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.