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: The Final Exam took place on Friday, August 5 from 8:30am to 11:30am in Harvard Hall 104 (our regular lecture hall). The exams have been graded. Course grades will be determined when all of the homework has been graded. Grades will be submitted to the Harvard Summer School no later than Wed, Aug 10.
HW #9 problems (due Mon, Aug 1). See the Course Calendar for additional details. HW #10 problems (do these as you prepare for the Final Exam, but don't turn in). See the Course Calendar for additional details. Lecture #16 Notes Supplement on nonlinear systems Supplement on Matrix Methods for Solving Systems of 1st Order Linear Differential Equations HW #8 problems (due in class on Wed, July 27). See the Course Calendar for additional details. Lecture #1415 Notes (for Wed, July 20 and Fri, July 22) Lecture #13 Notes (for Mon, July 18) Exam #2 (covering Chapters 46 and 7.17.4) took place on Wed, July 20 during the latter half of class. HW #7 problems (due in class on Fri, July 22). See the Course Calendar for additional details. Lecture #12 Notes (for Fri, July 15) Lecture #11 Notes (for Wed, July 13) HW #6 problems (due no later than Tues, July 19). See the Course Calendar for additional details. Lecture #10 Notes (for Mon, July 11 and Wed, July 13) There is a Dropbox now. It's on the 2nd floor of the Science Center on the corridor just around the corner from the elevators. Ours is the first one as you head down that corridor. HW #5 problems (due in class on Fri, July 15). See the Course Calendar for additional details. Exam #1 took place on Wednesday, July 6 during the latter part of class and covered topics from Chapters 13. The graded exams will be returned in class on Monday, July 11. HW #4 problems (due in class on Mon, July 11). See the Course Calendar for additional details. 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
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