Summer 2014

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

Instructor:
Robert Winters

office: SC 127 (expected)

Course Assistant:
Jeremy Marcq
(tentative)

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:

We will be doing the course again this summer. I hope you'll join us. - RW


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


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.

Course Assistant Jeremy Marcq will be holding a problem session and additional office hours.

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 (some topics to be covered Wed, July 24 and Fri, July 26)

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

Restore America's competitiveness!
Don't forget to pick up a textbook!

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: Saturday, March 22, 2014 12:16 PM