Lecture 6, Monday, 9/8/08:
Section 11.2/11.3: Vector-valued functions: Derivatives and integrals,
motion in space
Topics
- Derivatives of vector-valued functions: algebraic definition
(componentwise differentiation), limit definition,
geometric interpretation (tangent vector), physical interpretation
(velocity, acceleration)
- Differentiation rules (Theorem 2.3, p. 868) (note, in particular, the
three types of product rules)
- "Smooth" curves
- Vector-valued functions of constant magnitude
- Integrals of vector-valued functions
- Motion in space: position r(t),
arclength s(t)),
velocity v(t)=r'(t),
speed s'(t) = ||v(t)||=||r'(t)||,
acceleration a(t)=r''(t),
Newton's Law F = ma
Read
Sections 11.2 and 11.3. In 11.2, focus on the part dealing with the
derivative and integral of vector-valued functions (beginning with p.
867). In 11.3, focus on the first part (Examples 3.1 and 3.2).
Example 3.6 is a nice illustration of the use of rules for derivatives
and the properties of the cross product. You don't have to know the physical
concepts (torque, angular momentum), but you should be able to perform
derivative calculations (involving cross/dot products) similar to those
in this example.
Homework
Section 11.2: 13, 33, 35, 39.
Solutions.
Section 11.3: 1, 7, 9, 13, 21.
Solutions.
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Last modified Wed 10 Sep 2008 05:47:04 PM CDT