# Math 314. Linear Algebra With Applications. Spring 2015.

## Books:

Section 002. TR 11:00-12:15. Room: SMLC 356. Syllabus for Math 314-002 (18497)
Syllabus version from January 12th, 2015.
Steven J. Leon
Linear Algebra with Applications
8th Edition, Pearson.

## Office hours:

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

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 5th. (Solution published)
The exam will take place on Tuesday, May 5th, in the usual classroom at 12:30-2:30pm. One page (one side) 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);
• Eigenvalues and eigenvectors (SJL Section 6.1, p. 294: 1(a,c,d,e,f,g,k), 2, 3, 8, 9);
• Systems of ODEs (SJL Section 6.2, p. 305: 1(a,b,d,e), 2(a,b), 3, 4, 5, 8);
• Diagonalization of matrices (SJL Section 6.3, p. 322: 1(a,c), 2(a,c), 6, 7, 28(a), 30(d)).

Extra information
Another quiz on QR. (Solution published) Topic: QR-factorization.
Quiz 10 (never happened). (Solution published) Topic: Solution of initial value problems for systems of ODEs.
Another Quiz 10 with diagonalization. (Solution published) Topic: Solution of initial value problems for systems of ODEs (two ways).
-
11 Attention! Here is an additional set of problems for Matlab.
10 Quiz 07 on Thursday, April 28th. (Solution published) Topic: Least squares method.
Quiz 08 on Tuesday, April 28th. (Solution published) Topic: problem 5 in Exam 1 and Exam 2.
Quiz 09 on Tuesday, April 30th. (Solution published) Topic: QR-factorization.
SJL Section 5.4, p. 239: 1, 2, 3, 5, 9;
SJL Section 5.5, p. 257: 1, 2, 3, 6, 8;
SJL Section 5.6, p. 268: 1(a), 3, 4, 5, 8.
April 28th, 2015, class time.
9 Quiz 06 on Tuesday, April 21th. (Solution published) Topic: Vector (cross) product.
SJL Section 5.2, p. 221: 1(a,b,c,d), 2.
SJL Section 5.3, p. 231: 1(a,c), 3(a), 5, 6.
April 21st, 2015, class time.
- Exam 2 on Thursday, April 2nd. (Solution published) Topics covered: SJL Sections 3.3-4.3.
One page (one side) of formulae and definitions (not problems solutions!) is allowed. Calculators are prohibited.
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);
None.
8 SJL Section 4.3, p. 191: 1(a,b,e);
SJL Section 5.1, p. 212: 1(a,b), 2(a,b), 3(a,c), 4, 7, 9, 10;
April 7th 9th, 2015, class time.
7 Quiz 04 on Thursday, March 26th. (Solution published) Topic: Change of bases.
Quiz 05 on Tuesday, March 31st. (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).
March 31st, 2015 April 7th, 2015, class time.
6 Exam 1 on Tuesday, March 3rd. (Solution published) Topics: All section covered up to and including 3.3.
One page (one side) of formulae and definitions (not problems solutions!) 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.
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,d), 10(c);
For SJL Section 3.3 do your HW above.
March 17th, 2015, class time.
5 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 26th, 2015, class time.
4 Quiz 03 on Thursday, February 19th. (Solution published) Topic: LU-factorization.
SJL Section 2.1, p. 90: 3(a,d,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);
SJL Section 2.3, p. 105: 1(a,c), 2(a,c,d), 3, 5(a,b), 8.
February 17th, 2015, class time.
3 Quiz 02 on Thursday, February 12th. (Solution published) Topic: Calculation of inverse matrix using Gauss-Jordan reduction for augmented matrix.
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: 1, 2.
February 10th, 2015, class time.
2 Quiz 01 on Tuesday, February 3rd. (Solution published) 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, 2015, 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, 2015, class time.