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Linear Algebra (Math 301), Spring 2013


Course description

We discuss linear algebra from a matrix perspective. Topics to be covered include the algebra of vectors and matrices, elimination and decomposition methods for solving linear systems of equations, applications of eigenvalues and eigenvectors, vector spaces, linear transformations, and least squares techniques.

Course details

Send me an e-mail

If you haven't already done so, please send me an e-mail at donnacalhoun@boisestate.edu so that I can compile an e-mail list for the class. At the very least, include a subject header that says "Math 301". You may leave the message area blank, if you wish, or send me a short note about what you hope to get out of this course.


Basic course information

Instructor Prof. Donna Calhoun
Time MW 12:00-1:15
Place ILC 402
Office Hours (in my office, MG241A) Tuesdays, 11:00-12:00, or by special appt.
Prerequisites Math 175 (Calculus II)

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Course textbook

The required text for this course is

We will cover the material from topics from Chapters 1-6, with applications from Chapter 8 of the text.

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Course schedule and lectures

Below is a tentative course schedule, and electronic lecture material. Chapter and sections from the text book are indicated in parenthesis.

Links to assigned homework based on material covered lecture are also provided below. The .html version seems to work best on the Mac Safari browser. Please let me know about your experience with other browsers.

You are encouraged to read ahead in sections that will be covered in lectures. Thanks!

Week #1 (Jan. 23)

Wednesday : Review of linear systems of equations

(Lecture #1 : .pdf, .html)

Homework #1 due on Wednesday January 30.

Week #2 (Jan 28)

Monday : Introduction to vectors (1.1 and 1.2)

(Lecture #2 : .m4v, .html, .pdf) (Beta)

Wednesday : Matrices and solving linear systems (1.3 and 2.1)

(Lecture #3 : .m4v, .html, .pdf) (Corrected)

Homework #2 due on Wednesday February 6

Week #3 (Feb 4)

Monday : Using elimination to solve systems (2.2)

(Lecture #4 : .m4v, .html, .pdf) (Corrected)

Wednesday : Elimination using matrices; Matrix operations (2.3, 2.4)

(Lecture #5 : .m4v, .html, .pdf) (Corrected)

Homework #3 due on Wednesday February 13

Week #4 (Feb 11)

Monday : Inverse matrices; LU Factorization (2.5, 2.6)

(Lecture #6 : .m4v, .html, .pdf) (Final)

Wednesday : Tranposes and permutations (2.7)

(Lecture #7 : .m4v (coming soon), .html, .pdf) (Final)

Homework #4 due on Wednesday February 20th.

You may turn in your homework on Monday 2/18, if you'd like me to grade it before the midterm.

Week #5 (Feb 18)

Monday : President's Day

Wednesday : Review for Midterm #1 (Chapters 1-2)

No homework due next week

Week #6 (Feb 25)

Monday : Midterm #1 (Chapters 1-2)

Wednesday : Vectors and subspaces (3.1)

Homework #5 due on Wednesday March 6.

Week #7 (Mar 4)

Monday : The Nullspace (3.2)

(Lecture #8 : .m4v (coming soon), .html, .pdf) (Final)

Wednesday : Rank and row reduced form; the complete solution; (3.3, 3.4)

(Lecture #9 : .m4v, .html, .pdf) (Final)

Homework #6 due on Wednesday March 13

Week #8 (Mar 11)

Monday : Rank and the complete solution (3.3, 3.4) (see Lecture #9, Wednesday 3/6)

Wednesday : Independence, Basis and Dimension; dimensions of the four subspaces (3.5, 3.6)

(Lecture #10 : .m4v (upon request), .html, .pdf) (Final)

Homework #7 due on Wednesday March 20.

Week #9 (Mar 18)

Monday : Orthogonality; Projections; (4.1, 4.2)

(Lecture #11 : .m4v (upon request), .html, .pdf)

Wednesday : Least squares (4.3)

(Lecture #12 : .m4v (upon request), .html, .pdf)

Homework #8 due on Wednesday April 3rd.

You may turn in your homework on Monday if you'd like me to grade it before the midterm

Spring Break
Week #10 (Apr 1)

Monday : Gram-Schmidt Orthogonalization (4.4)

Wednesday : Review for Midterm #2 (Chapters 3-4)

No homework due next week

Week #11 (Apr 8)

Monday : Midterm #2 (Chapters 3-4)

Wednesday : Determinants (5.1, 5.2, 5.3)

Homework #9 due on Wednesday April 17th

Week #12 (Apr 15)

Monday : Introduction to Eigenvalues; Diagonalizing a matrix (6.1)

Wednesday : Introduction to Eigenvalues (6.1, continued)

Homework #10 due on Wednesday April 24

Week #13 (Apr 22)

Monday : Diagonalizing a matrix (6.2)

Wednesday : Diagonalizing a matrix (cont); Quiz #2 (6.2)

No homework assigned

Week #14 (Apr 22)

Monday : Symmetric Matrices (6.4)

Wednesday : Positive definite matrices (6.5)

Homework #11 due on Wednesday May 8

Week #15 (Apr 29)

Monday : Similar matrices; Singular Value Decomposition (6.6, 6.7)

Wednesday : Review for final

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Homeworks

Homework will be collected once a week and will generally be taken from the course textbook. You should hand in all problems to get credit for the assignment, but these will not be graded in detail. The problems which will be graded, are to be turned in are on a separate sheet, available at links below.

Homework #1 Due Wednesday, Jan 28, at the start of class.

  • Section 1.1 (page 8) : #2, 3, 4, 8, 16, 26

No graded portion of the assignment for this week

Homework #2 Due Wednesday, Feb. 6, at the start of class.

  • Section 1.2 (page 19) : #4, 7, 9, 12, 16, 20
  • Section 1.3 (page 29) : #1, 2, 4, 6
  • Section 2.1 (page 40) : #11, 12, 17, 18, 20

Graded assignment (.pdf)

Solutions to selected book problems (page1, page2, page3)

Homework #3 Due Wednesday, Feb. 13, at the start of class.

  • Section 2.2 (page 51) : #1, 2, 3, 4, 5, 6, 12, 21, 27
  • Section 2.3 (page 63) : #1, 3, 4, 12, 14, 16, 17, 24
  • Section 2.4 (page 75) : #1, 3, 4, 6, 11, 13

Graded assignment (.pdf)

Homework #4 Due Wednesday, Feb. 20, at the start of class.

You may turn in your homework on Monday 2/18, if you'd like me to grade it before the midterm.

  • Section 2.5 (Page 89) : #1, 2, 12, 13, 22, 24, 25, 26, 27, 28
  • Section 2.6 (Page 102): #1, 2, 3, 4, 5, 6, 15

Graded assignment (.pdf)

Homework #5 Due Wednesday, Mar. 6, at the start of class.

  • Section 2.7 (Page 115) : #1, 2, 3, 5, 18, 20, 21, 22
  • Section 3.1 (Page 127) : #1, 2, 10, 11, 20, 22, 26

Graded assignment (.pdf)

Homework #6 Due Wednesday, Mar. 13, at the start of class.

  • Section 3.2 (Page 140) : #5, 6, 24, 26, 27, 29
  • Section 3.3 (Page 151) : #1, 2, 8, 9, 10, 12, 15, 24
  • Section 3.4 (Page 163) : #4, 6, 16, 26, 28

Graded assignment (.pdf)

Homework #7 Due Wednesday, Mar. 20, at the start of class.

  • Section 3.5 (Page 178) : #1, 2, 3, 5, 7, 8, 11, 17, 20, 25
  • Section 3.6 (Page 190): #1, 2, 4, 9, 18, 21

Graded assignment (.pdf)

Quiz on Wednesday March 20th!

Homework #8 Due Wednesday, Apr. 3rd, at the start of class.

You may turn in your homework on Monday 4/1 if you'd like me to grade it before the midterm

  • Section 4.1 (Page 202) : #3, 5, 6, 7, 13, 16, 19, 21, 25
  • Section 4.2 (Page 214): #1, 2, 5, 11, 12, 13, 16, 17
  • Section 4.3 (Page 226) : #1, 2, 3, 4, 9, 12, 13, 15, 21.

Graded assignment (.pdf)

Homework #9 Due Wednesday, Apr. 17, at the start of class.

  • Section 5.1 (Page 251) : #1, 3, 7, 8, 12, 18
  • Section 5.2 (Page 263) : #11, 16,
  • Section 5.3 (Page 279) : #6, 8

Graded assignment (.pdf)

Homework #10 Due Wednesday, Apr. 24, at the start of class.

  • Section 6.1 (Page 293) : #3, 4, 6, 13, 14, 15, 17, 24, 29, 32
  • Section 6.2 (Page 307): #1, 2, 4, 11, 12, 15, 26, 32, 35

No Graded assignment this week, but you will have a homework quiz on Wednesday 4/24. Please turn in the book problems as usual.

Homework #11 Due Wednesday, May 8, at the start of class.

  • Section 6.4 (Page 337) : #3, 5, 13, 15, 19, 21, 24, 26
  • Section 6.5 (Page 418) : #2, 3, 4, 9, 21, 22
  • Section 6.6 (Page 360) : #1, 2, 3, 17, 18
  • Section 6.7 (Page 371) : #1, 2, 3, 9, 10, 11

No graded assignment, but there may be a short quiz on Wednesday 5/8 covering the homework.

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Quizzes

Quizzes will be short homework quizzes.

Quiz #1 Wednesday, March 20th

Copy of quiz1.pdf

Quiz #2 Wednesday, April 24th

Material will be from Chapters 6.1 and 6.2

Copy of quiz2.pdf

Quiz #4 Wednesday, May 8

Material will be from Chapters 6.4-6.7

Copy of quiz3.pdf

Solutions quiz3_solns.pdf

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In-class exercises

In class exercises will be done in-class and collected periodically, and will count towards attendance.

In-class exercise #1 Wednesday Jan. 23.

Practice solving linear systems (.pdf)

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Midterms

Midterm #1 Monday, February 25th.

Exam will cover material from Chapters 1 and 2.

Midterm #2 Monday April 8th.

Exam will cover material from Chapters 3 and 4.

You can download a practice set of questions here.

Thanks to Sam (solns (very complete)), Jarad (solns), Eric (solns), Jerry (solns), Adam (solns), Stephanie (solns) Ted (solns,unedited), Bobby (solns,unedited) for letting me post their solutions to the practice exam!

You will also be allowed to use a page of notes (both sides of an 8.5 by 11 sheet of paper) on the midterm.

Solutions to exam #2 (page 1, page 2, page 3, page 4, page 5, page 6)

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Final

Our final will be held in our regular class room.

Final Wednesday, May 15th, 2:30 - 4:30

To review for the final, retake old exams (midterm_1.pdf, midterm_2.pdf, midterm_1_alt.pdf) or quizzes (quiz1.pdf, quiz2.pdf, quiz3.pdf). The last quiz may be especially helpful for reviewing the material we hav covered since the last midterm. The solutions to this quiz are posted above.

Final exam : final. Solutions to the final : (final_solns_page1, final_solns_page2, final_solns_page3, final_solns_page4, final_solns_page5)

The Boise State final exam calendar.

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Grading

Homeworks and quizzes will count towards 15% of your grade, each of the two midterms will be 25% of your final grade, and the final exam will be worth 30% of your final grade. In-class exercises will count towards 5% of your grade.

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Make-up exams, late homework

If you should miss an exam, you may be given an opportunity to take a comprehensive make-up exam during the final week of class. This score will be used in place of the exam you missed. The decision as to whether to allow this option is made by the instructor.

Late homeworks will not be accepted.

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Other useful information


Linear Algebra, finite element design, and the auto industry (posted 1/21/2013)

Finite element design is a computational tool widely used in the auto industry to optimize the design of cars. A key feature in making finite element analysis a feasible tool is advanced techniques for solving large linear systems (millions of equations). In a recent radio interview, a Wall Street journalist talks about his impressions of a recent (2011) auto show, and mentions "finite element design" and computational advances in general as the key to the latest design innovations in the car industry. Listen to the podcast here.

One of the most widely used finite element analysis (FEA) packages in the automotive industry is NASTRAN. They advertise "direct solvers" (such as LU factorization we will learn in class) and "iterative solvers" (e.g. Conjugate Gradient) for linear systems which can handle up to 25 million "degrees of freedom", i.e. number of equations, or number of unknowns. Read about the solvers in NASTRAN here.

History of Gaussian Elimination (posted 1/21/2013)

You might think that Gaussian Elimination is such an obvious idea, that it is hard to imagine a time when there was no such algorithm. To get a feel for the history that dates back as far as 2000BC, see this link.

Lectures by G. Strang

Did you know that you can watch on-line lectures given Gilbert Strang (author of our course text), lecturing from an earlier edition of our class textbook? This would be a great way to get a different view of the material, taught by one of the major contributors to the field of Linear Algebra. His lectures are available on the MIT Open Course Ware website at this link.

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Last modified: Mon Aug 5 10:33:40 PDT 2013