Linear Algebra (MATH 511, Spring 2018)

Teacher: Alexandre Eremenko
OFFICE HOURS:  Math 600 TBA

PHONE: (765) 494-1975

EMAIL: eremenko@math.purdue.edu

GENERAL INFORMATION

Notice: We use FOURTH edition of Strang's text Linear Algebra and its applicatons. The Homework is assigned from the 4-th edition. It must be available in the University bookstore, and there is a copy on reserve in the MATH library on the 3-d floor of the Math building.

Midterm exam: February 28, 6:30 p.m., ME 1061.

HW 1 (due January 16, before the class begins) 1.2.5, 1.2.11, 1.2.13, 1.3.1, 1.3.4, 1.3.5, 1.4.1, 1.4.14, 1.4.17, 1.4.19.

HW 2: (due January 23) 1.5.4, 1.5.11, 1.5.14, 1.5.15, 1.6.6, 1.6.10, 1.6.11, 2.1.2, 2.1.7, 2.2.3, 2.2.6.

HW 3 (due January 30): 2.3.2, 2.3.7, 2.3.10, 2.3.13, 2.3.20, 2.4.3, 2.4.18, 2.4.20, 2.6.1, 2.6.6, 2.6.8, 2.6.9, 2.6.16.

HW 4 (due February 6): 2.6.18, 2.6.19, 2.6.21, 3.1.2, 3.1.6, 3.1.9, 3.1.16, 3.2.3, 3.2.5, 3.2.8, 3.2.9, 3.2.10.

HW 5 (due February 13): 3.3.4, 3.3.6, 3.3.12, 3.3.18, 3.4.6, 3.4.13, 3.4.14, 3.4.20, 3.4.21, 3.4.28.

Midterm exam is on Wednesday February 28, 6:30-8:00, ME 1061. It is an exam with closed books, no notes or calculators are allowed. Covers chapters 1,2,3, except 1.7, 2.5, 3.5. The problems in the exam will be similar to those in HW and in Review sections at the end of each chapter. Some problems are with full credit, and others yes/no or multiple choice type.

Practice exam Many multiple choice problems can be found here. The relevant quizzes are Elementary matrices, Inner product spaces, Linear algebra, Linear systems, Linear transformations, Vector spaces.

HW 6 (due February 20) is in the handout here, do all exercises WITHOUT star(*): pdf. In addition to this handout you may read "Complex numbers and their conjugates" on p. 281-282, and from "Complex roots of Unity" to "Fast Fourier transform" on p. 189-193. This material is not covered by the midterm exam.

Here you can see pictures of an analog Fourier synthesizer, a high-precision instrument, used to compute Fourier coefficients and to sum a Fourier series in pre-computer era (until the middle of XX century).
And here is a short biography of Cornelius Lanczos who invented the Fast Fourier transform while working at Purdue University.

There is no homework due no Febr 27. Practice for the exam. Practice exam with some answers On February 22 we will have a review. I will solve the rest of the problems in class.

Exam solutions

HW 7 (due March 6): 4.2.3, 4.2.4, 4.2.5, 4.2.17, 4.3.7, 4.3.8, 4.3.12, 4.3.13, 4.4.3, 4.4.13, 4.4.14, 4.4.24.

You may find this handout: Determinants useful (There are no problems in it, it is just a condensed exposition of the topic).

HW 8 (due March 20): 5.1.1, 5.1.5, 5.1.7, 5.1.14, 5.1.18, 5.2.1, 5.2.2, 5.2.5, 5.2.6, 5.2.9, 5.2.10, 5.2.15.

Additional topics: Spectral theorems for Hermitian and unitary matrices (required reading), 25 billion dollars eigenvector (optional reading).

HW 9 (due March 27): 5.3.4, 5.3.6, 5.3.9, 5.4.1, 5.4.8, 5.4.9, 5.4.14, 5.4.15, 5.5.7, 5.5.12, 5.5.17, 5.5.20.

Class on April 3 is cancelled

(as a compensation for the evening exam).

HW 10 (due April 5): 5.6.2, 5.6.14, 5.6.15, 5.6.16 (a) 5.6.23, 5.6.24, 5.6.28, 5.6.30, 5.6.31,
String with beads, Rotations in 3-space. (There is no HW in these handouts).

HW 11 (due April 10) 6.1.2, 6.1.7, 6.1.13. 6.2.1, 6.2.7, 6.2.10, 6.2.12, 6.2.15.

Singular Value Decomposition, Simultaneous diagonalization and small oscillations, Extremal principles.

HW 12 (due April 17, last one): 6.3.5, 6.3.2, 6.3.11, 6.3.12, 6.4.1, 6.4.5, 6.4.7, 6.4.11 (Read p. 339-341 for 6.4.1).

Final exam: Wed May 2, 1-3 p.m. 13, WTHR 172.

Practice problems. Some solutions (Misprints corrected on Apr. 25, 13:32.)

Final exam covers all material that we studied: that is Chapters 1-6 except 1.7, 2.5, 6.5.