- Face-to-face grading
- Use Google calendar to make appointments
- Intro to LaTeX
- LaTeX = widely used mathematical type-setting program, good to know for serious math writing
- Tuesday, Sept. 8, 6:00 - 7:30 PM, Welles 26
- Bring laptop
- Prof. Leary
- Class Google group
- math223-03-fal15-googlegroup@geneseo.edu
- Use for sending email to class
- Also shares this document
- Section 12.6
- Quadric equations are like quadratic (as presented here)
- But full general form is ax2 + by2 + cz2 + dxy + eyz + fxz + gx + hy + iz + j
- Cylinder not necessarily “cylindrical”
- For example…
- For example…
- Like surfaces of revolution
- Except quadrics can have elliptical cross sections where
surfaces of revolution always have circular cross sections.
- I believe but don’t have a proof immediately that every surface produced by revolving a quadratic curve is a quadric surface
- But not all quadrics are surfaces of revolution
- Except quadrics can have elliptical cross sections where
surfaces of revolution always have circular cross sections.
- Quadric equations are like quadratic (as presented here)
- “Implicit” equations
- y = x2 (an explicit equation in 2 variables)
- z = x2 + y2 (another explicit equation, in 3 variables)
- 1 = x2 + y2 - z2 (an implicit equation)
- “Reading” quadrics
- x2 + y2 = z
- Look for circles/ellipses that form cross-sections
- Look for profiles/silhouettes by setting variables to 0 (or other constant)
- x2 / 4 + y2 / 9 + z2 / 4 = 1
- x2 + y2 + z2 = r2 is sphere
- This is similar, except divisors expand it in some dimensions producing ellipsoid
- x2 + y2 - z2 = 2
- Circular cross-sections have radii that asymptotically
approach z—hyperboloid (1 sheet)
- Circular cross-sections have radii that asymptotically
approach z—hyperboloid (1 sheet)
- x2 + y2 = z
- Computer algebra systems (muPad)
- Bring laptops!
- With Matlab installed—see instructions under “Software” in syllabus
- No reading