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Math 51
Spring 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 (4/3-4/7)
[4/3 Preliminary study list deadline]
[4/3 First lecture; 4/4 first section]
L1: Vectors in Rn
L2: Linear Combinations, Span
L3: Linear Independence
L4: Dot Product: Angle, Orthogonality and Applications (see also projections, L14 p92-3)
Week 2 (4/10-4/14)
L5: Systems of Linear Equations
L6: Matrices, Rref
L7: Matrix-Vector Products
L8: Null Space
L9: Column Space
Week 3 (4/17-4/21)
[4/21 Final study list deadline]
L10: Subspaces of Rn
L11: Basis (see also coordinates, L21 p145-7)
L12: Dimension
L13-14 (thru p94): Linear Transformations and Examples
Week 4 (4/24-4/28)
[4/27 Exam 1, 7:30-9:30pm; covers thru end of Week 3 topics listed above]
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
C2.4 (p134-8): Higher-Order Derivatives; Interpretation of Contour Maps
Week 5 (5/1-5/5)
L15: Composition and Matrix Multiplication
L16: Inverses; Applications -- Linear Systems, Coordinates (see also L21, p145-9 only)
C2.5: Chain Rule
Week 6 (5/8-5/12)
C2.6 (p158-68 only): Directional Derivatives and Gradient; Application -- Tangent Planes to Implicit Surfaces
C4.1 (p252-55 only): Quadratic approximation (second-degree Taylor polynomial), Hessian matrix; Application -- Concavity in a given direction; Quadratic forms, Definiteness
L17: Determinants
Week 7 (5/15-5/19)
[5/18 Exam 2, 7:30-9:30pm; roughly 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
L22: Orthonormal Bases; Applications -- Projections, Coordinates (see also L21, p145-9 only)
Week 8 (5/22-5/26)
[5/26 Course withdrawal and change of grading basis deadline]
C4.2 (p263-67 & 270-74 only): Extrema of Functions
C4.3 (p278-286): Lagrange Multipliers [case of one constraint, thru p283]
Course handout: Eigenvalues/Eigenvectors, Definiteness, and Second Derivative Test [application of constrained extrema]
Week 9 (5/29-6/2)
[5/29 Memorial day; no classes]
C4.3 (p278-286): Lagrange Multipliers [continued; case of multiple constraints p284-6]
C4.4 (p293-7 & 301-3): Applications of Extrema -- Least Squares (Constrained & Unconstrained) Revisited; Applications in the Natural and Social Sciences
Week 10 (6/5-6/9)
[6/6 Last section; 6/7 last lecture]
[6/9 Final Exam, 7-10pm; comprehensive but more heavily emphasizes topics since Exam 2]

Spring 2017 -- Department of Mathematics, Stanford University
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