OFFICE HOURS: Math 600 TTh: 3-4. PHONE: (765) 494-1975 EMAIL: eremenko@math.purdue.edu
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 21, 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 28) 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 February 4): 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 11): 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 Wednesday March 4, 6:30-7:30pm in ME 1061 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 18): 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 25)
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, but will be covered on
the final.
Additional problems on complex numbers
(not a part of the HW),
Additional problems at the end of section 3.4:
3.4.21, 3.4.22, 3.4.23, 3.4.25 (not a part of HW).
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.
No HW due on March 3. You may start doing HW 7 and practice for the exam. Problems at the ends of chapters of the textbook are good for practice.
HW 7 (due March 12): 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).
I was asked who discovered the formula for Fibonacci numbers. My guess was correct: it was Abraham de Moivre, though the formula itself is called Binet's formula (Binet lived about 2 centuries after de Moivre). De Moivre also discovered the trigonometric form of complex roots of unity. He also discovered Stirling's formula for n! before Stirling.
Answers and comments to the midterm exam
Online lectures (live recording) will be posted on Blackboard, 1 lecture ahead of the scheduled time. So the lecture scheduled 3.24 has been posted today. In addition to this I post pdf's of some lectures and handouts.
Instead of office hours we have Piazza Forum where you can ask questions. The link is https://piazza.com/purdue/spring2020/ma511.
HW 8 (due March 24) 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.
Lecture 3.24 pdf: Matrices with non-negative entries.
Handout: Matrices with positive entires
Lecture 3.26 pdf: Hermitian, unitary and normal matrices.
HW 9 (due March 31): 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.
Lecture 3.31 pdf: Applications of symmetric and orthogonal matrices.
Lecture 4.2 pdf: Jordan normal form.
Additional topics: Handout: Spectral theorems for Hermitian and unitary matrices (required reading), 25 billion dollars eigenvector (optional reading).
HW 10 (due April 7): 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).
Lecture 4.7. Bilinear and quadratic forms
HW 11 (due April 14) 6.1.2, 6.1.7, 6.1.13. 6.2.1, 6.2.7, 6.2.10, 6.2.12, 6.2.15.
Lecture 4.9. Positive definite and semi-definite forms
Lecture 4.14. Simultaneous diagonalization and a generalized eigenvalue problem
Lecture 4.16. Extremal principles
Lecture 4.21. Singular Value Decomposition,
HW 12 (due April 21, 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).
There will be no lecture 4.23. On 4.28 and 4.30 there will be review lectures (posted on Blackboard).
From my point of view, the quiz was successfull.
The format of the final will be EXACTLY the same.
You can see your answers and scores and correct answers on BB.
Next Tuesday I will record the last lecture (a review).
If you have any questions you want me to address in this lecture,
please ask on BB or e-mail.
Review problems. Solutions Added solution of probl. 22 from Review problems.
An old final exam. Solutions Added explanation of multiple choice problems and corrected one answer on 4.28 at 1210 ET.
Please do not hesitate to ask questions about solutions on the forum. I will address them either by e-mail, or on the forum, or in the remaining lectures.