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Math 51
Winter 2017

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Textbook abbreviations
L = Linear Algebra (Levandosky); Part 1 of reader
C = Vector Calculus (Colley); Part 2 of reader

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

Week 1 (1/9-1/13)
[1/9 Preliminary study list deadline]
[1/9 First lecture; 1/10 first section]
L1: Vectors in Rn
L2: Linear Combinations, Span
L3: Linear Independence
L4: Dot Product, Cross Product (see also projections, L14 p92-3)
Week 2 (1/16-1/20)
[1/16 MLK day, no classes]
L5: Systems of Linear Equations
L6: Matrices, Rref
L7: Matrix-Vector Products
L8: Null Space
Week 3 (1/23-1/27)
[1/27 Final study list deadline]
L9: Column Space
L10: Subspaces of Rn
L11: Basis (see also coordinates, L21 p145-7)
L12: Dimension
Week 4 (1/30-2/3)
[2/2 Exam 1, approx 7:30pm; covers thru end of Week 3 topics listed above]
L13-14 (thru p93): Linear Transformations and Examples
C2.1: Multivariable Functions: Graphs, Level Sets
(As time permits) brief review of Single-Variable Calculus
C2.3 (p116-28 only); C4.1 (p244-51 only): Partial Derivatives, Differentiability; Applications -- Tangent Planes to Graphs; First-Order (Linear) Approximation and Differentials
Week 5 (2/6-2/10)
C2.4 (p134-8): Higher-Order Derivatives; Interpretation of Contour Maps
L15: Composition and Matrix Multiplication
L16: Inverses; Applications -- Linear Systems, Coordinates (see also L21, p145-9 only)
Week 6 (2/13-2/17)
C2.5: Chain Rule
C2.6 (p158-68 only): Directional Derivatives and Gradient; Application -- Tangent Planes to Implicit Surfaces
L17: Determinants
Week 7 (2/20-2/24)
[2/20 Presidents' Day, no classes]
[2/23 Exam 2, approx 7:30pm; covers thru end of Week 6 topics listed above]
L18-19: Transposes, Row Spaces, Orthogonal Complements; Application -- Minimum Magnitude Solution (Constrained Least Squares)
L20: Orthogonal Projections; Application -- Least Squares Approximation
Week 8 (2/27-3/3)
[3/3 Course withdrawal and change of grading basis deadline]
L22: Orthonormal Bases; Applications -- Projections, Coordinates (see also L21, p145-9 only)
C4.1 (p252-55 only): Quadratic approximation (second-degree Taylor polynomial), Hessian matrix; Application -- Concavity in a given direction; Quadratic forms, Definiteness
C4.2 (p263-67 & 270-74 only): Extrema of Functions
Week 9 (3/6-3/10)
C4.3 (p278-286): Lagrange Multipliers [case of one constraint, thru p283]
Applications of Extrema -- Definiteness of Quadratic Forms, Eigenvalues; Second Derivative Test -- Handout on eigenvalues, eigenvectors and definiteness
C4.3 (p278-286): Lagrange Multipliers [continued; case of multiple constraints p284-6]
Weeks 10-11 (3/13-3/20)
[3/16 Last section; 3/17 last lecture]
[3/20 Final Exam, 7-10pm; comprehensive but more heavily emphasizes topics since Exam 2]
C4.4 (p293-7 & 301-3): Applications of Extrema -- Least Squares (Constrained & Unconstrained) Revisited; Applications in the Natural and Social Sciences

Winter 2017 -- Department of Mathematics, Stanford University
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