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Mathematics 51, Fall 2012
Announcements ARC review sessions in
Braker Hall 001:September 30th, 12-2pm, October 28th, 12-2pm, December 2nd, 5-7pm, December 12th, 4-6pm. (Double-check these against the ARC schedule to be sure.)
If you are requesting an accommodation as a result of a documented
disability, you must register with the Disability Services Office at the
beginning of the semester. To do so, please call the Student Service Desk
at 617-627-2000 to arrange an appointment with the Program Director of
Disability Services. Your instructor does not need to be apprised of such
needs.
Students needing any special arrangements for exams due to scheduling conflicts or
because of accommodations arranged by the Program Director of Disability Services should contact
gail. kaufmann at Tufts. edu
well in advance, preferably in the first week of the semester.

The syllabus .
Archived syllabi for
Spring 2012
Fall 2011
Spring 2011
Fall 2010 ,
Spring 2010 ,
Fall 2009 ,
Spring 2009 ,
Fall 2008 ,
Spring 2008 ,
Fall 2007 ,
Spring 2007 .
The
Fall 2006 syllabus
was ordered differently, so the exams do not quite correspond.
Sections:
Hasselblatt (B block)
Adler (C block)
Barthelmé (F block)
Examination dates and grading policies are here
At the beginning of the semester, please check these dates against any
other examinations you have scheduled. If there are any time conflicts,
please notify
gail. kaufmann at Tufts. edu
immediately.
Homework: Homework is due at the
beginning of the next class. You are encouraged to collaborate, but you
must hand in solutions written in your own hand. Please mark your homework (and folder, if used in the course) with the
course and section numbers as well as an identifier to help you know that
it is yours---something that is likely unique to your section and something
that is pronounceable in case your instructor chooses to return homework by
calling out the identifiers. Please write it as clearly as possible and
make sure to tell your instructor well before the end of the semester what
your identifier is, so credit associated with it can be counted towards
your course grade.
Feel free to use your name as your identifier, but since homework is handed
off between instructor and grader in a way that does not ensure
confidentiality (such as by way of drawers in the lobby of the
Bromfield-Pearson building), putting your name on the homework or the
folder means that you opt out of being guaranteed the confidentiality of
this part of your course work. You receive one point if
your homework contains
a bona fide attempt at every exercise
(copying the statement does not suffice) and
the correct solution to at
least 60% of the exercises (answers only are not enough).
Do not
claim credit for any parts of solutions copied from the blackboard during
class! Your homework credit is
\(\displaystyle H=u_{26}(n)\cdot\frac{n-20}4\), where \(n\) is the number of homework points and
\(u\) is as on p. 449 of the text.
Textbook
Textbook: Reprint of M. M. Guterman, Z. H. Nitecki,
Differential Equations -- A First Course , 3rd ed., Saunders (1992).
Saunders ISBN 0-03-072878-9, reprint ISBN 81-89617-20-6
The Tufts bookstore web site can create the impression that there is a
6th edition. There is not. The reprint is good enough for the course.If you can get a used copy of the originally published book (the cover looks like the background of this web page), even better.
Where to buy the text inexpensively? Some fellow
students have suggested Amazon
or Half.com ,
and AddAll seems to be a another good start
(no endorsement implied, and note that you won't get the same return policy as
from the Tufts bookstore!).
There are many other options, so do look around.
The ISBN need not match exactly, but make sure that the authors, title and
edition match. There are earlier editions, and the same authors have another book with
a similar but different title.
The course uses portions of the book that are not included in the reprint (but can be found in the original Saunders book). These are
Chapter 1 (plus 2A)
of the text - for those whose book did not arrive on time.
A supplement
to the text that introduces complex numbers and how to do partial
fractions, undetermined coefficients and Laplace transforms using complex
numbers systematically.
Office hours, tutoring, review sessions
The purpose of going to office hours and to obtain tutoring is to deepen
your understanding of the subject matter of a course. If you are doing
well in this class, tutoring can help be an outstanding student in it. In
high school this is an expensive add-on, and here it is a free service.
The ARC has excellent tutors available.
Utilize the office
hours offered by the instructor of your section. We are happy to see
you, we'll get to know you better, and during office hours you may get a
perspective on the subject that you did not see in class.
During reading period there are special office
hours
The ARC drop-in hours are to be determined; last semester they were as follows:
Sundays 7:00 - 9:00pm Tilton Hall Study Lounge
Tuesdays 3:00 - 5:00pm Campus Center 209
4:30 - 6:30pm Hill Hall 2-31 / 2-32
Wednesdays 5:30 - 8:00 pm Campus Center 209
Thursdays 3:00 - 5:00pm Houston Hall 218
4:00 - 7:00pm Campus Center 209

Find a tutor
by checking
the schedule or as follows:
Log onto student web
center using your Student
ID Number and password.
From the Navigation Menu, choose Tutor Finder.
Choose View Available Tutoring Subjects.
Click the Subject, followed by the course number to find the tutors
available in that subject area.
You will see all of the available hours for tutors in that subject.
Click "Reserve" to reserve a one-on-one session with a tutor. Or click
"Notify" to let a tutor know you plan on attending their drop-in hours.
Fill out the information in the form.
The Online Tutor Finder will immediately email the tutor and you with a
confirmation of the tutoring appointment (subject, date, time, name,
location)
If you need to cancel, you can do so online up to 6 hours before
the appointment.
ARC review sessions are scheduled for September 30th, 12-2pm,
October 28th, 12-2pm, December 2nd, 5-7pm, and December 12th, 4-6pm, all in
Braker Hall 001.
Study aids and supplements to the text
A supplement
to the text that introduces complex numbers and how to do partial
fractions, undetermined coefficients and Laplace transforms using complex
numbers systematically.
Table of
Laplace
transform formulas . This will be provided for the second exam and the
final exam. Feel free to use it for homework as well.
Free online lectures
Examples of making it easier to find eigenvalues . These use
the properties of determinants summarized in Note 2. on page 192f of the
book — review these!
Help
with
Summary of spring dynamics
The Vandermonde
determinant (useful for Exercise 2.4.13a, but Exercise 2.5.26
provides a more interesting idea)
Simplifying characteristic polynomials by row or column operations
Summary of the row
reduction operations
Reading about Euler's method: Lamar University and Wikipedia and a demo at Cal State Fullerton about increasing the number of steps.
Answers to even-numbered review problems in Chapter 3
Worked solutions for Exercise 1 on page 321 ,
Exercise 2 on page 321 ,
Exercise 8 on page 322 .
Answers to even-numbered exercises on page 321f.
Phase portraits of linear systems .
Notes on
phase portraits of nonlinear systems .
Assistance for
phase portraits of nonlinear systems from
Rutgers
(very sensitive to spaces and the like in the input field!!!!).
Suggestions for exam preparation:
Exams from previous semesters are provided below and can be a useful guide,
but because in different semesters the exam dates occur in different
places in the syllabus, and because topics change over time you may have to pick and choose from different
exams for any one previous semester and make sure to work extra problems in any area not covered in previous semesters.
The homeworks assigned in the current semester provide the best indication
of the scope of exam preparation we expect. In addition, some of the review
exercises provided at the end of each chapter in the book can be useful.
Old exams
An online collection of exams is at the
Student Services website . It's a secure site - log
in as you would for SIS Online and choose the online
exams option once you're logged in.
Exam 1, Spring 1998
—
Solutions
Exam 2, Fall 2000
There is a misprint on problem 3: \(t^2D^2\) should
be \(tD^2\).
—
Solutions
Exam 2, Spring 2001
—
Solutions
Exam 1, Fall 2006, including solutions
Exam 2, Fall 2006, including solutions
Exam 3, Fall 2006, including solutions
Final examination, Fall 2006
—
Solutions
Exam 1, Spring 2007
—
Solutions
Exam 2, Spring 2007
—
Solutions
Exam 3, Spring 2007
—
Solutions
Final Exam, Spring 2007
—
Solutions
Exam 1, Fall 2007
—
Solutions
Exam 2, Fall 2007
—
Solutions
Exam 3, Fall 2007
—
Solutions
Final Exam, Fall 2007
—
Solutions
Exam 1, Spring 2008
—
Solutions
Exam 2, Spring 2008
—
Solutions
Exam 3, Spring 2008
—
Solutions
Final Exam, Spring 2008
—
Solutions
Exam 1, Fall 2008
—
Solutions
Exam 2, Fall 2008
—
Solutions
Exam 3, Fall 2008
—
Solutions
Final Exam, Fall 2008
—
Solutions
Exam 1, Spring 2009
—
Solutions
Exam 2, Spring 2009
—
Solutions
Exam 3, Spring 2009
—
Solutions
Final Exam, Spring 2009
—
Solutions
Exam 1, Fall 2009
—
Solutions
Exam 2, Fall 2009
—
Solutions
Exam 3, Fall 2009
—
Solutions
Final Exam, Fall 2009
—
Solutions
Exam 1, Spring 2010
—
Solutions
Exam 2, Spring 2010
—
Solutions
Exam 3, Spring 2010
—
Solutions
Final Exam, Spring 2010
—
Solutions
Exam 1, Fall 2010
—
Solutions
Exam 2, Fall 2010
—
Solutions
Exam 3, Fall 2010
—
Solutions
Final Exam, Fall 2010
—
Solutions
Exam 1, Spring 2011
—
Solutions
Exam 2, Spring 2011
—
Solutions
Exam 3, Spring 2011
—
Solutions
Final Exam, Spring 2011
—
Solutions
Exam 1, Fall 2011
—
Solutions
Exam 2, Fall 2011
—
Solutions
Exam 3, Fall 2011
—
Solutions
Final Exam, Fall 2011
—
Solutions
Exam 1, Spring 2012
—
Solutions
Exam 2, Spring 2012
—
Solutions
Exam 3, Spring 2012
—
Solutions
Exam 1, Fall 2012
—
Solutions
Other reading
About Wronski: MacTutor and Wikipedia
About Cramer
About Cramer's rule and Gaussian elimination
About population models .
Do you think forced spring models are complicated? Think again! They are
linear. A forced pendulum is really complicated.