Explore advanced calculus concepts in this comprehensive video tutorial covering Chapter 15 of Stewart Calculus on Multiple Integrals. Delve into topics such as the Midpoint Rule for double integrals, level curves, polar coordinates, and order of integration reversal. Learn to evaluate double integrals by changing to polar coordinates, find areas enclosed by cardioids, and calculate centroids of triangular regions. Master moments of inertia using double integrals and polar coordinates. Tackle triple integrals in cylindrical and spherical coordinates to find volumes of complex shapes. Understand the change of variables technique in multiple integrals and learn to find the Jacobian. Perfect for students seeking a thorough understanding of multiple integration techniques and their applications in calculus.
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
