## 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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