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Math 51
Winter 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 (1/4-1/8)
[1/4 Preliminary study list deadline]
[1/4 First lecture; 1/5 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 (1/11-1/15)
L5: Systems of Linear Equations
L6: Matrices, Rref
L7: Matrix-Vector Products
L8: Null Space
L9: Column Space
Week 3 (1/18-1/22)
[1/18 MLK day]
[1/22 Final study list deadline]
L10: Subspaces of Rn
L11: Basis (see also coordinates, L21 p145-7)
L12: Dimension
Week 4 (1/25-1/29)
[1/28 Exam 1, approx 7:30pm; covers thru end of Week 3 topics listed above]
C2.1: Multivariable Functions, Graphs, Level Sets
L13-14: Linear Transformations and Examples
(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
Week 5 (2/1-2/5)
C2.3; C4.1 (p244-251 only): Partial Derivatives, Differentiability; Applications -- Tangent Planes to Graphs; First-Order (Linear) Approximation and Differentials [continued]
C2.4: Higher-Order Derivatives; Interpretation of Contour Maps
L15: Composition and Matrix Multiplication
C2.5: Chain Rule
Week 6 (2/8-2/12)
C2.6: Directional Derivatives and Gradient; Application -- Tangent Planes to Implicit Surfaces
L16: Inverses; Applications -- Linear Systems, Coordinates (see also L21, p145-9 only)
L17: Determinants
Week 7 (2/15-2/19)
[2/15 President's day]
[2/18 Exam 2, approx 7:30pm; 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
Week 8 (2/22-2/26)
[2/26 Course withdrawal and change of grading basis deadline]
L22: Orthonormal Bases; Applications -- Projections, Coordinates (see also L21, p145-9 only)
C4.1 (p255 only): Hessian matrix
C4.2: Extrema of Functions
Week 9 (2/28-3/4)
C4.3 (p278-286): Lagrange Multipliers
C4.4 (p293-7 only): Applications of Extrema -- Least Squares (Constrained & Unconstrained) Revisited
Week 10 (3/7-3/11)
[3/10 Last section; 3/11 last lecture]
[3/14 Final Exam, 7-10pm; comprehensive but more heavily emphasizes topics since Exam 2]
Applications of Extrema in the Natural and Social Sciences; Definiteness of Quadratic Forms, Eigenvalues; Second Derivative Test Revisited

Autumn 2015 -- Department of Mathematics, Stanford University
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