Summer 2016

Harvard Summer School
Mathematics S-21b Summer 2016
Linear Algebra
and Differential Equations

Instructor:
Robert Winters

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:

Lecture #6 Notes

Exam #1 is scheduled for next Wednesday, July 6 during the latter part of class. It will cover topics from Chapters 1-3 and possibly a little bit of Chapter 4.

A Practice Exam will be posted soon. Solutions will follow.


Lecture #5 Notes

Supplement on Representation of Functions in Different Coordinates (a little additional explanation)


HW #3 problems (due in class on Wed, July 6). See the Course Calendar for additional details.

Lecture #4 Notes


Lecture #3 Notes


HW #2 problems (due in class on Wed, June 29). See the Course Calendar for additional details.

Lecture #2 Notes


HW #1 problems (due in class on Fri, June 24 or in Jeremy's 1-2pm section in Sever Hall 107). See the Course Calendar for additional details.

Lecture #1 Notes


Course Calendar (2016)      Math S21b syllabus (2016 - HTML)      Printable syllabus (2016 - PDF)


We will meet every Monday, Wednesday, and Friday (except Mon, July 4) from 9:30am to 11:30am in Harvard Hall 104.

Robert Winters' Office Hours: Mondays, Wednesdays, and Fridays immediately following class (if necessary we'll move from Harvard 104 to Harvard 102 to continue the conversation). Other times may be scheduled by appointment, if necessary.

Jeremy Marcq will have his weekly section on Fridays from 1:00-2:00pm in Sever Hall 107. Jeremy's office hours will be on Monday from 3:30-4:30pm in Science Center 105.


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 (used copies and older editions are considerably less expensive). 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.

Harvard Hall


Answers to frequently asked questions:

There is relatively little overlap between the Multivariable Calculus course and the Linear Algebra/Differential Equations courses, and they can be taken in either order or simultaneously. That said, there are a few vector-specific items that are necessary for the Math S-21b course but these are things that you may already know or can pick up pretty quickly. These include vector basics (adding and scaling) and the dot product (which we definitely will briefly develop and review). For the material on Differential Equations that we will primarily cover late in the course, it is not necessary to have had any previous exposure to Differential Equations.


The Math S-21b course is primarily a course in Linear Algebra with several applications to Differential Equations. It does not serve as a substitute for a full course in Differential Equations.


Harvard's Multivariable Calculus (21a) and Linear Algebra (21b) courses can be taken in either order or concurrently. During the Summer School we always have a number of students taking both courses, but it really is a lot of work to do that given the rapid pace of the Summer School courses.


Regarding any questions about being sufficiently "in-depth", we prove every result used in the course. It's not a course in which facts are simply given and applied. It's also not a course in "the art of proof" in that we tend to focus on the aspects of Linear Algebra that arise in many other contexts - applied and otherwise.


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.

HW Assignment #1 #2 #3 #4 #5 #6 #7 #8 #9
Total Pts. 135 130 120 70 140 100 130 110 90
median score -- -- -- -- -- -- -- -- --

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      Supplement on nonlinear systems

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URL: math.rwinters.com/S21b
Last modified: Friday, July 1, 2016 8:13 PM