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Math 51
Fall 2015

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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 (9/21-9/25)
[9/21 Preliminary study list deadline]
[9/21 First lecture; 9/24 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 (9/28-10/2)
L5: Systems of Linear Equations
L6: Matrices, Rref
L7: Matrix-Vector Products
L8: Null Space
L9: Column Space
Week 3 (10/5-10/9)
[10/9 Final study list deadline]
L10: Subspaces of Rn
L11: Basis (see also coordinates, L21 p145-7)
L12: Dimension
Week 4 (10/12-10/16)
[10/13 Exam 1, approx 7:30pm; roughly covers thru end of Week 3 topics listed above]
L13-14: Linear Transformations and Examples
C2.1: Multivariable Functions, Graphs, Level Sets
Review of Single-Variable Calculus
Week 5 (10/19-10/23)
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
L15: Composition and Matrix Multiplication
Week 6 (10/26-10/30)
C2.5: Chain Rule
C2.6: Directional Derivatives and Gradient; Application -- Tangent Planes to Implicit Surfaces
L16: Inverses; Applications to Linear Systems
Week 7 (11/2-11/6)
[11/5 Exam 2, approx 7:30pm; roughly covers thru end of Week 6 topics listed above]
L17: Determinants
L18-19: Transposes, Row Spaces, Orthogonal Complements; Application -- Minimum Magnitude Solution (Constrained Least Squares)
L20: Orthogonal Projections; Application -- Least Squares Approximation
Week 8 (11/9-11/13)
[11/13 Course withdrawal and change of grading basis deadline]
L22: Orthonormal Bases; Applications -- Projections, Coordinates (see also L21, p145-7 only)
C4.1 (p252-5 only): Hessian matrix
C4.2: Extrema of Functions
Week 9 (11/16-11/20)
C4.3 (p278-286): Lagrange Multipliers
C4.4: Applications of Extrema in the Natural and Social Sciences; Least Squares (Constrained & Unconstrained) Revisited; Definiteness of Quadratic Forms, Eigenvalues
Weeks 10-11 (11/30-12/7)
[12/3 Last section; 12/4 last lecture]
[12/7 Final Exam, 7-10pm]

Autumn 2015 -- Department of Mathematics, Stanford University
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