Quadric surfaces and cylinders FULL EXPLANATION
▼ IMPORTANT ▼ Quadratic surfaces and cylinders, graph of surfaces in three dimensions using Traces and cross sections (and contour lines), using the equations of conics (circumference, ellipse, parabola and hyperbola). We will see what three-dimensional conics, cylinders, elliptical paraboloid, cone, ellipsoid, one-sheet hyperboloid, two-sheet hyperboloid, hyperbolic paraboloid, and various examples look like.
0:00 Start
0:12 subject index
0:55 Requirements
1:45 Brief review of the conics
4:25 General equation of the second degree with 2 variables
7:25 General equation in 3 variables
10:40 Example 1, using traces (Ellipses)
15:05 Graph in Geogebra from example 1
18:00 More cross sections
25:25 Graph in Geogebra
29:30 Example 2, using traces (Parabolas and circles)
38:35 Graph in Geogebra from example 2
41:30 Types of quadric surfaces, classification
42:10 Cylinders (when z is missing)
43:52 Parabolic cylinder in Geogebra
45:13 Cylinders (when y is missing)
46:15 Circular cylinder in Geogebra
47:02 Cylinders (When x is missing)
48:02 Trigonometric cylinder in Geogebra
49:44 Ellipsoid
51:03 Elliptical paraboloid
52:35 Elliptical Paraboloid Plots (Cases)
53:35 Hyperbolic paraboloid
54:35 Hyperbolic Paraboloid Plots (Cases)
56:10 Cone
56:41 Cone graphs (Cases)
57:25 Hyperboloid of a leaf
58:20 Plots of one-leaf hyperboloids (Cases)
58:57 Two-leaf hyperboloid
59:35 Graphs of two-leaf hyperboloids (Cases)
1:00:25 List of exercises
Calculus # Geometry # Conics
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