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Math 51
Spring 2014

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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 (3/31-4/4)
[3/31 Preliminary study list deadline]
[3/31 First lecture; 4/1 first section]
LA 1: Vectors in Rn
LA 2: Linear Combinations, Span
LA 3: Linear Independence
LA 4: Dot Product, Cross Product
LA 5: Systems of Linear Equations
LA 6: Matrices, Rref
Week 2 (4/7-4/11)
LA 7: Matrix-Vector Products (see also LA 15: Matrix Multiplication, p99-101 only)
LA 8: Null Space
LA 9: Column Space
LA 10: Subspaces of Rn
LA 11: Basis
Week 3 (4/14-4/18)
[4/18 Final study list deadline]
LA 12: Dimension
LA 13: Linear Transformations
LA 14: Examples of Linear Transformations
LA 15: Composition and Matrix Multiplication
Week 4 (4/21-4/25)
[4/24 Exam 1, 7:30-9:30pm; roughly covers thru end of Week 3 topics listed above]
LA 16: Inverses
LA 17: Determinants
LA 21: Systems of Coordinates
Week 5 (4/28-5/2)
LA 21: Systems of Coordinates (ctd)
LA 23: Eigenvectors and Eigenvalues
LA 25: Symmetric Matrices
  • Reference for matrix transpose: p124-5
  • Reference for orthonormal basis: p162
  • Reference for orthogonal matrix: p164-5
  • Week 6 (5/5-5/9)
    LA 26: Quadratic Forms
    DVC 1: Multivariable Functions, Graphs, Level Sets
    DVC 4: Parametric Curves
    DVC 7: Partial and Higher Order Derivatives; Differentiability and Total Derivative
    Week 7 (5/12-5/16)
    [5/15 Exam 2, 7:30-9:30pm; roughly covers thru end of Week 6 topics listed above]
    DVC 7: Partial and Higher Order Derivatives; Differentiability and Total Derivative (ctd)
    DVC 10.3; 11: Applications of Differentiation -- Tangent Planes to Graphs; Linearization and Quadratic Approximation
    DVC 8: Chain Rule
    Week 8 (5/19-5/23)
    [5/23 Course withdrawal and change of grading basis deadline]
    DVC 9; 10.2: Directional Derivatives and Gradient; Application -- Tangent Planes to Implicit Surfaces
    DVC 12: Extrema of Multivariable Functions (I)
    DVC 13: Extrema of Multivariable Functions (II)
    Week 9 (5/26-5/30)
    [5/26 Memorial Day, no classes]
    DVC 14: Lagrange Multipliers
    Week 10 (6/2-6/6)
    [6/3 Last section; 6/4 last lecture]
    [6/6 Final Exam, 7-10pm; comprehensive but more heavily emphasizes topics since Exam 2]
    Google Lecture (optional) [notes]

    Spring 2014 -- Department of Mathematics, Stanford University
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