Harvard Summer School 
Instructor: Course Assistant: 
If you're not sure whether the contents of this page (or any other page) are current, Course Textbook Linear Algebra with Applications, 4th Edition
OR Linear Algebra with Applications, 3rd Edition
OR Linear Algebra with Applications, 5th Edition
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:
Note: If you have email in the "hbs.edu" domain (Harvard Business School), it is likely that Math S21b related mail being sent to you is being blocked. They use a Japanbased service to block mail from domains that they have (wrongly) determined to be sending Spam. If you want to receive mail, please use a different email address not associated with the Harvard Business School. Note: If you must turn in homework assignments outside of class, you can use the Math S21b 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 righthand wall. We're in the first bank of boxes you pass, at the left near the middle.
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 GaussJordan 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 leastsquares approximation; inner product spaces; determinants; eigenvalues, eigenvectors, and the spectral theorem; discrete and continuous dynamical systems; phaseplane 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 PrenticeHall. 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 #67 Notes Week #3 Notes: Lecture #78 Notes Lecture #9 Notes Week #4 Notes: Lecture #10 Notes Lecture #11 Notes Lecture #12 Notes Week #5 Notes: Lecture #13 Notes Lecture #1415 Notes Week #6 Notes: Lecture #16 Notes Supplement on nonlinear systems
by permission of Bill Griffith
Useful Links:
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