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Math 51
Spring 2014

Home Syllabus Homework Office Hours Exams Useful hints Errata Coursework (for members)
Textbook abbreviations
LA = Linear Algebra (Levandosky)
DVC = Differential Vector Calculus (Licata)

This schedule is tentative, and may be adjusted as necessary.

Week 1 (6/23-627)
Monday: Vectors in Rn (LA 1)
Tuesday: Linear Combinations, Span, Linear Independence (LA 2, 3)
Wednesday: Systems of Linear Equations, Matrices (LA 5 mostly)
Thursday: RREF (LA 6)
Friday: Dot product, cross product (LA 4). Deadline to tell me if you will be away on the day of the midterm (as opposed to can make the same day at a different time).
Week 2 (6/30-7/3)
Monday: Matrix-Vector products, Null Space (LA 7, 8)
Tuesday: Column Space, Rank (LA 9)
Wednesday: Subspaces of Rn (LA 10)
Thursday: Basis, Dimension (LA 11, 12)
Week 3 (7/7-7/11)
Monday: Linear Transformations (LA 13, 14)
Tuesday: Matrix multiplication and Examples (LA 14, 15)
Wednesday: Composition (LA 15)
Thursday: Inverses (LA 16)
Friday: Determinants (LA 17) Deadline to give me informal notice of access needs for midterm (and final).
Week 4 (7/14-7/18)
Monday: Systems of coordinates (change of basis) (LA 21)
Tuesday: Eigenvectors and Eigenvalues (LA 23)
Wednesday: Trace, determinant, examples (no specific chapter) Deadline to notify me of midterm time conflicts, and give OAE letters.
Thursday: Symmetric matrices (LA 25)
Friday: Quadratic forms (LA 26)
We will skip chapter 22 as you can see but you may need a little information from it:
  • Reference for matrix transpose: p124-5
  • Reference for orthonormal basisx: p162
  • Reference for orthogonal matrix: p162,
  • Reference for orthonormal basis: p164-5
  • Week 5 (7/21-7/25)
    Monday: Multivariable functions, Graphs, Level Sets
    Tuesday: Level sets of quadratic forms
    Wednesday: Limits and continuity, Squeeze Theorem.
    7-9pm Midterm on the material of weeks 1-4.
    Thursday: Parametric Curves, and how to make them
    Friday: More on tangent lines and using curves in limits; partial and higher-order derivatives
    Week 6 (7/28-8/1)
    Monday: Total derivative, differentiability
    Tuesday: Linearization and Quadratic approximation
    Wednesday: Chain Rule, tree diagrams
    Thursday: Directional derivatives and gradient
    Friday: Gradient, graphs, level sets bigger picture
    Deadline to give informal notice of access needs for final exam.
    Week 7 (8/4-8/8)
    Monday: Conceptual review of surfaces, planes, normal vectors, gradient
    Tuesday: Tangent planes to implicit surfaces, more gradient uses
    Wednesday: Extrema of Multivariable Functions (DVC 12)
    Thursday: Examples and discussion
    Friday: Extrema of Multivariable Functions (DVC 13)
    Week 8 (8/11-8/16)
    [8/16 Final exam, 12:15pm-3:15pm]
    Monday: Lagrange Multipliers (DVC 14)
    Tuesday: More on Lagrange multipliers and local extrema
    Wednesday: Last on Lagrange, and Google PageRank
    Thursday: Review, 1:15-3:15
    Saturday: FINAL EXAM

    Summer 2014 -- Department of Mathematics, Stanford University
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