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
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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, 41--65(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, 33-53(odd), 59-65(odd), proofs of Theorems 2.16 and 2.17
3.1: #3,5,7,9,13,15, 19-31(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
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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), 39-45(odd),51,53,55
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6 |
Feb 24, 26, 28 |
3.2, 3.3 |
Matrix algebra. Inverses. |
3.3: #1-13(odd),21,23,25,27(a),31,35,41,43,47-53(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
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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: #1-15(odd),23,25,27,35,45-51(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
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8 |
Mar 10, 12, 14 |
4.2, 4.3 |
Null, row, and column spaces of a matrix. Rank-nullity theorem. |
4.2: #25-31(odd),41,47-53(odd) 4.3: #1,3,9,11,15-33(odd),43,45,47,51-57(odd)
for grade: 4.2: #34,50, 4.3: #22,24,34,36
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9 |
Mar 24, 26, 28 |
5.1, 5.2, 5.3 |
Determinants and their applications.
Application 6: calculation of area. |
5.1: #11,13,17,19,21,35,37,39,49,51,69-75(odd)
5.2: #3,7,11,13,25,35,39,47-57(odd),61; 5.3: #1,3,13,15,23,25 |
HW7 due Mar 28
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10 |
Mar 31, Apr 2, 4 |
6.1, 3.5 |
Eigenvalues and eigenvectors. Application to the Markov process.
Application 7: population model. |
6.1: #1,5,7,9,13,21,27,29,33,37-53(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
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11 |
Apr 7, 9, 11 |
6.3, 6.4, 6.5 |
Change of basis. Diagonalization. Complex eigenvalues. |
6.3: #1,5-17(odd),21,25,27,29 6.4: #5-15(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, Gram-Schmidt process. |
8.1: #5(d),15,17,25-51(odd),65-71(odd)
8.2: #1-13(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
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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: #1-9(odd),17,19,21,25; 7.3: #1-9(odd),21-27(odd)
for grade: 8.5: #4,14; 7.1: #24; 7.2: #6,18; 7.3: #22 |
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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
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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 |
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16 |
Review exams, quizzes, homework. |
Final Exam (topics of Exams 1,2,3; chapters 7,10) on May 14 (Wednesday), 10 am - 12 pm |