Fall 2011

Math 314

Math 375

Math 314. Linear Algebra With Applications. Fall 2011.

Description:

This is an introductory numerical analysis course. We study numerical methods to solve linear and nonlinear equations, to interpolate and approximate data, and to perform numerical integration and differentiation. We will learn and use MATLAB to implement all algorithms.

Instructor:

Daniel Appelö

Location:

TR 9:30-10:45. Room: DSH 234.

Book:

Steven J. Leon, Linear Algebra with Applications, 8th Edition, Pearson.

Office hours:

Tuesday: 8.00-9.15 and 2.00-3.00.
Thursday: 2.00-3:00.
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 (not higher than):
A = 495, B = 440, C = 380, D = 330.

Schedule / Syllabus:

Notation SJL 1.2 means Steven J. Leon book, Chapter 1, Section 2.
Week Tuesday Thursday Other notes
1 Aug. 23, SJL 1.1 Aug. 25, SJL 1.2
2 Aug. 30, SJL 1.2, 1.3 Sep. 1, SJL 1.3, 1.4 Registration ends Sep. 2
3 Sep. 6, SJL 1.4, 1.5 Sep. 8, SJL 1.5, 2.1 Last day to drop w/o grade
4 Sep. 13, SJL 2.1, 2.2 Sep. 15, SJL 2.2, 2.3
5 Sep. 20, SJL 3.1, 3.2 Sep. 22, SJL 3.2
6 Sep. 27, SJL 3.3 Sep. 29, SJL 3.4 + review
7 Oct. 4, Exam 1 in class Oct. 6, SJL 3.5
8 Oct. 11, SJL 3.6 Oct. 13, Fall break
9 Oct. 18, SJL 4.1 Oct. 20, SJL 4.1, 4.2
10 Oct. 25, SJL 4.3, 5.1 Oct. 27, SJL 5.1, 5.2
11 Nov. 1, SJL 5.2 + review Nov. 3, Exam 2 in class
12 Nov. 8, SJL 5.3 Nov. 10, SJL 5.4
13 Nov. 15, SJL 5.5 Nov. 17, SJL 5.5, 5.6
14 Nov. 22, SJL 6.1, 6.2 Nov. 24, Thanksgiving holiday
15 Nov. 29, SJL 6.3 Dec. 1, SJL 6.3, 6.4
16 Dec. 6, SJL 6.4 Dec. 8, Review
17 Dec. 13, Final Exam 7.30-9.30 Dec. 15

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).
August 30th, 2011, class time.
2 Quiz 01 on Thursday, September 1st.
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).
September 6th, 2011, class time.
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.
September 13th, 2011, class time.
4 Quiz 02 on Thursday, September 15th.
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).
September 20th, 2011, class time.
5 Quiz 03 on Thursday, September 29th.
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.
September 29th, 2011, class time.
6 Exam 1 on Tuesday, October 4th. (Now with solution) 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.
October 11th, 2011, class time.
7 Quiz 04 on Thursday, October 20th. 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).
October 25th, 2011, class time.
8 Quiz 05 on Thursday, October 27th.
Topic: you will need to show whether some mapping is a linear transformation or not.
Solution to Exam 2 on Thursday, November 3rd.
Review 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.
November 10th, 2011, class time.
9 Quiz 06 on Thursday, November 17th.
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.
November 17th, 2011, class time.
10 Quiz 07 on Tuesday, November 29.
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;
SJL Section 6.1, p. 294 (310): 1(a,c,f,g,k), 2, 3, 8 (6 in 7th), 9 (7 in 7th).
November 29th, 2011, class time.
11 Quiz 08 on Thursday, December 6st.
Topic: Eigenvalues .
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.
December 6th, 2011, class time.
Final Quiz 09 on Thursday, December 8th.
Topic: Solution of initial value problems for systems of ODEs.
Final Exam on Tuesday, December 13th.
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);
December 13th, 2011.