playlist: Lesson 25 of 45]

This 12-minute video lesson shows how to use the convolution Theorem to solve an initial value problem. [Differential Equations playlist: Lesson 45 of 45]

This 19-minute video lesson shows how to solve a non-homogeneous differential equation using the Laplace Transform. [Differential Equations playlist: Lesson 35 of 45]

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.

This lesson using activities to help students enjoy studying math revising rules ,vocab and their learning Knowledge .

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.

This is a lesson using Digital Age Skills in Sinusoidal Modeling Trigonometry, High School

Original Author: Melinda Stelling
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This resource was created by Marshall Payer in collaboration with Aaron Delhay as part of the 2019-20 ESU-NDE Digital Age Pedagogy Project. Educators worked with coaches to create Lesson Plans promoting both content area and digital age skills. This Lesson Plan is designed for 7th-12th Grade Mathematics/Geometry.

This resource was created by Ryan Brand in collaboration with Aaron Delhay as part of the 2019-20 ESU-NDE Digital Age Pedagogy Project. Educators worked with coaches to create Lesson Plans promoting both content area and digital age skills. This Lesson Plan is designed for 10th, 11th, and 12th Grade Mathematics

This resource was created by Suzanne Ras in collaboration with Aaron Delhay as part of the 2019-20 ESU-NDE Digital Age Pedagogy Project. Educators worked with coaches to create Lesson Plans promoting both content area and digital age skills. This Lesson Plan is designed for High School Mathematics.

This resource was created by Deb Bulin in collaboration with Aaron Delhay as part of the 2019-20 ESU-NDE Digital Age Pedagogy Project. Educators worked with coaches to create Lesson Plans promoting both content area and digital age skills. This Lesson Plan is designed for 7th-12th Grade Math.