Harvard University 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: Exam #1 took place during the latter part of class on Wed, July 5. It covered topics in Chapter 13 of the text. Exam #2 took place during the latter part of class on Wed, July 19. It covered topics in Chapter 46 and Chapter 7, Sections 7.17.4 of the text. The graded exams will be returned in class on Monday. Scores are accessible via the Canvas site. The Final Exam took place on Friday, August 4 from 8:30am to 11:30am in Harvard Hall 201.
Note regarding submission of homework via email: We REALLY prefer that you do not submit homework as email attachments. Paper is so much easier to work with for the grading of homework. However, if you feel you must turn in an assignment via email, here are a few rules: (1) Get the OK first from Jeremy; (2) please don't send photographs unless the images are as good as what might be expected from a scanner; and (3) limit your file size to no more than about 150KB per page. If you don't know how to limit the file size, then don't submit your homework in this manner. We REALLY would prefer paper. HW #10 problems (PDF)  not to be turned in, but do them. The topics will be covered on the Final Exam. HW #9 problems (PDF)  due Mon, July 31. Turn in only those problems designated as such. There are also additional practice problems that you may try at your convenience but which are not to be turned in. HW #8 problems (PDF)  due Wed, July 26. Turn in only those problems designated as such. There are also additional practice problems that you may try at your convenience but which are not to be turned in. HW #7 problems (PDF)  due Fri, July 21. Turn in only those problems designated as such. There are also additional practice problems that you may try at your convenience but which are not to be turned in. We meet every Monday, Wednesday, and Friday from 9:30am to 11:30am in Harvard Hall 201. Robert Winters' Office Hours: Mondays, Wednesdays, and Fridays immediately following class (if necessary we'll move from Harvard 201 elsewhere to continue the conversation). Other times may be scheduled by appointment, if necessary. My Summer School office is Science Center 308. TA Jeremy Marcq has scheduled his weekly section each Friday from 12:00pm to 1:00pm at a location to be determined. This day/time is preliminary and may change. Jeremy will communicate this information via email. Course Calendar (2017) Math S21b syllabus (2017  HTML) Printable syllabus (2017  PDF) 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 (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. Answers to frequently asked questions:
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.
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:
Download your free Adobe Acrobat Reader for reading and printing PDF formatted documents. Please send comments to Robert Winters. 