This schedule is very tentative, and it will be adjusted as necessary.

 Week 1 (1/91/13)
 [1/9 Preliminary study list deadline]
 [1/9 First lecture; 1/10 first section]
L1: Vectors in R^{n}
L2: Linear Combinations, Span
L3: Linear Independence
L4: Dot Product, Cross Product (see also projections, L14 p923)

 Week 2 (1/161/20)
 [1/16 MLK day, no classes]
L5: Systems of Linear Equations
L6: Matrices, Rref
L7: MatrixVector Products
L8: Null Space

 Week 3 (1/231/27)
 [1/27 Final study list deadline]
L9: Column Space
L10: Subspaces of R^{n}
L11: Basis (see also coordinates, L21 p1457)
L12: Dimension

 Week 4 (1/302/3)
 [2/2 Exam 1, approx 7:30pm; covers thru end of Week 3 topics listed above]
L1314 (thru p93): Linear Transformations and Examples
C2.1: Multivariable Functions: Graphs, Level Sets
(As time permits) brief review of SingleVariable Calculus
C2.3 (p11628 only); C4.1 (p24451 only): Partial Derivatives, Differentiability; Applications  Tangent Planes to Graphs; FirstOrder (Linear) Approximation and Differentials

 Week 5 (2/62/10)
C2.4 (p1348): HigherOrder Derivatives; Interpretation of Contour Maps
L15: Composition and Matrix Multiplication
L16: Inverses; Applications  Linear Systems, Coordinates (see also L21, p1459 only)

 Week 6 (2/132/17)
C2.5: Chain Rule
C2.6 (p15868 only): Directional Derivatives and Gradient; Application  Tangent Planes to Implicit Surfaces
L17: Determinants

 Week 7 (2/202/24)
 [2/20 Presidents' Day, no classes]
 [2/23 Exam 2, approx 7:30pm; covers thru end of Week 6 topics listed above]
L1819: Transposes, Row Spaces, Orthogonal Complements; Application  Minimum Magnitude Solution (Constrained Least Squares)
L20: Orthogonal Projections; Application  Least Squares Approximation

 Week 8 (2/273/3)
 [3/3 Course withdrawal and change of grading basis deadline]
L22: Orthonormal Bases; Applications  Projections, Coordinates (see also L21, p1459 only)
C4.1 (p25255 only): Quadratic approximation (seconddegree Taylor polynomial), Hessian matrix; Application  Concavity in a given direction; Quadratic forms, Definiteness
C4.2 (p26367 & 27074 only): Extrema of Functions

 Week 9 (3/63/10)
C4.3 (p278286): Lagrange Multipliers [case of one constraint, thru p283]
Applications of Extrema  Definiteness of Quadratic Forms, Eigenvalues; Second Derivative Test  Handout on eigenvalues, eigenvectors and definiteness
C4.3 (p278286): Lagrange Multipliers [continued; case of multiple constraints p2846]

 Weeks 1011 (3/133/20)
 [3/16 Last section; 3/17 last lecture]
 [3/20 Final Exam, 710pm; comprehensive but more heavily emphasizes topics since Exam 2]
C4.4 (p2937 & 3013): Applications of Extrema  Least Squares (Constrained & Unconstrained) Revisited; Applications in the Natural and Social Sciences

