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Prof. Jesenko Vukadinovic
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Office: 1S-228 phone: (718)
982-3632 Email: vukadino at mail.csi.cuny.edu Website: http://www.math.csi.cuny.edu/~vukadino |
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| Course Time and Place: |
Tuesdays: 6.30pm - 8.10pm in 1S-217 Thursdays: 6.30pm - 8.10pm in 1S-116 |
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Textbook: Bernard Kolman and David R. Hill, Introductory Linear Algebra: An Applied First Course Eighth Edition, 2005. ISBN 0131437402. Available at the University Bookstore or online: AddALL.
Material Covered: This course is an introduction to linear algebra. The central part is the study of linear equations, matrices, real vector spaces, and linear transformations.
Homework: The listed exercises from the textbook are strongly recommended as practice, but they will not be collected. Several quizzes out of this homework will be conducted. Answers for almost all of these are in the back of the book. I highly recommend working jointly on homework problems with fellow students, but in the end you must hand in your own work.
WeBWorK: WeBWorK is an online program that generates individualized problems, and provides immediate feedback. Incorrect answers may be corrected, so that I hope you will often submit perfect homework sets. These problems will be mostly computational exercises. This will count as part of your HW score.
MATLAB: MATLAB is powerful computer algebra software designed to solve linear algebra problems. The CSI Math Department has computer labs with access to MATLAB, and our textbook has many homework problems designed for MATLAB. Using MATLAB will be required for this course. For an introduction to MATLAB, see Chapter 12 of our textbook.
Grading: The course grade will be determined as follows: 20% Midterm Exam 1 + 20% Midterm Exam 2 + 30% Final Exam +30% WebWork and Quizzes.
Without exception, you must take the final exam at the time scheduled by the university.
Help: My office hours are Tuesdays 2.30-4.10 and Thursdays 3.40-4.30.
Optimal Method of Study: (1.) Come to class. (2.) Read the relevant sections after class. (3.) Do the homework. Leave time to think--do not put homework off until it is due! (4.) Compare your solutions with other students to improve what you hand in. (5.) Come to office hours or the help room with any remaining questions.
Written work: We write to communicate. Work must be neat and legible to receive consideration. You must explain your work to obtain full credit. For specific suggestions see A guide to writing in mathematics classes.
Goals: Many problems in linear algebra are computational -- the first goal is to make calculations with accuracy, intelligence and flexibility. But linear algebra is also a course filled with new concepts and new vocabulary, often with a geometric flavor -- the second goal is to explain the basic concepts clearly, reason logically with them, and use them to solve extended problems.
| Class | Topic | Read | Exercises |
| Jan 29 |
Linear systems |
§1.1 |
1.1: 5,7,9,11,13,15,22,27,T4 |
| Jan 31 |
Matrix multiplication | §1.3 | 1.2: 1,5,7,9,T1,T5,T7, 1.3: 1,5,7,9,11,13,15,19,21,25,T1,T3,T4,T7,T10 |
| Feb 05 | Matrix operations | §1.4 | 9,11,13,15,T6,T9,T23,T24,T27 |
| Feb 07 | Matrix transformations | §1.5 | 1,5,9,15,19 |
| Feb 14 | Solving linear systems | §1.6 | 3,5,8,9,13,19,23,27,31,47,T8,T11 |
| Feb 19 |
Inverse matrix | §1.7 | 3,5ab,11,13,15,18,25,T7,T9,T10 |
| Feb 21 | Determinants | §3.1 | 3,5abv,9,15,17,22,23,T5,T9,T16 |
| Feb 26 | Cofactor expansion | §3.2, 3.3 | 3.2: 1,5,9,11,15,19,23,T4,T5,T10,T11 |
| Feb 28 |
Vectors | §4.1, 4.2 | 4.1: 9,13,15,19,21,24,27,T5,T9 4.2: 1,4,11,13,17,21,23,26,27,T5,T13 |
| Mar 04 | Linear transformations | §4.3 | 1,7,13,15,17,21,25,27,29,T5,T11 |
| Mar 06 | MIDTERM EXAM 1 | ||
| Mar 11 |
Vector spaces | §6.1, 6.2 | 6.1: 1,3,4,9,13,15,20,T5 6.2: 3,7,9,17,19,20e,23,25,27,T3,T12 |
| Mar 13 | Linear independence | §6.3 | 1ab,3ac,5,7,9,11bc,12ab,13ab,14,16,T2,T8,T11,T13 |
| Mar 18 |
Basis, dimension | §6.4 | 1,3ab,5bc,9,11,13,19,23,27,29,31,33,35,T3,T4,T8,T12,T15 |
| Mar 20 | Homogeneous systems | §6.5 | 3,5,11,13,21,T3 |
| Mar 25 | Matrix rank | §6.6 | 1,3,5,7,11,17,19,21,23,27,29,33,T7,T12 |
| Mar 27 | Change of basis | §6.7 | 1,3,5,7,11,13,15,17,21,25,T4,T7c |
| Apr 01 |
Orthonormal bases | §6.8 | 1,3,5,9,11,15,17,19,21,T6,T9 |
| Apr 03 | Orthogonal complements | §6.9 | 1,3,7,9ab,11,13,T5 |
| Apr 08 |
Linear transformations | §10.1, 10.2 | 10.1/1,3,5,17,19,T5; 10.2/1,3,9,11,17,T2 |
| Apr 10 | Matrix of linear transformation | §10.3, B2 | 1,3,13,15,17 |
| Apr 15 |
MIDTERM EXAM 2 | ||
| Apr 17 |
Eigenvalues, eigenvectors | §8.1 | 5,9,11,13,15,17cd,19,21,25,T6,T9,T11,T15 |
| Apr 29 |
Diagonalization | §8.2 | 1,3,5,9,13,15,19,23,25,29,39,41,46,T2,T6,T7 |
| May 01 | Symmetric matrices | §8.3 | 1,2,5,9,17,T1,T6,T8 |
| May 06 |
Dynamical systems | §9.3 | 1,2,3,4,5 |
| May 08 |
Review | ||
| May 13 | Review | ||
| May ?? | FINAL EXAM |