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5.0 A better way to understand Differential Equations | Nonlinear Dynamics | Bendixson's Criterion
Bendixson's criterion is another method used to disprove the existence of closed orbits. A periodic solution is a type of closed orbit. This theorem only holds for simply connected regions in 2D. The statement is that if on a simply...
APMonitor
MathCAD Graphing and Calculus
Plotting expressions is important to visualize data, relationships between variables, and perform analysis. Mathcad plotting allows visualization of variable values, functions, and data points. Included in this demonstration is common...
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Second Moment of Area Example 1
To find the second moment of area about the x axis use Ix = /int y^2 dA To find the second moment of area about the y axis use Iy = /int x^2 dA In this video I solve this problem using the double integral method (which is more robust)....
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Second Moment of Area Example 2
In this video I use the double integral to solve for the moment of inertia of area of a triangle about a vertex Ix = /int y^2 dA This can also be done without using double integrals if we choose a 'larger' value of dA which is a...
Professor Dave Explains
Stokes's Theorem
Stokes's Theorem is kind of like Green's Theorem, whereby we can evaluate some multiple integral rather than a tricky line integral. This works for some surface integrals too. Let's see how it works!
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Second Moment of Area Example 3
Ix is the second moment of area about the x axis. Choosing the value of dA is the important part for this problem. In this example where we're dealing with a section of a circle, it's easier to use cylindrical coordinates dA = r dr...
Professor Dave Explains
Double and Triple Integrals
An introduction to multivariable calculus in the way of double and triple integrals.
Khan Academy
Khan Academy: Calculus: Double Integrals 6
Video lesson finishing an example of how to evaluate the double integral to find the volume under a specific surface when the bounds are variable. Initially integrates with respect to x first and then solves the problem again integrating...
Khan Academy
Khan Academy: Calculus: Double Integral 1
Video lesson introducing double integrals by first reviewing definite integrals. Includes an understanding of how to use double integrals to calculate the volume under a surface using a visual representation but no mathematical...
Khan Academy
Khan Academy: Calculus: Double Integrals 5
Video lesson showing how to compute the double integral to find the volume under a specific surface when the bounds are variable. Includes a visual representation. Shows how to set up the integral but not how to evaluate it. [9:51]
Khan Academy
Khan Academy: Calculus: Double Integrals 2
Video lesson showing how to compute the double integral to find the volume under a specific surface defined as a function of x and y. Includes a visual representation. [9:50]
Khan Academy
Khan Academy: Calculus: Double Integrals 4
Video lesson showing an alternate way to understand double integrals by integrating with respect to A instead of x and y in order to find the volume under a surface. [9:24]
Khan Academy
Khan Academy: Calculus: Double Integrals 3
Video lesson showing how to compute the double integral from the previous video with respect to y first. Includes a visual representation. [8:03]
Khan Academy
Khan Academy: Surface Integrals: Part 3 the Home Stretch
Part 3 of a 3-part video series showing how to calculate the surface integral of the unit sphere.
Khan Academy
Khan Academy: Stokes' Theorem: Stokes Example Part 4 Curl and Final Answer
Finding the curl of the vector field and then evaluating the double integral in the parameter domain
Khan Academy
Khan Academy: Divergence Theorem Proof: Divergence Theorem Proof (Part 5)
This is part five of a series of video about the Divergence Theorem.
Khan Academy
Khan Academy: Stokes' Theorem: Part 3 Surface to Double Integral
A video showing converting the surface integral to a double integral.