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Math 51
Spring 2016

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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 (3/28-4/1)
[3/28 Preliminary study list deadline]
[3/28 First lecture; 3/29 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 (4/4-4/8)
L5: Systems of Linear Equations
L6: Matrices, Rref
L7: Matrix-Vector Products
L8: Null Space
L9: Column Space
Week 3 (4/11-4/15)
[4/15 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 (4/18-4/22)
[4/21 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; C4.1 (p244-251 only): Partial Derivatives, Differentiability; Applications -- Tangent Planes to Graphs; First-Order (Linear) Approximation and Differentials
C2.4: Higher-Order Derivatives; Interpretation of Contour Maps
Week 5 (4/25-4/29)
L15: Composition and Matrix Multiplication
C2.5: Chain Rule
C2.6 (p158-68 only): Directional Derivatives and Gradient; Application -- Tangent Planes to Implicit Surfaces
Week 6 (5/2-5/6)
L16: Inverses; Applications -- Linear Systems, Coordinates (see also L21, p145-9 only)
L17: Determinants
C4.1 (p252-55 only): Quadratic approximation (second-degree Taylor polynomial), Hessian matrix; Application -- Concavity in a given direction; Quadratic forms, Definiteness
Week 7 (5/9-5/13)
[5/12 Exam 2, 7:30-9:30pm; 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
L22: Orthonormal Bases; Applications -- Projections, Coordinates (see also L21, p145-9 only)
Week 8 (5/16-5/20)
[5/20 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]
Week 9 (5/23-5/27)
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]
C4.4 (p293-7 & 301-3): Applications of Extrema -- Least Squares (Constrained & Unconstrained) Revisited; Applications in the Natural and Social Sciences
Week 10 (5/30-6/3)
[5/30 Memorial day]
[5/31 Last section; 6/1 last lecture]
[6/3 Final Exam, 7-10pm, Hewlett 200; comprehensive but more heavily emphasizes topics since Exam 2]

Spring 2016 -- Department of Mathematics, Stanford University
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