HW #

Homework problems

Due date

Final

Cumulative Final Exam.
The exam will take place on Thursday, May 9th, in the usual classroom at 7:309:30am. 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)).



11

Quiz 10 on Thursday, May 2nd. (Solution published) Topic: solution of initial value problem for system of ODEs.
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).
Attention! Here is an additional set of problems for Matlab.

May 2nd, 2019, class time.

10

Quiz 08 on Thursday, April 25th. (Solution published) Topic: problem 5 in Exam 1 and problem 6 in 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 25th, 2015, class time.

9

Quiz 07 on Tuesday, April 23rd. (Solution published) Topic: Least squares method.
SJL Section 5.2, p. 221 in 8th ed., p. 224 in 9th ed.: 1(a,b,c,d), 2;
SJL Section 5.3, p. 231 in 8th ed., p. 237 in 9th ed.: 1(a,c), 3(a), 5, 6.

April 9th, 2019, class time.



Exam 2 on Tuesday, April 9th. (Solution published) Topics covered: SJL Sections 3.35.2.
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 in 8th ed., p. 140 in 9th ed.: 9(a);
SJL Section 3.4, p. 143 in 8th ed., p. 146 in 9th ed.: 10, 14(c);
SJL Section 3.5, p. 153 in 8th ed., p. 156 in 9th ed.: 1(a), 10;
SJL Section 3.6, p. 159 in 8th ed., p. 162 in 9th ed.: 4(d), 15;
SJL Section 4.1, p. 174 in 8th ed., p. 177 in 9th ed.: 4, 6(a);
SJL Section 4.2, p. 187 in 8th ed., p. 190 in 9th ed.: 4(a);
SJL Section 4.3, p. 194 in 8th ed., p. 197 in 9th ed.: 1(a,b,e);
SJL Section 5.1, p. 212 in 8th ed., p. 215 in 9th ed.: 3(a,c);
For SJL Section 5.2 do your HW above.

None.

8

Quiz 05 on Thursday, March 28th. (Solution published) Topic: you will need to show whether some mapping is a linear transformation or not.
Quiz 06 on Tuesday, April 2nd. (Solution published) Topic: Vector (cross) product.
SJL Section 4.3, p. 194 in 8th ed., p. 197 in 9th ed.: 1(a,b,e);
SJL Section 5.1, p. 212 in 8th ed., p. 215 in 9th ed.: 1(a,b), 2(a,b), 3(a,c), 4, 7, 9, 10;

April 2nd, 2019, class time.

7

Quiz 04 on Tuesday, March 26th. (Solution published) Topic: Change of bases.
SJL Section 3.6, p. 159 in 8th ed., p. 162 in 9th ed.: 1, 2(b), 3, 4(b,d), 5, 6, 8, 9, 11, 15, 16;
SJL Section 4.1, p. 174 in 8th ed., p. 177 in 9th ed.: 1(a,b,d), 3, 4, 5(a,c,d), 6(a,d), 8(a,c),10;
SJL Section 4.2, p. 187 in 8th ed., p. 190 in 9th ed.: 1, 2(a,b,c), 3(a,b), 4(a), 5(a,b,c).

March 26th, 2019, class time.

6

Exam 1 on Thursday, February 28th. (Solution published) Topics: All sections covered, up to and including 3.3.
One page (one side) of formulae and definitions (no problems solutions!) is allowed. Calculators are prohibited.
SJL Section 3.3, p. 137 in 8th ed., p. 140 in 9th ed.: 1(a,c), 2(a,c), 4(a), 6, 8(a,c), 9(a), 12(a,b);
SJL Section 3.4, p. 143 in 8th ed., p. 146 in 9th ed.: 3, 4, 5(a,b,c), 7, 10, 14(c,d);
SJL Section 3.5, p. 153 in 8th ed., p. 156 in 9th ed.: 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 in 8th ed., 45 in 9th ed.: 1(h);
SJL Section 1.5, p. 66 in 8th ed., p. 68 in 9th ed.: 8(d);
SJL Section 2.1, p. 90 in 8th ed., p. 93 in 9th ed.: 6;
SJL Section 2.2, p. 97 in 8th ed., p. 100 in 9th ed.: 3(e), 4, 5 (Hint: use induction);
SJL Section 2.3, p. 105 in 8th ed., p. 108 in 9th ed.: 1(c), 2(c);
SJL Section 3.2, p. 125 in 8th ed., p. 128 in 9th ed.: 4(a,d), 10(c);
For SJL Section 3.3 do your HW above.

February 28th, 2019, class time.

5

SJL Section 3.1, p. 116 in 8th ed., p. 118 in 9th ed.: 3, 6, 7, 9, 10, 14;
SJL Section 3.2, p. 125 in 8th ed., p. 128 in 9th ed.: 1(a,c,e), 3(a,d), 4(a,d), 10(a,c), 12(a,c), 8th ed. 16(a,d) or 9th ed. 19, 8th ed. 18 or 9th ed. 21.

February 19th, 2019, class time.

4

Quiz 03 on Thursday, February 14th. (Solution published) Topic: LUfactorization.
SJL Section 2.1, p. 90 in 8th ed., p. 93 in 9th ed.: 3(a,d,f,g,h), 4, 5, 6;
SJL Section 2.2, p. 97 in 8th ed., p. 100 in 9th ed.: 1, 2, 3(a,c,e,f), 4, 5, 7(c,d), 9, 12(a);
SJL Section 2.3, p. 105 in 8th ed., p. 108 in 9th ed.: 1(a,c), 2(a,c,d), 3, 5(a,b), 8.

February 14th, 2019, class time.

3

Quiz 02 on Thursday, February 8th. (Solution published) Topic: Calculation of inverse matrix using GaussJordan reduction for augmented matrix.
SJL Section 1.4, p. 56 in 8th ed., p. 58 in 9th ed.: 12, 13(a), 24(a), 25(a), 36;
SJL Section 1.5, p. 66 in 8th ed., p. 68 in 9th ed.: 1, 2, 8(a,d), 10(a,f), 12 (a,d);
SJL Section 2.1, p. 90 in 8th ed., p. 93 in 9th ed.: 1, 2.

February 8th, 2019, class time.

2

Quiz 01 on Thursday, January 24th. (Solution published) Topic: GaussJordan reduction.
SJL Section 1.2, p. 24: 6(a,d), 8, 11, 12;
SJL Section 1.3, p. 42 in 8th ed., 45 in 9th ed.: 1, 2, 3, 4, 5(a,c), 8, 9, 10, 13 (a), 15;
SJL Section 1.4, p. 56 in 8th ed., p. 58 in 9th ed.: 1(a), 6, 7.

January 31st, 2019, 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, 2019, class time.

