This short video and interactive assessment activity is designed to teach second graders about determining time changes in 5-minute intervals.
This short video and interactive assessment activity is designed to teach second graders an overview of subtraction (numbers to 1,000).
This short video and interactive assessment activity is designed to give fourth graders an overview of subtraction (numbers to 1,000).
This short video and interactive assessment activity is designed to teach third graders an overview of subtraction (numbers to 1,000).
This is the first semester of a two-semester sequence on Differential Analysis. Topics include fundamental solutions for elliptic; hyperbolic and parabolic differential operators; method of characteristics; review of Lebesgue integration; distributions; fourier transform; homogeneous distributions; asymptotic methods.
In this course, we study elliptic Partial Differential Equations (PDEs) with variable coefficients building up to the minimal surface equation. Then we study Fourier and harmonic analysis, emphasizing applications of Fourier analysis. We will see some applications in combinatorics / number theory, like the Gauss circle problem, but mostly focus on applications in PDE, like the Calderon-Zygmund inequality for the Laplacian, and the Strichartz inequality for the Schrodinger equation. In the last part of the course, we study solutions to the linear and the non-linear Schrodinger equation. All through the course, we work on the craft of proving estimates.
This 10-minute video lesson provides an introduction to 2nd order, linear, homogeneous differential equations with constant coefficients. [Differential Equations playlist: Lesson 13 of 45]
This 8-minute video lesson continues the discussion from the previous video and shows how to find the general solution. [Differential Equations playlist: Lesson 14 of 45]
This 6-minute video lesson continues the discussion from the previous videos and introduces some initial conditions to solve for the particular solution. [Differential Equations playlist: Lesson 15 of 45]
This 9-minute video lesson continues the discussion from the previous videos and provides another example using initial conditions. [Differential Equations playlist: Lesson 16 of 45]
This 10-minute video lesson looks at what happens when the characteristic equations has complex roots. [Differential Equations playlist: Lesson 17 of 45]
This 10-minute video lesson continues the discussion of what happens when the characteristic equation has complex roots. [Differential Equations playlist: Lesson 18 of 45]
This 10-minute video lesson concludes the series on complex roots of characteristic equations and demonstrates an example with initial conditions. [Differential Equations playlist: Lesson 19 of 45]
This 12-minute video lesson gives the first example of solving an exact differential equation. [Differential Equations playlist: Lesson 6 of 45]
This 8-minute video lesson provides some more examples of exact equations. [Differential Equations playlist: Lesson 7 of 45]
This 10-minute vidoe lesson provides one more exact equation example [Differential Equations playlist: Lesson 8 of 45]
This 10-minute video lesson provides intuiton on exact equations including the chain rule using partial derivatives (not a proof; more intuition). [Differential Equations playlist: Lesson 4 of 45]
This 11-minute video lesson provides more intuitive building blocks for exact equations. [Differential Equations playlist: Lesson 5 of 45]
This 7-minute video lesson provides an introduction to first order homogenous equations. [Differential Equations playlist: Lesson 11 of 45]
This 8-minute video lesson provides another example of using substitution to solve a first order homogeneous differential equations. [Differential Equations playlist: Lesson 12 of 45]