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: Exam #1 is scheduled for next Wednesday, July 6 during the latter part of class. It will cover topics from Chapters 13 and possibly a little bit of Chapter 4. A Practice Exam will be posted soon. Solutions will follow. 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. HW #2 problems (due in class on Wed, June 29). See the Course Calendar for additional details. HW #1 problems (due in class on Fri, June 24 or in Jeremy's 12pm section in Sever Hall 107). See the Course Calendar for additional details. 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 1:002:00pm in Sever Hall 107. Jeremy's office hours will be on Monday from 3:304:30pm in Science Center 105. 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. 