syllabus
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University of Toronto Division of Engineering Science Linear Algebra MAT185H1 S Nuts & Bolts MAT185 is a continuation of linear algebra that was begun in ESC103. The essential topics in this course are vector spaces, determinants, eigenvalues and eigenvectors, diagonalization, and the solution of a system of ordinary differential equations. Our lectures will follow the notes, which will be available online at portal.utoronto.ca (Blackboard). The course begins at Chapter 4 but you must be familiar with the content of the first three chapters of the notes. Please take the time to review this material. The suggested supplementary volume, taken from Nicholson, is intended as a source of exercises and problems. The Nicholson text itself may be consulted as a second voice on the topic. This is a mathematics course and so you will see many proofs. You need to know not only the definitions and theorems but also to understand the proofs you encounter. The statements of results, and often their proofs, endow you with the tools and insight that you will need to do the suggested exercises and to understand future courses you may take. There are some applications in our notes and we shall include some in our lectures as time permits. Notes: J.W. Lorimer & G.M.T. D’Eleuterio, An Algebra Professor in the House of the Medici: A First Course in Linear Algebra for Engineers, Scientists and the Renaissance Man or Woman, 2012. . . Supplementary Volume: “MAT185 Linear Algebra Problems,” from W.K. Nicholson, Elementary Linear Algebra with Applications, Sixth Edition, McGraw-Hill, 2009. [Available from the UofT Bookstore by “print on demand.”] Reference Text: W.K. Nicholson, Linear Algebra with Applications, All Editions, McGraw-Hill.
description
mat185
Transcript of syllabus
University of Toronto
Division of Engineering Science
Linear Algebra MAT185H1 S
Nuts & Bolts
MAT185 is a continuation of linear algebra that was begun in ESC103.
The essential topics in this course are vector spaces, determinants, eigenvalues and eigenvectors, diagonalization, and the solution of a system of ordinary differential equations. Our lectures will follow the notes, which will be available online at portal.utoronto.ca (Blackboard). The course begins at Chapter 4 but you must be familiar with the content of the first three chapters of the notes. Please take the time to review this material. The suggested supplementary volume, taken from Nicholson, is intended as a source of exercises and problems. The Nicholson text itself may be consulted as a second voice on the topic.
This is a mathematics course and so you will see many proofs. You need to know not only the definitions and theorems but also to understand the proofs you encounter. The statements of results, and often their proofs, endow you with the tools and insight that you will need to do the suggested exercises and to understand future courses you may take.
There are some applications in our notes and we shall include some in our lectures as time permits. Notes: J.W. Lorimer & G.M.T. D’Eleuterio, An Algebra Professor in the House of the Medici: A First Course in Linear Algebra for Engineers, Scientists and the Renaissance Man or Woman, 2012. . .
Supplementary Volume: “MAT185 Linear Algebra Problems,” from W.K. Nicholson, Elementary Linear Algebra with Applications, Sixth Edition, McGraw-Hill, 2009. [Available from the UofT Bookstore by “print on demand.”]
Reference Text: W.K. Nicholson, Linear Algebra with Applications, All Editions, McGraw-Hill.
Lecture Sections L0101 L0102
Lecturer G.M.T. D'Eleuterio G.S. ScottInst for Aerospace Studies Dept of Mathematics
416 667 [email protected] [email protected]
Lectures M 15h00 SF1105 M 16h00 BA1130T 15h00 SF1105 R 15h00 BA1130F 9h00 MB128 F 9h00 SF1101
Office Hours to be Announced or by Appointment
Tutorial Sections TUT01/TUT08 TUT02/TUT10 TUT03/TUT07
Tutor Adam Sniderman Dmitri Chouchov Alex [email protected] [email protected] [email protected]
Tutorials W10h00/W11h00 W10h00/W11h00 W10h00/F11h00BA2159/BA2159 BA3008/BA3008 BA3012/BA3012
TUT04/TUT06 TUT05/TUT09Tutor Adina Goldberg Ozgur Esentepe
[email protected] [email protected] W10h00/F11h00 F11h00/W11h00
BA3116/BA3008 BA2159/BA2139
Suggested Exercises [from “MAT185 Linear Algebra Problems”]
You should do as many suggested exercises each week as possible. In the syllabus included at the end of this document, the problems indicated are from Nicholson’s “MAT185 Linear Algebra Problems,” available from the UofT Bookstore. You should especially attempt the ones that are indicated in boldface as these will be taken up for discussion in the following week’s tutorial, time permitting. At the end of each chapter of the notes, there are also problems. These have appeared on past tests and exams.
Please observe that the path through our course does not follow the same linear path in Nicholson. As a result, the batches of suggested problems appear a little unbalanced.
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Required Preparation: ESC103F
Cancellations and Rescheduling: Owing to the Engineering Science Education Conference, lectures and tutorials are canceled on Friday, 23 Jan 2015. The lectures are rescheduled as follows:
L0101: Tuesday, 6 Jan 2015, 9h00-10h00, SF1101 L0102: Tuesday, 13 Jan 2015, 10h00-11h00, BI131 (Banting Institute, 100 College St) Tutorials: Tutorials will begin the week of 12 Jan 2015.
Term Tests: The number and dates of the tests are to be determined. The duration of any test will be 90 minutes, commencing at 9h10 on the day of the test. Location of any test is also to be determined. Every student will write the same test at the same time. No aid is permitted.
Appeals: The grade on any test may be appealed by resubmitting the test paper indicating on the front page which question is to be regraded. Any such appeal must be submitted by the end of the tutorial period in which the test paper is returned. Any appeal submitted later will not be addressed.
Dates of the Term Tests: To be determined.
Absence from Term Tests: Consideration for absence from a term test due to illness or extraordinary circumstances will require the student to present formal documentation.
Final Exam: The final examination will cover the entire course work. The duration will be 2 hours and 30 minutes. Every student will write the same exam at the same time. No aid is permitted. The final exam will represent 60% of the final course grade.
Date of the Final Exam: To be established by the Faculty Office.
Composition of Final Course Grade:
40% Term Test(s) 60% Final Examination
All grades for this course can be reviewed and checked via Blackboard at portal.utoronto.ca.
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Syllabus
The following week-by-week syllabus is a guide only.
Week Dates Topic Readings1 5–9 Jan Introduction and the Vector Space §4.1
In Nicholson Problems [§6.1] 1–4
2 12–16 Jan More on Vector Spaces §§4.2–4.3In Nicholson Problems [§6.1] 8, 9, 13–15, 17, 18 (except f )
3 19–22 Jan Subspaces Chapter 5In Nicholson Problems [§5.1] 1, 2, 4, 12, 13, 18
Problems [§6.2] 1–5, 7–11, 13, 14, 16, 17, 20, 22, 25, 26
4 26–30 Jan Bases Chapter 6In Nicholson Problems [§5.2] 1, 2, 4, 5, 9, 11, 13–15, 17
Problems [§6.3] 1–8, 10–13, 17, 18–21, 23, 24, 29, 31, 34, 35Problems [§6.4] 1–5, 7, 9, 12–14, 16, 20, 23
5 2–6 Feb Row and Column Spaces §§7.1, 7.2For problems, see Notes
6 9–13 Feb Rank and the Dimension Formula §§7.3, 7.4In Nicholson Problems [§5.4] 1–3, 8, 9, 11, 18
Problems [§6.4] 22, 24
, 16–20 Feb Reading Week7 23–27 Feb Coordinates and Change of Basis Chapter 8
For problems, see Notes
8 2–6 Mar Determinants §§9.1–9.3In Nicholson Problems [§3.1] 2, 5–8, 11, 14–16, 22, 23, 24, 24
9 9–13 Mar More Determinations §§9.4, 9.5In Nicholson Problems [§3.2] 3–5, 8, 10–15, 26–29, 32–34
Problems [§3.6] 3
10 16–20 Mar Eigenanalysis §10.1–10.3In Nicholson Problems §3.3] 1, 3, 4, 6, 10, 11 (except c), 14, 16, 20, 21, 23
11 23–27 Mar Diagonalizability §§10.4, 10.5In Nicholson Problems [§5.5] 4, 7, 14, 16
12 30 Mar–3 Apr Linear Differential Equations §§10.6, 10.7In Nicholson Problems [§3.5] 1, 2, 3, 4
13 6–9 Apr Review
