Syllabus

Wk	Lec	Date	Topic	Book	Hwk
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15	1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45	01/12 01/14 01/16 01/19 01/21 01/23 01/26 01/28 01/30 02/02 02/04 02/06 02/09 02/11 02/13 02/16 02/18 02/20 02/23 02/25 02/27 03/01 03/03 03/05 03/15 03/17 03/19 03/22 03/24 03/26 03/29 03/31 04/02 04/05 04/07 04/09 04/12 04/14 04/16 04/19 04/21 04/23 04/26 04/28 04/30	Systems of Linear Equations Gauss-Jordan Elimination Gauss-Jordan Elimination in Matrix Notation Introduction to Solutions of Linear Systems Introduction to Linear Transformations and Their Inverses Linear Transformations in Geometry The Inverse of a Linear Transformation Matrix Products Image and Kernel of a Linear Transformation Subspaces. Bases and Linear Independence The Dimension of a Subspace Snowstorm. No class Coordinates Introduction to Linear Spaces Linear Transormations Coordinates in a Linear Space Orthonormal Bases and Orthogonal Projections Gram-Schmidt Process and QR Factorization Orthogonal Transformations and Orthogonal Matrices Least Squares and Data Fitting Inner Product Spaces Review Review Midterm Introduction to Determinants Properties of the Determinant Geometrical Interpretations of the Determinant Eigenvalues and Eigenvectors Characteristic Polynomial Dynamical Systems Eigenbasis and Eigenspace; Multiplicity of eigenvalues Complex eigenvalues Diagonalizability The Jordan Canonical Form Stability Continuous Dynamical Systems Complex case Linear Differential Equations Symmetric Matrices Symmetric Matrices Quadratic Forms Singular Values Review of Linearity Review of Orthogonality Review of the Eigenvalue Problem	1.1 1.2 1.3 1.3 2.1 2.2 2.3 2.4 3.1 3.2 3.3 3.4 4.1 4.2 4.3 5.1 5.2 5.3 5.4 5.5 6.1 6.2 6.3 7.2 7.2 7.1 7.3 7.5 7.4 Notes 7.6 9.1 9.2 9.3 8.1 8.1 8.2 8.3	#1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13