- SOFIs
- Helpful to me in teaching this (or other) courses in future
- Access through myGeneseo/KnightWeb
- Problem 2?
- Vector field equations for “radial force”
- Parameterize path (a,f(a)) to (b,f(b))
- Evaluate line integral
- V(x,y,z) = ⟨ y - x/2, -x - y/2 ⟩. Does this really describe an inward flow?
- Summary of section 16.3
- Path independence
- Theorem 2: F is conservative iff F = grad(f) for some f
- f is “antiderivative” (“anti-gradient”?) of F
- Loop property: Follows from idea that 2 paths from A to B allows negation of 1, then net integral over both = 0
- Conclusion: integral of conservative field around any closed path = 0
- 3 equivalent statements:
- Line integrals of F depend only endpoints not on path
- F is conservative
- F is a gradient field
- Simple connectedness?
- Region (e.g., function domain) with no holes
- Region (e.g., function domain) with no holes
- Examples