This 9-minute video lesson gives an example of using initial conditions to solve a repeated-roots differential equation .[Differential Equations playlist: Lesson 21 of 45]

This 12-minute video lesson looks at what happens when the characteristic equation only has one repeated root. [Differential Equations playlist: Lesson 20 of 45]

This 12-minute video lesson introduces separable differential equations. [Differential Equations playlist: Lesson 2 of 45]

This 14-minute video lesson looks at 3 basic differential equations that can be solved by taking the antiderivatives of both sides.

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]

Watch this video to learn about the working of the differential in tractors and the purpose of final drive in tractor.

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.

Differentiation is what we do to enable more students to meet outcomes. It is the way in which we respond to the learning differences our students have which means it is also an ongoing reflective process.

We gather data before, during and after instruction in order to choose the right tools in order to reach the needs of our learners. The teacher who plans instruction to accommodate the differences among student’s, designs or chooses the best pre-assessment tools. The results are then used to enhance the instruction and learning experiences on the journey.

This Module discusses the importance of differentiating three aspects of instruction: content, process (instructional methods), and product (assessment). It explores the student traits—readiness level, interest, and learning preferences—that influence learning (est. completion time: 3 hours).

Various PDF Handouts on:
Choice Menus, Graphic Organizers, RAFTS, Cubing & Think Dots, Sample Centers, Literacy Stations, Measurement Choice Board, RAN Organizer, KWHLAW Chart

Differentiation is a teaching method that varies the content, process, product or learning environment relate to student interest, learning profile or readiness.

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.