Linear Algebra (MATH 511, Spring 2019)

Teacher: Alexandre Eremenko
OFFICE HOURS:  Math 600 TTh: 1:30-2:30.

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.

HW 1 (due January 15, 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 22) 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 29): 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 5): 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.

Midterm exam is on Thursday February 28, in class. It is 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.

HW 5 (due February 12): 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.

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 19) 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 26. Practice for the exam. Practice exam with some answers On February 26 we will have a review.

HW 7 (due March 5): 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).