Section:  1  Time:  MWF 11:00  11:50 a.m.  Room:  SMLC 120  Syllabus 
Instructor Info:  Anna Skripka, skripka [at] math [dot] unm [dot] edu 
Office hours:  MWF 3:00  3:50 pm and also by appointment, in SMLC 212 
Week 
Class Dates 
Book Sections 
Topics 
Homework 
Important Dates, Solutions 
1 
Jan 22, 24 
1.1 
Linear systems of equations. 
1.1: #7(a,b),19,20,21,23,24,27,28,51,53,54,57,58,60,61
1.2: #11,13,21,22,23,24,25,43,45,46,47,49,50 (submit even #) 
Pretest on Jan 22 
2 
Jan 27, 29, 31 
1.2 
Elementary row operations. Solving systems. Basic logic, I.
Application 1: photosynthesis. 
1.1: #35,37; 1.2:#53,55 for grade, submit the following > HW2


3 
Feb 3, 5, 7 
2.1, 2.2, 2.3 
Vectors. Span. Connection to systems of equations. Basic logic, II. 
2.1: #11,13,15,17,25,27; 2.2: #11,15,17,25,27, 4165(odd)
for grade, submit the following > HW3 

4 
Feb 10, 12, 14 
2.3, 3.1 
Linear independence. Linear transformations.
Basic logic, III.
Application 2: pharmaceutics. 
2.3: #3,5,9,15,21,23,27,29, 3353(odd), 5965(odd), proofs of Theorems 2.16 and 2.17
3.1: #3,5,7,9,13,15, 1931(odd), 39,41,43,47,49,55,58,59,61
for grade: 2.2: #58,64; 2.3: #42,48,50; 3.1: #6,14,16,50(c) 
HW3 due Feb 14

5 
Feb 17, 19, 21 
3.1, 3.2 
Linear transformations. Matrix algebra.
Application 3: expenses calculation. 
3.2: #1,3,9,13(a,b),15,23,25(a,b), 3945(odd),51,53,55


6 
Feb 24, 26, 28 
3.2, 3.3 
Matrix algebra. Inverses. 
3.3: #113(odd),21,23,25,27(a),31,35,41,43,4753(odd),57,59,67
for grade: 3.2: #14(b), 3.3: #22,26,52,56 
Exam1 (1.1, 1.2, 1.3, 2.2, 2.3, 3.1) on Feb 26

7 
Mar 3, 5, 7 
3.3, 4.1, 4.2 
Inverse of a matrix. Subspaces. Basis and dimension.
Application 4: encoding messages. Application 5: change of population distribution. 
4.1: #115(odd),23,25,27,35,4551(odd),57,65
4.2: #1,3,9,15,17,19,21
for grade: 4.1: #6,30,58, 4.2: #2,8,14,24


8 
Mar 10, 12, 14 
4.2, 4.3 
Null, row, and column spaces of a matrix. Ranknullity theorem. 
4.2: #2531(odd),41,4753(odd) 4.3: #1,3,9,11,1533(odd),43,45,47,5157(odd)
for grade: 4.2: #34,50, 4.3: #22,24,34,36


9 
Mar 24, 26, 28 
5.1, 5.2, 5.3 
Determinants and their applications.
Application 6: calculation of area. 
5.1: #11,13,17,19,21,35,37,39,49,51,6975(odd)
5.2: #3,7,11,13,25,35,39,4757(odd),61; 5.3: #1,3,13,15,23,25 
HW7 due Mar 28

10 
Mar 31, Apr 2, 4 
6.1, 3.5 
Eigenvalues and eigenvectors. Application to the Markov process.
Application 7: population model. 
6.1: #1,5,7,9,13,21,27,29,33,3753(odd)
for grade: 5.2: #26(d),62; 5.3: #6; 6.1:#30,52; 6.3:#8 
Exam2 (3.2, 3.3, 4.1, 4.2, 4.3, 5.1) on Mar 31

11 
Apr 7, 9, 11 
6.3, 6.4, 6.5 
Change of basis. Diagonalization. Complex eigenvalues. 
6.3: #1,517(odd),21,25,27,29 6.4: #515(odd),19,21,23,33,35,41; 6.5: #3,5,7
for grade: 6.4: #18,22,34; 6.5: #6; extra credit: Application 8 

12 
Apr 14, 16, 18 
8.1, 8.2 
Orthogonality, orthogonal complements, #8.1.69. Projections, GramSchmidt process. 
8.1: #5(d),15,17,2551(odd),6571(odd)
8.2: #113(odd),23,25,27,29,37,39,41,51
for grade: 8.1: #32,34,42,44; 8.2: #30,54 
HW9 due Apr 18 Withdrawal deadline: Apr 18

13 
Apr 21, 23, 25 
8.5, 7.1, 7.2, 7.3 
Application 9: least squares solutions.
General vector spaces. Subspace, span, linear independence, basis. 
8.5: #1,3,9,11,13, set the normal equation, but do not solve 35,37; 7.1: #13,15,19,23,25,27,41,43
7.2: #19(odd),17,19,21,25; 7.3: #19(odd),2127(odd)
for grade: 8.5: #4,14; 7.1: #24; 7.2: #6,18; 7.3: #22 

14 
Apr 28, 30, May 2 
10.1 
Exercises on diagonalization, orthogonality, and vector spaces. Inner product spaces. 
10.1: #5,7,19,21,27,29,59,61,63,69,71 
Exam3 (5.2, 6.1, 6.3, 6.4, 6.5, 8.1, 8.2, 8.5) on Apr 30,
HW11 on May 2

15 
May 5, 7, 9 
10.2, 10.3 
Applications of inner products. Review.
Application 10: polynomial and Fourier approximations. 
10.2: #2,8,10,15,16,21,23,37,39,41; 10.3: #11,15,17,25,35 

16 
Review exams, quizzes, homework. 
Final Exam (topics of Exams 1,2,3; chapters 7,10) on May 14 (Wednesday), 10 am  12 pm 