Quadric Surfaces in 3D Space | Calculus 3 Lesson 20 - JK Math
How to Sketch Quadric Surfaces in 3D Space (Calculus 3 Lesson 20)
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In this video you will learn about a special group of surfaces in 3D space known as Quadric Surfaces. This includes the ellipsoid, hyperboloid of one sheet, hyperboloid of two sheets, elliptic cone, elliptic paraboloid, and hyperbolic paraboloid. We look at the shape of these surfaces, their standard equations, and how to sketch them in 3D space.
This video series is designed to help students understand the concepts of Calculus 3 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!
Calculus 3 requires a solid understanding of concepts from calculus 2, calculus 1, precalculus, and algebra. This includes limits, differentiation, advanced integration techniques, applications of derivatives and integrals, polar coordinates, parametric equations, trigonometric functions, logarithms, factoring, equation manipulation, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!
Video Chapters:
0:00 What are Quadric Surfaces?
5:19 Ellipsoid
8:51 Example: Sketching 4x²+16y²+z²=64
13:05 Hyperboloid of One Sheet
16:46 Example: Sketching 16x²+16z²-4y²=64
23:20 Hyperboloid of Two Sheets
26:38 Example: Sketching -y²+x²+16z²+16=0
35:15 Elliptic Cone
38:42 Example: Sketching 4x²+16y²-z²=0
42:43 Elliptic Paraboloid
45:30 Example: Sketch z=x²+3y²-3
49:03 Hyperbolic Paraboloid
51:50 Example: Sketching x²-y²-4z=0
📝 Examples Video: • Quadric Surfaces in 3D Space Examples | Ca...
⏩ Next Lesson: • Surfaces of Revolution in 3D Space | Calcu...
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