This course explores the techniques for computing double, triple and multiple integrals in both cartesian and non-cartesian coordinates systems like polar, cylindrical and spherical. Learners will gain experience evaluating double integrals using change of variable techniques and level curves, altering the order of integration, and computing the area, volume and centroid enclosed by shapes like a cardioid, triangle, sphere and cone. Furthermore, learners will be able to use triple integrals to calculate the volume of a cylindrical, sphere and cone as well as calculate moments of inertia. Finally, learners will learn about the Jacobian for computing changes of variables in multiple integrals.
Overview
Syllabus
Midpoint Rule Double Integrals Using Level Curves!.
Double Integrals in Polar Coordinates.
Evaluate by Reversing the Order of Integration :: integral bounds include ln(x)!!.
Evaluate by Changing to Polar Coordinates Double Integral Full Ex.
Double Integral to find Area Enclosed by a Cardioid r=2-2cos(t).
Find the Centroid of the Triangular Region Given the Vertices :: Double Integrals.
Moments of Inertia :: Double Integrals :: Polar Coordinates.
Evaluate by Changing to Cylindrical Coordinates :: 2 Ways!!!.
Triple Integral to find Volume Cylindrical and Spherical Coordinates :: Inside Sphere Outside Cone.
Triple Integral in Spherical Coordinates to find Volume :: Under Sphere Between Two Cones..
Evaluate By Changing to Spherical Coordinates :: Above Cone Between Two Spheres.
Change of Variables in Multiple Integrals (Find the Jacobian).
Taught by
Jonathan Walters
