## Syllabus

Note: This is the approximate syllabus for the course. This copy will NOT be updated during the term. An updated syllabus will be maintained on the Math 9 Canvas site.

Lecture Sections Topic
Sept 11 Stewart 12.1; Stewart 12.2 or A-R 3.1 Intro to Course; Coordinates and vectors in ${\mathbb{R}}^2$ and ${\mathbb{R}}^3$
Sept 13 Posted notes Vectors, linear combinations, linear independence
Sept 14 Posted notes Linear combinations (cont.)
Sept 15 Stewart 12.5 through page 866, A-R 3.4 up through Example 5 (skip Examples 3 and 4) Vector and parametric equatons of lines and planes
Sept 18 Stewart 12.3 (Read Stewart first. For a different presentation of projections, you might want to read A-R, bottom of 282–285) Dot products
Sept 20 Stewart 12.3 (cont), 12.4 Dot products (cont), cross product
Sept 22 Stewart 12.5 (from bottom of p. 866), See also A-R pp 281–282 Scalar equations of planes
Sept 25 Matrices: Read either A-R 1.3 up to p. 56 or Lerner Chapter 1 up to middle of p. 12. Linear transformations: Read A-R 4.9 up to p. 460 Linear transformations and their matrices
Sept 27 Posted notes Composition of linear transformations, geometry of linear transformations
Sept 29 A-R p. 461–464 (ending with Example 4) Examples of linear tranformations: rotations, reflections, etc.
Oct 2   Review
Oct 3 4–6 P.M. Exam I
Oct 4 Posted notes Geometric interpretation of determinants
Oct 6 Stewart 13.1 Vector functions, space curves
Oct 9 Stewart 13.2, 13.3 up through Example 2. Derivatives and integrals of vector functions, velocity and acceleration, arclength
Oct 11 Stewart 14.1 Functions of several variables and their graphs. (We will introduce functions from ${\mathbb{R}}^n$ to ${\mathbb{R}}^m$ but graph only real-valued functions.)
Oct 12 Stewart 14.1 (cont) Level sets. (Emphasize real-valued functions. Include level sets of linear functions.)
Oct 13 Stewart 14.2 Limits and continuity
Oct 16 Stewart 14.3 Partial Derivatives
Oct 18 Lerner 9.1–9.2 Derivatives as linear transformations; Jacobian matrix
Oct 20 Stewart 14.4 Tangent Planes
Oct 23 Posted notes and Stewart 14.5 Chain Rule.
Oct 25 Stewart 14.6 and Posted notes Directional derivatives, another interpretation of the derivative

Oct 27   Review
Oct 30 Stewart 14.6 Gradient of real-valued functions.
Nov 1 Stewart p. 1007, Posted notes Second-order directional derivatives, Hessian, quadratic approximation of functions
Nov 2 X-hour if needed quadratic approximation of functions (cont)
Nov 3 Stewart 14.7 Maxima and Minima; critical points
Nov 6 Stewart 14.7, cont. Maxima and Minima
Nov 8 Stewart 14.8 Lagrange multipliers
Nov 10   Wrap up
Nov 13   Review

Disclaimer: This web page will not be updated during the term. Updated course material can be found on Canvas.