Math 314. Linear Algebra With Applications. Spring 2013.


Sections:

Books:

Section 003. TR 14:00-15:15. Room: SMLC 356. Syllabus for Math 314-003 (30233)
Syllabus version from January 15th, 2013.
Steven J. Leon
Linear Algebra with Applications
8th Edition, Pearson.

Office hours:


TR 12:30-13:45. Room: SMLC 220.

How grades are assigned?

All homeworks: 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 quizes: 50 points.
Final exam: 200 points.
Total: 550 points.
Lowest bondaries for grades (not higher than):
A = 495, B = 440, C = 380, D = 330.
No late HWs are accepted after graded HW is returned. Even before for a late submission you shall get -1 point from the late HW grade.
HW # Homework problems Due date
Final Cumulative Final Exam on Tuesday, May 7th. (Solution published)
The exam will take place on Tuesday, May 7th, in the usual classroom at 10:00am-12:00pm. One page (two sides) of formulae is allowed. Calculators are prohibited.
Topics:
  • Solution of systems of linear equations by Gauss-Jordan reduction (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, 2).
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12 Quiz 10 on Thursday, May 2nd. (Solution published) Topic: Solution of initial value problems for systems of ODEs.
Detailed explanation of solution of IVP for ODEs using matrix exponent.
SJL Section 6.1, p. 294: 1(a,c,d,e,f,g,k), 2, 3, 8, 9;
SJL Section 6.2, p. 305: 1(a,b,d,e), 2(a,b), 3, 4, 5, 8;
SJL Section 6.3, p. 322: 1(a,c), 2(a,c), 6, 7, 28(a), 30(d).
Attention! Here is an additional set of problems for Matlab. You have to print out commands and results.
May 2nd, 2013, class time.
11 Quiz 09 on Tuesday, April 30th. (Solution published) Topic: QR-factorization.
SJL Section 5.6, p. 268: 1(a), 3, 4, 5, 8.
Start doing additional set of problems for Matlab from the next HW.
April 25th, 2013, class time.
10 Quiz 08 on Thursday, April 18th. (Solution published) Topic: problem 5 in Exam 1 and problem 6 in Exam 2.
SJL Section 5.4, p. 239: 1, 2, 3, 5, 9;
SJL Section 5.5, p. 257: 1, 2, 3, 6, 8. Attention! Here are additional problems.
April 18th, 2013, class time.
9 Quiz 07 on Thursday, April 11th. (Solution published) Topic: Least squares method.
SJL Section 5.3, p. 231: 1(a,c), 3(a), 5, 6.
April 11th, 2013, class time.
- Exam 2 on Tuesday, April 9th. (Solution published) Topics covered: SJL Sections 3.3-5.2.
One page (one side) of formulae is allowed. Calculators are prohibited.
Common mistake in HW on column and row spaces.
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);
SJL Section 4.3, p. 191: 1(a,b,e);
SJL Section 5.1, p. 212: 7, 10;
SJL Section 5.2, p. 221: 1(a,b,c,d), 2.
None.
8 Quiz 06 on Thursday, April 4th. (Solution published) Topic: Vector (cross) product (work through pp. 102-103 and examples in SJL 5.1).
SJL Section 5.1, p. 212: 1(a,b), 2(a,b), 3(a,c), 4, 7, 10;
SJL Section 5.2, p. 221: 1(a,b,c,d), 2.
April 4th, 2013, class time.
7 Quiz 05 on Thursday, March 28th. (Solution published) Topic: you will need to show whether some mapping is a linear transfomation or not.
SJL Section 3.6, p. 159: 1, 2(b), 3, 4(b,d), 5, 6, 8, 9, 11, 15, 16;
SJL Section 4.1, p. 174: 1(a,b,d), 3, 4, 5(a,c,d), 6(a,d), 8(a,c),10;
SJL Section 4.2, p. 187: 1, 2(a,b,c), 3(a,b), 4(a), 5(a,b,c);
SJL Section 4.3, p. 191: 1(a,b,e).
March 28th, 2012, class time.
6 Quiz 04 on Thursday, March 7th. (Solution published) Topic: Change of bases.
Exam 1 on Tuesday, February 26th. (Solution published) Topics: All section covered up to and including 3.3.
One page (one side) of formulae is allowed. Calculators are prohibited.
SJL Section 3.3, p. 137: 1(a,c), 2(a,c), 4(a), 6, 8(a,c), 9(a), 12(a,b);
SJL Section 3.4, p. 143: 3, 4, 5(a,b,c), 7, 10, 14(c,d);
SJL Section 3.5, p. 153: 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: 4(a,c), 10(c), 12(a,c)(updated);
For SJL Section 3.3 do your HW above.
March 5th, 2013, class time.
5 Quiz 03 on Thursday, February 21st. (Solution published) Topic: LU-factorization.
SJL Section 2.3, p. 105: 1(a,c), 2(a,c,d), 3, 5(a,b), 8;
SJL Section 3.1, p. 116: 3, 6, 7, 9, 10, 14;
SJL Section 3.2, p. 125: 1(a,c,e), 3(a,d), 4(a,d), 10(a,c), 12(a,c), 16(a,d), 18.
February 19th, 2013, class time.
4 Quiz 02 on Thursday, February 7th. (Solution published) Topic: Calculation of inverse matrix using Gauss-Jordan reduction for augmented matrix.
SJL Section 2.1, p. 90: 1, 3(f,g,h), 4, 5, 6;
SJL Section 2.2, p. 97: 1, 2, 3(a,c,e,f), 4, 5, 7(c,d), 9, 12(a).
February 12th, 2013, class time.
3 Quiz 01 on Thursday, January 31st. (Solution published) Topic: Gauss-Jordan reduction.
SJL Section 1.4, p. 56: 12, 13(a), 24(a), 25(a), 36;
SJL Section 1.5, p. 66: 1, 2, 8(a,d), 10(a,f), 12 (a,d);
SJL Section 2.1, p. 90: 2, 3(a,d).
February 5th, 2013, class time.
2 Quiz 01 on Thursday, January 24th (Canceled). 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, 13 (a), 15;
SJL Section 1.4, p. 56: 1(a), 6, 7.
January 29th, 2013, class time.
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).
January 22nd, 2013, class time.