- Meeting:
MWF, 12:30pm-1:20 pm, PDL C-36
- Office hours:
WF 2-3pm; also by appointment
- TA:
Elliot Paquette (paquette at
math)
- TA Office hours:
Th 1-3pm, PDL C-8K
- Lecture Notes (fairly draft-y)
- Lecture 1, Linear
Algebra Review (09/24)
- Lecture 2, Linear
Algebra Review and Duality (09/26)
- Lecture 3, Duality,
Annihilators, Bi/Sesquilinear forms (09/28)
- Lecture 4, Inner
Products and Norms
(10/01)
- Lecture 5, Norm
Properties in Finite Dimensional Spaces and Completeness
(10/03)
- Lecture 6, Completeness;
Completeness of Metric Spaces; Series in Complete Normed
Spaces (10/05)
- Lecture 7, Norms
on Operators; Boundedness, Completeness, and Dual
Norms (10/08)
- Lecture 8, Geometric
Properties of the Dual Norm
(10/10)
- Lecture 9, Geometric
Properties; Submultiplicativity; Matrix Norms
(10/12)
- Lecture 10,
Consistent Norms and Analysis with Operators
(10/15)
- Lecture 11,
Norms on Operators; The Dual and Adjoint Transformations, Condition Numbers and Error Sensitivity
(10/17)
- Lecture 12,
Condition Numbers and Error Sensitivity. Finite Dimensional Spectral Theory: Intro
(10/19)
- Lecture 13,
Finite Dimensional Spectral Theory: Hermitian,
skew-Hermitian, unitary, normal matrices
(10/22)
- Lecture 14,
Normal matrices; Unitary Equivalence; and the Schur
Triangular Transformation
(10/24)
- Lecture 15,
The Cayley-Hamilton theorem, Rayleigh Quotients and the
Courant-Fischer Minimax Principle
(10/26)
- Lecture 16,
The Jordan Form, I
(10/29)
- Lecture 17,
The Jordan Form, II
(10/31)
- Lecture 18,
The Jordan Form, III
(11/02)
- Lecture 19,
The Singular Value Decomposition
(11/05)
- Lecture 20,
Applications of the SVD; The Gram-Schmidt Process and the
QR factorization
(11/07)
- Lecture 21,
The Gram-Schmidt Process and the QR factorization; Least
Squares
(11/09)
- Lecture 22,
Least Squares and the Moore-Penrose pseudo-inverse
(11/12)
- Lecture 23,
The LU factorization
(11/14)
- Lecture 24,
The QR Algorithm
(11/19)
- Lecture 25,
The Resolvent, I
(11/21)
- Lecture 26,
The Resolvent, II
(11/26)
- Lecture 27,
The Spectral Mapping Theorem and Applications
(11/28)
- Lecture 28,
Intro to ODEs
(11/30)
- Lecture 29,
Local Existence and Uniqueness for Lipschitz f
(12/03)
- Lecture 30,
Local Existence for continuous f
(12/05)
- Lecture 31,
Uniqueness for locally Lipschitz f
(12/07)