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Math 51
Spring 2015

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Textbook abbreviations
LA = Linear Algebra (Levandosky)
DVC = Differential Vector Calculus (Licata)

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

Week 1 (3/30-4/3)
[3/30 Preliminary study list deadline]
[3/30 First lecture; 3/31 first section]
LA 1: Vectors in Rn
LA 2: Linear Combinations, Span
LA 3: Linear Independence
LA 4: Dot Product, Cross Product (see also projections, p92-3)
Week 2 (4/6-4/10)
LA 5: Systems of Linear Equations
LA 6: Matrices, Rref
LA 7: Matrix-Vector Products (see also matrix multiplication, p99-101)
LA 8: Null Space
LA 9: Column Space
Week 3 (4/13-4/17)
[4/17 Final study list deadline]
LA 10: Subspaces of Rn
LA 11: Basis (see also coordinates, p145-7)
LA 12: Dimension
LA 13-14: Linear Transformations and Examples
Week 4 (4/20-4/24)
[4/23 Exam 1, 7:30-9:30pm; roughly covers thru end of Week 3 topics listed above]
DVC 1: Multivariable Functions, Graphs, Level Sets
DVC 4: Parametric Curves
DVC 7: Partial and Higher Order Derivatives; Differentiability and Total Derivative
Week 5 (4/27-5/1)
DVC 10.3; 11.1: Applications of Differentiation -- Tangent Planes to Graphs; Linearization; Interpretation of Contour Maps
LA 15: Composition and Matrix Multiplication
DVC 8: Chain Rule
Week 6 (5/4-5/8)
DVC 9; 10.2: Directional Derivatives and Gradient; Application -- Tangent Planes to Implicit Surfaces
LA 16: Inverses
LA 17: Determinants
LA 21: Systems of Coordinates (p145-9 only) (see also orthonormal basis, p162 only)
Week 7 (5/11-5/15)
[5/14 Exam 2, 7:30-9:30pm; roughly covers thru end of Week 6 topics listed above]
LA 23: Eigenvectors and Eigenvalues
LA 25: Symmetric Matrices
  • Reference for matrix transpose: p124-5
  • Reference for orthonormal basis: p162
  • LA 26: Quadratic Forms
    Week 8 (5/18-5/22)
    [5/22 Course withdrawal and change of grading basis deadline]
    DVC 11.2: Quadratic Approximation
    DVC 12: Extrema of Multivariable Functions (I)
    DVC 13: Extrema of Multivariable Functions (II)
    Week 9 (5/25-5/29)
    [5/25 Memorial Day, no classes]
    DVC 14: Lagrange Multipliers
    Week 10 (6/1-6/5)
    [6/2 Last section; 6/3 last lecture]
    [6/5 Final Exam, 7-10pm; comprehensive but more heavily emphasizes topics since Exam 2]
    Google Lecture (optional) [notes]

    Spring 2015 -- Department of Mathematics, Stanford University
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