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 AR 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, AR 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 AR, 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 AR pp 281–282  Scalar equations of planes 
Sept 25  Matrices: Read either AR 1.3 up to p. 56 or Lerner Chapter 1 up to middle of p. 12. Linear transformations: Read AR 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  AR 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 realvalued functions.) 
Oct 12  Stewart 14.1 (cont)  Level sets. (Emphasize realvalued 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 realvalued functions. 
Nov 1  Stewart p. 1007, Posted notes  Secondorder directional derivatives, Hessian, quadratic approximation of functions 
Nov 2  Xhour 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.