MAT 532 Fall 2014

by Graham

Basic Info

Instructor
Prof. Graham Leuschke
gjleusch@syr.edu
Time & Place
TR 2:00–3:20 in Carnegie 316
Textbook
Peter J. Olver and Chehrzad Shakiban, Applied Linear Algebra (website)
Office Hours
Mon 2-4, Tues 10:30-12, Wed 3-4, Thurs 1-2; by appointment; and any time my door is open (317G Carnegie)
Important documents
syllabus

Announcements

  • My office hours for finals week are M 2-4, T 10:30-12, and W 2-4. You can pick up your graded HW 13 at those times.
  • The final exam will be on Wednesday December 10 at 5:15pm. It will be cumulative, with an emphasis on the material since the second exam (modifications of Gram-Schmidt, orthogonal matrices, QR factorization, orthogonal projections, the Fredholm Alternative, and singular value decompositions).
  • The second midterm exam was postponed one week from the date in the syllabus. It was given in class on Thursday 13 November and covered up through page 230 (the “unmodified” Gram-Schmidt process).
  • The first midterm exam was given in class on 2 October. It covered up through section 3.3 on examples of inner products3.2 on norms.

Problem Sets

  • Here are some problems on the material that hasn’t been covered by any homework sets.
    • (Fredholm Alternative) 5.6.20 (and compare page 109 and problem 2.5.3)
    • (SVD) 8.5.1 cde for practice finding eigenvalues
    • (SVD) 8.5.2 for finding the SVD given the eigenvalues: (a) 3+sqrt(5), 3-sqrt(5), (b) 1 and 1, (c) 5sqrt(2) and 0, (d) 3, 2, and 0, (e) sqrt(7), sqrt(2), and 0 (f) 3, 1, and 0.
  • HW #13, due Thursday 4 Dec:
    • 5.3.1 (a,b,c)
    • 5.3.27 (a,b,c,d)
    • 5.3.28 (i) and (ii)
    • 5.4.1 (a,b,c)
    • 5.4.2 (a)
  • HW #12, due Thursday 20 Nov:
    • 5.2.17 (b,c)
    • 5.2.18 (b,c)
  • HW #11, due Thursday 13 Nov:
    • 5.1.1 (a,b,c,d)
    • 5.1.5 (all)
    • 5.1.21 (b)
    • 5.1.25
    • 5.2.1 (b,c)
    • 5.2.8 part (i) (b,c)
  • HW #10, due Thursday 6 Nov:
    • 4.3.1
    • 4.3.7
    • 4.3.15 (b,c) and also compute the error
    • 4.4.1 (a,b)
    • 4.4.5
    • 4.4.12 (b,c)
  • HW #9, due Thursday 30 Oct:
    • 6.2.1(b,c,d)
    • 6.2.2
    • 6.2.4
    • 4.2.1
    • 4.2.3(a,c)
    • 4.2.5(a,c)
    • 6.1.13(b,c)
  • HW #8, due Thursday 23 Oct:
    • 6.1.1
    • 6.1.2
    • 6.1.3
    • 6.1.4(a)
    • 6.1.8(a)
  • HW #7, due Thursday 16 Oct:
    • 3.4.1 (b,d,f)
    • 3.4.22 (parts a and b for problems (i),(iii), and (v))
    • 3.4.25
    • 3.4.27
    • 3.5.2 (b,d,f)
    • 3.5.4
    • 3.5.19 (a,c)
  • HW #6, due Thursday 9 Oct:
    • 3.3.20 (a,c,d)
    • 3.3.28 (a,b,c)
    • 3.4.1 (b,d,f)
    • 3.4.22 (parts a and b for problems (i),(iii), and (v))
    • 3.4.25
    • 3.4.27
  • HW #5, due Thursday 2 Oct:
    • 3.1.19 (a,b)
    • 3.1.20 (a,b)
    • 3.2.1 (b,c)
    • 3.2.4 (a,b,c) (Equation (3.9) is at the bottom of p. 132)
    • 3.2.13 (a,b)
    • 3.3.2 (a,b,c)
    • 3.3.6 (a,b,c)
  • HW #4, due Thursday 25 Sept:
    • 2.3.21 (a,c,e)
    • 2.4.9 (a,b,c)
    • 2.5.2 (b,d,f)
    • 2.5.22
    • 2.5.24 (all parts, items (ii) and (v))
    • 2.6.1 (a,b,c,d)
    • 2.6.3 (a,b,c,d)
    • 2.6.4 (a,b,c,d)
  • HW #3, due Thursday 18 Sept:
    • 1.7.9 (b)
    • 11.4.14 (a,b) (on splines)
    • 1.7.16 (a,b,c)
    • 1.8.7 (b,d,g,i)
    • 1.8.23 (a,b)
    • 2.3.2
    • 2.3.9
  • HW #2, due Thursday 11 Sept:
    • 1.4.1 (a,c,e)
    • 1.4.3 (a; be sure to use GE exactly)
    • 1.4.15
    • 1.4.19 (a,b,d)
    • 1.4.20 (a)
    • 1.5.32 (a,c,e)
    • 1.6.25 (b,d)
  • HW #1, due Thursday 4 Sept:
    • 1.3.5
    • 1.3.14
    • 1.3.15
    • 1.3.22 (a,c,e,g)
    • 1.3.31 (a,c,e,g)

It has been said that ‘the human mind has never invented a labor-saving machine equal to algebra.’ If this be true, it is but natural and proper that an age like our own, characterized by the multiplication of labor-saving machinery, should be distinguished by the unexampled development of this most refined and most beautiful of machines.

Josiah Willard Gibbs, 1887