MAT 303: Calculus IV with Applications
Spring 2004
Department of Mathematics
SUNY at Stony Brook
The course is an introduction to ordinary differential equations.The
material
covers standard techniques of solving linear differential equations
with
constant coefficients and systems of differential equations.
Differential
equations play a profound role in expressing physical laws and have
numerous
applications in applied science, economics, life and social sciences.
We
will discuss most common applications, as well as numerical methods for
solving differential equations.
Textbook: Differential Equations and Boundary Value
Problems:
Computing and Modeling, 3rd Edition, by Edwards & Penney,
Pearson/Prentice
Hall, 2004.
Note that the second and third editions of the book have similar
text,
but the problems are different. If you own the second edition, in order
to do the homework you'll need to borrow the third edition from a
friend,
or look at the book in the library, or in the Math Learning Center.
Prerequisite: The completion of one of the standard calculus
sequences
(MAT 125-127, MAT 131-132, or MAT 141-142) with the grade C or higher
in
MAT 127 or 132 or 142 or AMS 161. The course will heavily rely
on the material covered in the standard calculus sequence. The
familiarity with complex numbers and the knowledge of the basic
concepts of linear algebra are required. The 200-level courses
MAT 203/205 (Calculus III) or AMS 261, and MAT 211 (Linear Algebra) are
strongly recommended.
Instructor: Leon Takhtajan, Math Tower 5-111,
Office Hours: Tu W, 4-5 pm, and by appointment.
Phone: 632-8287 email: leontak@math.sunysb.edu
Recitation instructor and grader: Anirban Dutta, Math. Tower
2-121,
e-mail: dutta@math.sunysb.edu
Lectures: New material is presented each week at the
lectures.You
are encouraged to read the corresponding section of the text before
attending each lecture.
Class schedule:
LEC 1 |
TuTh |
9:50am-11:10am |
Hvy Engr Lab |
201 |
Takhtajan, Leon |
R01 |
F |
11:45am-12:40pm |
S B Union |
237 |
Dutta, Anirban |
R02 |
W |
11:45am-12:40pm |
Earth&Space |
69 |
Dutta, Anirban |
Syllabus
Homework: Doing the homework is a fundamental part of the
course
and you are supposed to work hard on the problems assigned in order to
succeed in the course. Homework will be posted weekly on the web
page and will be collected in class on Thursdays, a week
after the material is covered in lectures. Late homework will not
be accepted,
no exceptions. The homework will consist of two parts. The first
part deals with analytic
problems, solutions to which require only pencil and paper.
Problems
marked by asterisk are required in order to get the full homework
grade. The second part
consists of application modules and is based on Maple,
Mathematica or MATLAB
software packages, as described in the textbook
and in the Applications Manual.
Sofware: Maple and Mathematica disks can be purchased
from the Seawolves store for $5 each. The disks are not on the shelves,
so you have to ask for them (if someone says that they do not sell
them, ask for Donald Linne). The Seawolves do not sell MATLAB, which
can be purchased
directly from Academic Superstore on-line. Maple, Mathematica and MATLAB are
installed on ten SINC site
computers around campus (in particular, in S-235, Math. Tower).
- HW1 (due Thursday, 2/5 in
class) Ch. 1.1: 6*, 7*, 8*, 10, 15*, 20, 27, 33, 34, 35*,
43*; Ch. 1.2: 2, 6, 8, 10*,
18, 25*, 35*, 42*.
- HW2 (due Thursday, 2/12 in
class) Part I. Ch. 1.3: 2 ,4, 8, 12*, 14*, 15*, 27*; Ch. 1.4: 1, 2, 3*, 5*, 11*, 12,
17*, 19*, 27*, 38, 47*. Part II.
Application module 1.3 on p. 29, Investigations A & B (only
B will be graded). You may
warm up by generating the slope fields and some solution curves for
Problems 1 through 10 in Ch. 1.3
by using Maple, Mathematica or MATLAB resources.
- HW3 (due Thursday, 2/19 in
class) Ch. 1.5: 1, 3*, 4*, 6, 8, 13*, 17*, 30*, 35, 37*,
38*; Ch. 1.6: 1*, 2*, 3, 8*,
16*.
- HW4 (due Thursday, 2/26 in
class) Part I. Ch. 1.6: 21*, 28, 29*, 31*, 32, 33*, 34,
35*, 37*, 39, 42, 43*, 44*, 45, 46*, 53*, 57*. Part II.
Application module 1.6, Investigation on p. 75 (fine tune
parameters of DEplot
window, etc., so that your direction field and typical solution curves
would be of
the same quality as those in fig. 1.3.25 on p. 29).
- HW5 (due Thursday, 3/4 in class;
extended until Tuesday, 3/9)
Ch. 2.1: 3*, 11*, 22*; Ch.
2.2: 4, 6*, 8, 12, 14*, 21*;
Ch. 2.3: 2*, 4*, 10*, 27*, 28*.
- HW6 (due Thursday, 3/11) Part II
(there is no Part I). Ch. 2.4: 5*,
27* and famous numbers investigation on p. 121; Ch. 2.5: 5*, 27* and famous numbers investigation
revisited on p. 131; Ch. 2.6:
5*, 27* and famous numbers revisited one last time, on p. 142. Here is the
link to implementation of
numerical methods using Maple and Mathematica.
- HW7 (due Thursday, 3/18 in
class)
Ch. 3.1: 1*, 3, 7, 9*, 11, 13*, 15, 19*, 20, 22, 24*, 29*, 33*,
37*, 45*, 46*.
- HW8 (due Thursday, 3/25 in
class)
Ch. 3.2: 1, 3, 5*, 8*, 10, 12, 15*, 22*, 27*, 30*, 31; Ch. 3.3: 8*, 9*, 21*, 22*, 23*.
- HW9 (due Thursday, 4/1 in class)
Part I. Ch. 3.3: 11*, 14*, 15*, 17*, 19*, 20*, 27*, 33*, 36*,
51. Part II. Application module 3.3
on p. 181-182
1,3,5.
- HW10 (due Thursday, 4/15 in
class)
Ch. 3.5: 2*, 4*, 6*, 8, 25*, 27*, 29*, 35*, 41*, 47*, 49*, 51,
53, 55*.
- HW11 (due Thursday, 4/29 in
class) Ch. 5.1: 12, 14*, 21*, 27*; Ch. 5.2: 1*-15* odd, 31*, 35, 38*,
39, 40*, 41.
- HW 12 (due Thursday, 5/6 in
class) Ch. 5.4: 1, 3, 5*, 7*, 9, 11*, 12, 15*, 17, 19*, 21*; Ch. 5.5: 3, 5, 9*, 11*; Ch. 6.1: 1-5, 13*-15*; Ch. 6.2: 1*, 3*, 5*, 7*.
Exams:
- Midterm I: (in class)
Thursday, March 4. Solutions.
- Midterm II: (in class) Thursday, April 22 Solutions.
- Final Exam - Time: Tuesday, May 18, 8:00-10:30 am; Place:
HARRIMAN 137. The exam is cumulative; it covers all material used for
Midterms I and II, as well as Sections 4.1, 5.1, 5.2, 5.4, 5.5, 6.1 and
6.2. To prepare for the exam it is important to review all homework
problems (no Part II problems!) and solutions to Midterms I and II. For
the material covered after Midterm II, the best practice is to go over
homework assignments 11 and 12. While understanding how to solve these
problems it is very helpful to consult corresponding material in the
textbook and examples.
- Additional office hours during the finals week: May 12-14:
3-4 pm, May 17 3-4 pm and by appointment (by e-mail).
Make sure that you are available at these times, as there will
be
no make-ups for missed midterm exams. Laptops, cell phones,
calculators, books,
notes, etc., are not allowed during exams. If you miss an
exam for an acceptable reason
and provide a valid
written excuse,
the relevant midterm will be dropped in computing your course grade.
Incomplete
grade will be granted only if documented circumstances beyond your
control
prevent you from taking the final exam. The final exam is cumulative
and
will be based on all material covered in the course.
Grading: Your course grade will be based on your examination
performance and homework, weighted as follows: two midterms in class
20%
each, homework Part I 20%, homework Part II 10%, and the final exam
30%.
Help: The Math Learning Center (MLC) is in S-240A, Math. Tower. This
is a place where students can go for help and where study groups can
meet.
The MLC is open 10 am-9pm Monday through Wednesday, 10am-6pm
Thursday
and 10am-2pm on Friday. If you want a private tutoring, there is a list
of mathematics graduate students who tutor in the Undergraduate
Mathematics Office, Math. Tower, P-143.
All necessary information regarding the course will be regularly
posted
on the World Wide Web, and can be accessed by pointing your browser to
http://www.math.sunysb.edu/courses.html
Americans
with Disabilities Act
If you have a physical, psychological, medical
or learning disability that
may impact your course work, please contact Disability Support
Services,
ECC (Educational Communications Center) Building, room 128, (631)
632-6748.
They will determine with you what accommodations are necessary and
appropriate. All information and documentation is confidential.
Students requiring emergency evacuation are encouraged to discuss their
needs with their professors and Disability Support Services. For
procedures
and information, go to the following web site:
http://www.www.ehs.stonybrook.edu/fire/disabilities.asp