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 12:302:30pm. One page (one side) of formulae is allowed. Calculators are prohibited.
Topics:
 Solution of systems of linear equations by GaussJordan reduction (SJL Section 1.2, p. 23: 5(d,e,k));
 LUfactorization (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);
 QRfactorization (SJL Section 5.6, p. 268: 5, 8 (find QR for the A=(x1,x2,x3));
 GramSchmidt 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: QRfactorization.
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.

Just for your information.

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: QRfactorization.
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.
Attention!
Here are additional problems.

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 3.34.3.
One page (one side) of formulae and definitions (not problems solutions!) is allowed. Calculators are prohibited.
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);

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.
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,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: LUfactorization.
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 GaussJordan 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: GaussJordan 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.

