Vectors and the Geometry of Space: Cylinders and Quadric Surfaces
In this video I explore the wonderful world of cylinders and quadric surfaces. Cylinders are defined as a 3D surface that consists of all lines (called rulings) that are parallel to a given line and pass through a given plane curve. Quadric surfaces are the graphs of a second-degree equation in three variables x, y, and z. Unlike quadric surfaces, cylinders have 1 of the x, y, or z variables missing from its equation. This makes the cylinder extend outwards along the missing variable. I also go over some exercises and show that the Earth can be more accurately modeled as an ellipsoid, which is a type of quadric surface. This section is part of the Vectors and Geometry of Space chapter in my Calculus book.
The topics covered as well as their timestamps are listed below.
- Intro: 0:00
- Calculus Book Reference: 0:50
- Sections in Calculus Book Chapter: 1:03
- Topics to Cover: 1:49
1. Cylinders and Quadric Surfaces: 3:22
2. Cylinders: 5:10
- Example 1: Parabolic Cylinder: 5:28
- Example 2: Circular Cylinders: 10:31
- (a) Vertical Cylinder: 10:44
- (b) Horizontal Cylinder: 14:45
- Note: 3D Surfaces vs 2D Traces: 17:40
3. Quadric Surfaces: 18:54
- Example 3: Ellipsoid: 24:23
- Example 4: Elliptic Paraboloid: 37:25
- Example 5: Hyperbolic Paraboloid: 45:01
- Example 6: Hyperboloid of One Sheet: 1:06:03
- Computer-Drawn Graphs of Quadric Surfaces: 1:12:19
- Table 1: Graphs of Quadric Surfaces: 1:12:57
- Example 7: Hyperboloid of Two Sheets: 1:18:13
- Example 8: Elliptic Paraboloid: 1:29:36
- Applications of Quadric Surfaces: 1:41:25
4. Exercises
- Exercise 1: Modeling Earth as an Ellipsoid: 1:46:54
- (a) Earth's Ellipsoid Equation: 1:48:06
- (b) Parallels or Circular Lines of Equal Latitude: 1:53:24
- (c) Meridians or Elliptical Lines of Equal Longitude: 1:58:56
- Exercise 2: Hyperbolic Paraboloid Generated from Lines: 2:05:51
- Outro: 2:21:43
Video notes and playlists:
- PDF notes: https://1drv.ms/b/s!As32ynv0LoaIiuEh0Jh0kNq5HCbRSg
- HIVE notes: https://peakd.com/hive-128780/@mes/cylinders-and-quadric-surfaces
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EfmYwT81SebJnU1Ny8Fc5u
- Full Vectors and the Geometry of Space series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
------------------------------------------------------
Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
MES Links: https://mes.fm/links
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes
Email me: contact@mes.fm
Free Calculators: https://mes.fm/calculators
BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm
Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps
-
14:52
Math Easy Solutions
6 days ago $0.08 earnedDistance Between Intersecting Lines, Parallel Lines, and Skew Lines
1434 -
2:27:54
Twisted History
1 day agoThe Twisted History of Assassinations Part III
138K29 -
1:05:33
Michael Franzese
1 day agoWhy Biden dropped out, and Kamala’s agenda to destroy America | MF LIVE | EP 13
175K193 -
35:21
MYLUNCHBREAK CHANNEL PAGE
1 day agoOld World Underground Cities & Maps?
184K102 -
8:07:11
Right Side Broadcasting Network
3 days agoLIVE REPLAY: President Trump Keynotes TPUSA Faith's Believers' Summit in West Palm Beach 7/26/24
564K373 -
1:18:33
Dexerto League of Legends
1 day agoAre Fnatic REALLY Better Than G2? Is Jankos RETIRING? LEC Playoffs Review
140K11 -
47:00
The Based Mother
1 day ago $0.07 earnedThe Based Mother Ep. 12 - Evil Olympics | Obama-Harris | Agenda 47 Prescriptions | Alexandra Levine
119K178 -
51:01
Legal Insurrection
1 day agoWhat in the House of Cards is Going on with the Democrats?
110K45 -
13:13
justintech
1 day ago $0.02 earnediBUYPOWER Y40 Review - The most INSANE Deal I've Seen!
94.5K11 -
1:00:02
Trumpet Daily
1 day ago $3.56 earnedNew Regime Narrative: Biden Is George Washington, Kamala Is Obama, and Trump Is Terrified - Trumpet Daily | July 26, 2024
98K61