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Math 51
Winter 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 (1/5-1/9)
[1/5 Preliminary study list deadline]
[1/5 First lecture; 1/6 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 (1/12-1/16)
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 (1/19-1/23)
[1/19 Martin Luther King Day, no classes]
[1/23 Final study list deadline]
LA 10: Subspaces of Rn
LA 11: Basis (see also coordinates, p145-7)
LA 12: Dimension
Week 4 (1/26-1/30)
[1/29 Exam 1, 7:30-9:30pm; covers thru end of Week 3 topics listed above]
LA 13: Linear Transformations
LA 14: Examples of Linear Transformations
LA 15: Composition and Matrix Multiplication
LA 16: Inverses
Week 5 (2/2-2/6)
LA 17: Determinants
LA 21: Systems of Coordinates (p145-9 only) (see also orthonormal basis, p162 only)
LA 23: Eigenvectors and Eigenvalues
Week 6 (2/9-2/13)
LA 25: Symmetric Matrices
  • Reference for matrix transpose: p124-5
  • Reference for orthonormal basis: p162
  • LA 26: Quadratic Forms
    DVC 1: Multivariable Functions, Graphs, Level Sets
    Week 7 (2/16-2/20)
    [2/16 Presidents' Day, no classes]
    [2/19 Exam 2, 7:30-9:30pm; covers thru end of Week 6 topics listed above]
    DVC 4: Parametric Curves
    DVC 7: Partial and Higher Order Derivatives; Differentiability and Total Derivative
    DVC 10.3; 11: Applications of Differentiation -- Tangent Planes to Graphs; Linearization and Quadratic Approximation
    Week 8 (2/23-2/27)
    [2/27 Course withdrawal and change of grading basis deadline]
    DVC 10.3; 11: Applications of Differentiation (ctd)
    DVC 8: Chain Rule
    DVC 9; 10.2: Directional Derivatives and Gradient; Application -- Tangent Planes to Implicit Surfaces
    Week 9 (3/2-3/6)
    DVC 12: Extrema of Multivariable Functions (I)
    DVC 13: Extrema of Multivariable Functions (II)
    DVC 14: Lagrange Multipliers
    Week 10-11 (3/9-3/16)
    [3/12 Last section; 3/13 last lecture]
    [3/16 Final Exam, 7-10pm; comprehensive but more heavily emphasizes topics since Exam 2]
    DVC 14: Lagrange Multipliers (ctd)
    Google Lecture (optional) [notes]

    Winter 2015 -- Department of Mathematics, Stanford University
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