- Colloquium
- “ARE U Planning for Next Summer / Modeling Cardiovascular Dynamics During Blood Withdrawal”
- REU programs and the work of one particular one
- Jacob Goldberg, Geneseo Math major
- Wednesday, Oct. 21, 2:45, Newton 202
- Extra credit as usual (but connections need to be more than “I want to do an REU”)
- Please cancel appointments you can’t keep as early as possible
- Is there an analog of L’Hôpital’s Rule for multi-variable functions? Probably not, although it might be possible in certain special cases (e.g., function can be parameterized in a way that makes it a single-variable function)
- Demonstrate a function for which the mixed derivative theorem doesn’t hold? Harder than it seems, theorem in book actually puts more restrictions on the function and its derivatives than necessary
- Level curves?
- f(x,y) = k defines implicit equation that relates x and y
- So use implicit curve plotter to draw it
- e.g., muPad
plot::Implicit2d
- e.g., muPad
- f(x,y) = k defines implicit equation that relates x and y
- Section 14.4
- Chain rule feels optional, especially when x, y are functions of 1 variable
- But lets you isolate components
- Branch diagrams helpful
- Examples
- Find dw/dt if w = xy, x = t2, y = 2t
- Find ∂w/∂u and ∂w/∂v if w = xey, x = uv, y = u lnv
- Find dw/dt if w = xy, x = t2, y = 2t
- Gradients and Directional Derivatives
- Read section 14.5