Spring 2013

Math 314

Math 375

Math 314. Linear Algebra With Applications. Spring 2013.

Description:

This is an introductory course in linear algebra.

Instructor:

Daniel Appelö

Location:

TR, 11:00-12:15, Mitchell Hall 221.

Book:

You may use either of the editions
Steven J. Leon, Linear Algebra with Applications, 7th Edition, Pearson.
Steven J. Leon, Linear Algebra with Applications, 8th Edition, Pearson.

Office hours:

TR: 13.30-15.00.
Room: SMLC 226.

How grades are assigned:

All homework: 100 points (only few key problems from the homework will be graded, approximately 8 points for homework).
Two midterm exams: 100 points each (100+100 points).
In class quizzes: 50 points.
Final exam: 200 points.
Total: 550 points.
Lowest boundaries for grades:
A = 495, B = 440, C = 380, D = 330.

Calculators:

A scientific calculator is required for this class. Some exam and homework questions will ask that the student use his/her calculator to emulate the steps a computer would take when performing a particular algorithm.

Missed Exams:

In almost all cases, a missed exam will simply be awarded zero points. In some very special cases, I may be willing to make alternative arrangements. If at all possible let me know well in advance that you might miss an exam and, if you have a valid reason, I'll see what I can do. Only in extreme circumstances will a student be allowed to make up an exam that was missed without prior arrangements.

Dishonesty Policy:

Each student is expected to maintain the highest standards of honesty and integrity in academic and professional matters. The University reserves the right to take disciplinary action, including dismissal, against any student who is found responsible for academic dishonesty. Any student who has been judged to have engaged in academic dishonesty in course work may receive a reduced or failing grade for the work in question and/or for the course. Academic dishonesty includes, but is not limited to, dishonesty on quizzes, tests or assignments; claiming credit for work not done or done by others; and hindering the academic work of other students.

American Disabilities Act:

In accordance with University Policy 2310 and the American Disabilities Act (ADA), academic accommodations may be made for any student who notifies the instructor of the need for an accommodation. It is imperative that you take the initiative to bring such needs to the instructor's attention, as the instructor is not legally permitted to inquire. Students who may require assistance in emergency evacuations should contact the instructor as to the most appropriate procedures to follow. Contact Accessibility Services at 505-661-4692 for additional information

Disclaimer:

I reserve the right to make reasonable and necessary changes to the policies outlined in this syllabus. Whenever possible, the class will be notified well in advance of such changes. An up-to-date copy of the syllabus can always be found on the course website. It is your responsibility to know and understand the policies discussed therein. If in doubt, ask questions.

Schedule:

Notation SJL 1.2 means Steven J. Leon book, Chapter 1, Section 2.
Week Tuesday Thursday Other notes
1 Jan. 15, Intro + Matlab Jan. 17, SJL 1.1, SJL 1.2
2 Jan. 22, SJL 1.2, 1.3 Jan. 24, SJL 1.3, 1.4
3 Jan. 29, SJL 1.4, 1.5 Jan. 31, SJL 1.5, 2.1
4 Feb. 5, SJL 2.1, 2.2 Feb. 7, SJL 2.2, 2.3
5 Feb. 12, SJL 3.1, 3.2 Feb. 14, SJL 3.2
6 Feb. 19, SJL 3.3 Feb. 21, SJL 3.4 + review
7 Feb. 26, Exam 1 in class Feb. 28, SJL 3.5
8 March 5, SJL 3.6 March 7, SJL 4.1
9 March 12, spring break March 14, spring break
10 March 19, SJL 4.1, 4.2 March 21, SJL 4.3, 5.1
11 March 26, SJL 5.1, 5.2 March 28, SJL 5.2 + review
12 April 2, Exam 2 in class April 4, SJL 5.3
13 April 9, SJL 5.4, 5.5 April 11, SJL 5.5, 5.6
14 April 16, SJL 5.6 April 18, SJL 6.1, 6.2
15 April 23, SJL 6.3 April 25, SJL 6.3, 6.4
16 April 29, SJL 6.4 May 2, Review
17 May 7, Final Exam 12.30-14.30

Homework, quizzes and exams:

HW # Homework problems Due date
1 SJL Section 1.1, p. 10: 1(a,b,d), 2(a,c), 3(a,b,d), 4(a,b,c), 5(a,b,c), 6(a,c,f), 7, 8;
SJL Section 1.2, p. 23: 1, 2, 3, 5(a,c,e,f,h).
Jan. 24th, 2013, in class.
2 Quiz 01 on Thursday, Jan. 24.
Topic: Gauss-Jordan reduction.
SJL Section 1.2, p. 24: 6(a,d), 8, 11, 12;
SJL Section 1.3, p. 42: 1, 2, 3, 4, 5(a,c), 8, 9, 10, 15 (28 in 7th edition).
Jan. 31, 2013, in class.
3 8th edition:
SJL Section 1.4, p. 56: 1(a), 6, 7, 12, 24(a), 28, 30(a);
SJL Section 1.5, p. 66: 1, 2, 8(a,d),15 10(a,f), 12 (a,d);
SJL Section 2.1, p. 90: 1, 2.
7th edition:
SJL Section 1.3, p. 60: 20(a), 9, 15, 24, 26(b), 29(a);
SJL Section 1.4, p. 69: 1, 2, 8(a,d), 10(a,f), 12 (a,d);
SJL Section 2.1, p. 96: 1, 2.
Feb. 7, 2013, in class.
4 Quiz 02 on Thursday, Feb. 14.
Topic: Calculation of inverse matrix using Gauss-Jordan reduction for an augmented matrix.
SJL Section 2.1, p. 90 in 8th, 96 in 7th: 3(a,d,f,g,h), 4, 5, 6;
SJL Section 2.2, p. 97 in 8th, 103 in 7th: 1, 2, 3(a,c,e,f), 4, 5, 7(c,d), 9, 12(a).
Feb. 14, 2013, in class.
5 Quiz 03 on Thursday, Feb. 21.
Topic: LU-factorization.
SJL Section 2.3, p. 105 in 8th, 109 in 7th: 1(a,c), 2(a,c,d), 3, 5(a,b), 8;
SJL Section 3.1, p. 116 in 8th, 121 in 7th: 3, 6, 7, 9, 10, 14;
SJL Section 3.2, p. 125 in 8th: 1(a,c,e), 3(a,d), 4(a,d), 10(a,c), 12(a,c), 16(a,d), 18.
SJL Section 3.2, p. 131 in 7th: 1(a,c,e), 3(a,d), 4(a,d), 8(a,c), 10(a,c), 14(a,d), 16.
Feb. 21, 2013, in class.
6 Exam 1 on Tuesday, Feb. 26. Topics: All section covered up to and including 3.3.
SJL Section 3.3, p. 137 (8th): 1(a,c), 2(a,c), 4(a), 8(a,c), 9(a), 12(a,b);
SJL Section 3.3, p. 144 (7th): 1(a,c), 2(a,c), 4(a), 6(a,c), 7(a), 10(a,b);
SJL Section 3.4, p. 143 (8th), p. 150 (7th): 3, 4, 5(a,b,c), 7, 10, 14(c,d);
SJL Section 3.5, p. 153 (8th), p. 161 (7th): 1(a), 2(a), 3, 4, 5, 6, 7, 8, 10.
Additional training for Exam 1:
SJL Section 1.2, p. 24: 6(d);
SJL Section 1.3, p. 42: 1(h);
SJL Section 1.5, p. 66: 8(d);
SJL Section 2.2, p. 97: 3(e), 4, 5 (Hint: use induction);
SJL Section 2.3, p. 105: 1(c), 2(c);
SJL Section 3.2, p. 126: 10(c);
For SJL Section 3.3 do your HW above.
March 7, 2013, in class.
7 Quiz 04 on Thursday, March 21. Topic: Change of bases.
SJL Section 3.6, p. 159 (8th): 1, 2(b), 3, 4(b,d), 5, 6, 8, 9, 15, 16;
SJL Section 3.6, p. 167 (7th): 1, 2(b), 3, 4(b,d), 5, 6, 7, 8, 11, 10;
SJL Section 4.1, p. 174 (8th) p. 182 (7th) : 1(a,b,d), 3, 4, 5(a,c,d), 6(a,d), 8(a,c),10;
SJL Section 4.2, p. 187 (8th) p. 196 (7th): 1, 2(a,b,c), 3(a,b), 4(a), 5(a,b,c).
March 21, 2013, in class.
8 Quiz 05 on Thursday, March 28.
Topic: you will need to show whether some mapping is a linear transformation or not.
Solution to Exam 2 on Tuesday, April 2.
Topics covered: SJL Sections 3.3-5.1.
SJL Section 4.3, p. 204 (7th) p. 191 (8th) : 1(a,b,e);
SJL Section 5.1, p. 224 (7th) 212 (8th): 1(a,b), 2(a,b), 3(a,c), 4, 7;
SJL Section 5.2, p. 233 (7th) 221 (8th) : 1(a,b,c,d), 2.
Additional training for Exam 2:
SJL Section 3.3, p. 137: 9(a);
SJL Section 3.4, p. 143: 10, 14(c);
SJL Section 3.5, p. 153: 1(a), 10;
SJL Section 3.6, p. 159: 4(d), 15;
SJL Section 4.1, p. 174: 4, 6(a);
SJL Section 4.2, p. 187: 4(a);
For SJL Sections 4.3, 5.1, and 5.2 do your HW above.
April 4, 2013, in class.
9 Quiz 06 on Thursday, April 11.
Topic: Vector (cross) product.
SJL Section 5.3, p. 231 (8th) p. 243 (7th): 1(a,c), 3(a), 5, 6;
SJL Section 5.4, p. 239 (8th) p. 252 (7th): 1, 2, 3, 5, 9.
April 11, 2013, in class.
10 Quiz 07 on Thursday, April 18.
Topic: Least squares method.
SJL Section 5.5, p. 257 (270): 1, 2, 3, 6, 8;
SJL Section 5.6, p. 268 (281): 1(a), 3, 4, 5, 8;
April 18, 2013, in class.
11 Quiz 08 on Thursday, April 25.
Topic: Eigenvalues .
SJL Section 6.1, p. 294 (310): 1(a,c,f,g,k), 2, 3, 8 (6 in 7th), 9 (7 in 7th).
SJL Section 6.1, p. 294: 1(d,e);
SJL Section 6.2, p. 305 (323): 1(a,b,d,e), 2(a,b), 3, 4, 5;
SJL Section 6.3, p. 322 (340): 1(a,c), 2(a,c), 6, 7.
April 29, 2013, in class.
Final Quiz 09 on Thursday, May 2.
Topic: Solution of initial value problems for systems of ODEs.
Final Exam on Tuesday, May 7.
Topics:
  • Solution of systems of linear equations by Gauss-Jordan elimination (SJL Section 1.2, p. 23: 5(d,e,k));
  • LU-factorization (SJL Section 1.5, p. 66: 8(a,d));
  • Change of bases (SJL Section 3.5, p. 153: 3, 6);
  • Least squares method (SJL Section 5.3, p. 231: 5, 6);
  • QR-factorization (SJL Section 5.6, p. 268: 5, 8 (find QR for the A=(x1,x2,x3));
  • Gram-Schmidt orthogonalization for functions, linear independence of functions (SJL Section 3.3, p. 137: 8(a,c), 9(a); SJL Section 5.6, p. 268: 4);
  • Systems of ODEs (SJL Section 6.2, p. 305: 2(a,b));
  • Diagonalization of matrices (SJL Section 6.3, p. 322: 1(a,c), 2);
May 2, 2013.