Math 458/508 (Fall 2007)

Syllabus

Office Hours and Contact Information

• MW 10:30 -- 12:00 am, 3:00 -- 4:30 pm, or by appointment
• Shelby Center 258M
  (256) 824-2229
  ais@email.uah.edu
  

Assignments

• &1.1: 7, 9, 10, 11, 14, 16, 17, 18, 20, 22, 26, 27, 28, 32
• &2.1: 3, 6 (a)-(e), 12, 13, 14, 17, 18
• &2.2: 1, 2, 3, 5, 8-11, 14, 15, 18, 19, 22
• &2.3: 1 (1)-(c), 2-6, 8-10, 12, 15, 21
• &3.1: 1-5, 9, 10, 14, 15
• &3.2: 1 (a), (c), (e), 2, 3, 4, 7, 8, 9, 10, 12
• &3.3: 1, 5, 6, 7, 8, 9, 10, 11, 12
• &3.4: 1-4, 6, 8-11, 13
• &4.1: 1, 2, 5, 6, 9, 10
• &4.2: 1, 2, 3, 8
• &4.3: 1, 5, 7, 8, 9, 16
• &5.4: 1, 3, 6, 7, 8, 9, 10, 12 - 16
• Solution to Test 1 (old) (pdf )
• Solution to Test 2 (old) (pdf )
• &6.1: 1, 2, 3, 4, 9, 11, 12, 13
• &6.2: 1, 2, 5, 6, 8, 9, 10, 11, 13, 14
• Solutions to two problems in &6.2: pdf , pdf
• &7.1: 3, 4, 5, 7, 9, 10, 11, 14, 16
• Requirements for the final (from 11:30 am --2:00 pm on Dec. 5): Gauss-Jordan elinimination method to solve linear systems; basis for the null space and column space of a matrix; bases and dimensions for vector spaces and subspaces; linear transformations; eigenvalues, eigenvectors, eigen-space, algebraic and geometric multiplicities of an eigenvalue; diagonlizations; Jordan canonical matrix, Jordan blocks; computations of A^k and e^A, solve differential equations; inner product spaces, orthogonality, orthogonal projection of a vector on a subspace, orthogonal projection matrix in R^n, Gram-Schmidt orthogolization process, finding othogonal bases for subspaces; unitary matrix, rotation matrix, reflection matrix, the Housholder matrix, properties of unitary matrices, unitary similarity, extension of an orthogonal set to an orthogonal basis for R^n; the Schur decomposition; normal matrix, properties of normal matrices and Hermitian matrices, unitarily diagonalize a normal matrix; singular value decomposition; the least squares problems. Here are two old finals I gave previously: 1, 2 .

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