Week 10 -- Sections 6.2-6.4
- Find the expansion of a vector in terms of an orthonormal or
orthogonal basis. (Sec. 6.2)
- Find the matrix representing a linear function with respect to an
orthonormal basis. (Sec. 6.2)
- Construct an orthonormal set in R^n, using the Gram-Schmidt process.
- Construct the first few elements of an orthonormal set of polynomials,
with respect to an integral inner product of functions. (Sec. 6.2)
- Differentiate (with respect to a parameter) the inverse of a matrix.
- Calculate the basic vector differential operations (grad, div, curl).
- Use, and if necessary rederive, identities involving the vector
differential operations. (Sec. 6.4)
- Understand concepts of arc length, unit tangent vector, and line
integral (for later comparison with analogous concepts for surfaces).
- Become familiar with normal vector, binormal vector, curvature, and
torsion of a curve (their geometrical meaning and their calculational
construction). (Sec. 6.3) ._.
NOTE: The short-term (testable skills) list could very well
include "Calculate the normal vector, ... of a curve." However,
our syllabus is too crowded to insist on this.
- Understand the origin of the vector differential operations, and the
identities satisfied by them, in elementary algebraic and calculus
operations and facts. (Sec. 6.4)