Summer 2014

Harvard Summer School
Mathematics S-21b Summer 2014
Linear Algebra
and Differential Equations

Instructor:
Robert Winters

office: SC 127

Course Assistant:
Jeremy Marcq

Calendar of topics and
homework assignments
Solutions
(password required)

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Course Textbook

Linear Algebra with Applications, 4th Edition
by Otto Bretscher

ISBN: 0136-00926-3
ISBN 13: 978-0136-00926-9
Publisher: Prentice Hall

Compare prices:
Linear Algebra With
Applications, 4th Ed.

OR

Linear Algebra with Applications, 3rd Edition
by Otto Bretscher

ISBN: 0131-45334-3
ISBN 13: 978-0131-45334-0
Publisher: Prentice Hall

Compare prices:
Linear Algebra With
Applications, 3rd Ed.

OR

Linear Algebra with Applications, 5th Edition
by Otto Bretscher

ISBN: 0321-79697-7
ISBN 13: 978-0321-79697-4
Publisher: Prentice Hall
Bretscher, 5th Edition

Compare prices:
Linear Algebra With
Applications, 5th Ed.

A key matching HW exercises in different editions is available on request.

The older 2nd edition of the text may also be used. The material is fundamentally the same in all editions and all homework assignments will be made available as printable PDFs. Additional supplements on various topics in differential equations will also be made available during the course.

 

Announcements:

HW #8 problems (due Thurs, July 31) are now posted in the Course Calendar.

HW #9 problems (due Mon, Aug 4) are now posted in the Course Calendar.

HW #10 problems (do, but don't turn in) are now posted in the Course Calendar.


Exam #2 took place on Wed, July 23 during the latter half of class. It covered topics from Chapters 4, 5, 6, and 7.1-7.4.

Week #5 Notes: Lecture #13 Notes     Lecture #14-15 Notes

Approximate letter grades for Exam #1
Total points on exam was 50. Median score was 40.5.
Mean score was 39.5. Standard deviation was 10.0.
score grade    score grade
45+ A 30+ C+
42+ A- 27+ C
39+ B+ 25+ C-
36+ B 23+ D
33+ B- 0-22 E
Exam #1 solutions
Practice Exam #1     Solutions
    
Approximate letter grades for Exam #2
Total points on exam was 50. Median score was 44.
Mean score was 41.0. Standard deviation was 9.3.
score grade    score grade
45+ A 30+ C+
42+ A- 27+ C
39+ B+ 25+ C-
36+ B 22+ D
33+ B- 0-21 E
Exam #2 solutions
Practice Exam #2     Solutions

HW #6 problems (due Tues, July 22) are now posted in the Course Calendar.

HW #7 problems (due Fri, July 25) are now posted in the Course Calendar.

Week #4 Notes: Lecture #10 Notes     Lecture #11 Notes     Lecture #12 Notes


HW #5 problems (due Thurs, July 17) are now posted in the Course Calendar.


HW #4 problems (due Mon, July 14) are now posted in the Course Calendar.

Week #3 Notes: Lecture #6 Notes     Lecture #7-8 Notes     Lecture #9 Notes


Note: If you must turn in homework assignments outside of class, you can use the Math S-21b Dropbox located on the 2nd floor of the Science Center. As you exit the elevators on the 2nd floor, turn left and take an immediate left down the corridor with wooden mailboxes mounted on the right-hand wall. We're in the first bank of boxes you pass, at the left near the middle.

HW Assignment #1 #2 #3 #4 #5 #6 #7 #8 #9
Total Pts. 135 120 120 70 140        
median score 129 113 116 67 134        

Exam #1 took place during the latter part of class on Wed, July 9. It covered topics from Chapters 1-3 of the text (and HW #1-3).


HW #3 problems (due Wed, July 9) are now posted in the Course Calendar.

Week #2 Notes: Lecture #4 Notes     Lecture #5 Notes


HW #2 problems (due Wed, July 2) are now posted in the Course Calendar.

Week #1 Notes: Lecture #1 Notes     Lecture #2 Notes     Lecture #3 Notes


HW #1 problems (due Fri, June 27) are now posted in the Course Calendar.

Classes began on Monday, June 23.


Course Calendar (2014)      Math S21b syllabus (2014 - HTML)      Printable syllabus (2014 - PDF)


Robert Winters' Office Hours: Mondays, Wednesdays, and Fridays following class either in our classroom or in my office (SC 127). Other times may be scheduled by appointment. On some days I may go to lunch after class and return to the office afterwards.

Course Assistant Jeremy Marcq will be holding a problem session and additional office hours. Jeremy has reserved Sever Hall 211 for Thursdays from noon through 3:00pm. The plan for now is to dedicate the first 90 minutes to a problem session and then be available for additional questions/office hour for the next 90 minutes. We are aware that this time period is in conflict with a couple of other courses, so we may change the day/time depending on what works best for (almost) everyone.


Topics to be covered include Gauss-Jordan reduction and systems of linear equations; matrices and linear transformations; linear independence; subspaces; matrices and coordinates relative to different bases; general linear spaces; orthogonality and least-squares approximation; inner product spaces; determinants; eigenvalues, eigenvectors, and the spectral theorem; discrete and continuous dynamical systems; phase-plane analysis of linear and nonlinear systems of ordinary differential equations; and function spaces and differential operators.

This course is primarily a course in Linear Algebra. It has always included applications to Differential Equations (perhaps 15% of the course), but the intention has never been to serve as a substitute for a full course in Differential Equations. This summer we will likely provide more focus on the applications of Linear Algebra to Differential Equations than in summers past.

Text: Linear Algebra With Applications, 4th Edition (2008) or 3rd Edition (2005) by Otto Bretscher, published by Prentice-Hall. The new 5th Edition (2013) of the text may also be used, but HW problems are currently keyed to the 4th Edition. Use the links to the left to find the best online prices for a text. We will cover almost all topics in this book, and homework will be assigned from its large collection of exercises. The material is fundamentally the same in all editions and all homework assignments will be made available as printable PDFs. A key matching HW exercises in different editions is available on request. Additional supplements on various topics in differential equations will also be made available during the course.


Week #1 Notes: Lecture #1 Notes     Lecture #2 Notes     Lecture #3 Notes

Week #2 Notes: Lecture #4 Notes     Lecture #5 Notes     Lecture #6-7 Notes

Week #3 Notes: Lecture #7-8 Notes     Lecture #9 Notes

Week #4 Notes: Lecture #10 Notes     Lecture #11 Notes     Lecture #12 Notes

Week #5 Notes: Lecture #13 Notes     Lecture #14-15 Notes

Week #6 Notes: Lecture #16 Notes

The notes will be modified for 2014 and additional Notes will be developed for the last two weeks of the course.

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Birds on a wire

Out of the Equation - Zippy the Pinhead, by Bill Griffith

by permission of Bill Griffith



(adapted from a Gary Larsen cartoon)



Click for today's comic.

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Please send comments to Robert Winters.
URL: math.rwinters.com/S21b
Last modified: Monday, July 28, 2014 1:46 AM