University of Waterloo
Department of Management Sciences
MSCI 271
Advanced Calculus and Numerical Methods
Fall 2008
Instructor:
Emre Çelebi, CPH 4349, ext: 33675, e-mail: ecelebi@uwaterloo.ca. O¢ ce hours: Tuesday, 5:30pm-6:30pm
Objectives:
This course will be centered around several main topics covering partial di¤erentiation, multiple integrals,
ordinary di¤erential equations and numerical methods. We will extend the concepts of basic calculus to functions of several variables for a …rm background. Ordinary di¤erential equations (ODE) will be introduced
with some applications from management and economics. Throughout the course, numerical methods will
provide an introduction to numerical techniques used to obtain solutions to engineering and management
problems (unconstrained optimization problems, linear and non-linear systems of equations, numerical integration, initial and boundary value problems). Many software packages provide implementations of these
methods, but this does not eliminate the need for a thorough understanding of principles and practice. For
a particular application, an informed choice of method and sometimes customization of this method is often needed. Acquiring the fundamentals of scienti…c computation using MATLAB software is a secondary
objective.
Class Schedule:
Lectures
Tuesday, Thursday
Wednesday
MC 4020
15:30 - 16:20
16:30 - 17:20
Tutorial
Wednesday
Friday
MC 4020
17:30 - 18:20 (if needed)
14:30 - 15:20
Course website:
All course information and announcements are available through UW-ACE at http://uwace.uwaterloo.ca
Textbook:
Calculus for Engineers, 4th ed., Donald Trim, Prentice-Hall, 2008.
Supplementary Textbook:
A Friendly Introduction to Numerical Analysis, Brian Bradie, Prentice-Hall, 2006. (QA297 .B73x 2006)
Teaching Assistant:
Shuang David Liu, e-mail: s14liu@engmail.uwaterloo.ca.
Assessment:
To do well in this course, there are pre-class and post-class activities you must complete. Before each
class, you must read the textbook sections or posted course notes to get acquainted with the course
material and after each class you must solve some of the even-numbered exercises in the textbook
(answers are provided at the end of the textbook) for a …rm understanding of the course material.
You must develop problem solving skills week by week throughout the term. These skills cannot be
developed by cramming lecture notes at the last minute or looking at solution sets for a few hours before
exam time. There is simply too much material to learn in this way. Lectures will also mean more to you if
you are keeping up as new material is presented.
Assignments (4)
Quizzes (4)
Midterm
Final
20%
10%
30%
40%
There will be four assignments and they will be posted on Tuesday of the week as indicated in the
course outline. They are to be done individually. While you are encouraged to discuss the course material
with other students in the course, each assignment submitted for marking must be students’own
work.
Assignments are due at the beginning of the tutorials on Friday of the week as indicated in the
course outline (not any other time). Due dates are strict unless an extension is announced by the instructor.
Late assignments are not accepted.
Some assignments may involve using MATLAB, a high level computing language for algorithm development and numerical computation. MATLAB may be used at no-charge for coursework on UW-owned
computers.
Additionally there will be four quizzes which will be randomly held in tutorial sessions. This is for you
to attend tutorial sessions and it will act as a participation mark to your overall grade. Best three
out of four quizzes will count towards your …nal grade and there will be no make-up for a missed quiz
for any reason.
Midterm: Time and location: Wednesday, October 15th, 4:30pm-6:30pm, MC 4020. Midterm
will be closed book.
Final exam: Time and location TBA. It will be scheduled during the …nal exam period of December
5 to December 19. The …nal exam will be closed book.
You can appeal to any assignment, quiz or exam within two weeks after they are returned
back. You should appeal to the instructor or the TA by person. Appeals by e-mail are not accepted.
Course Outline:
Some of the topics listed are covered in the indicated textbook sections. Supplementary materials will
be available via UW-ACE. This is a tentative outline and can change as the course progresses.
Week
1
2
3
4
5
6
7
8
9
10
11
12
Topics
PARTIAL DIFFERENTIATION
Review of basic concepts and de…nitions
Directional derivatives and gradient
Relative and absolute maxima & minima
Lagrange multipliers
Systems of linear equations
Matrix methods
Systems of non-linear equations
Gradient search methods
MIDTERM
MULTIPLE INTEGRALS
Double integrals and double iterated integrals
Triple integrals and triple iterated integrals
Numerical integration
ORDINARY DIFFERENTIAL EQUATIONS
Review of basic concepts and de…nitions
First-order di¤erential equations
Initial value problems
Second order linear di¤erential equations
Boundary value problems
Review
FINAL EXAM
Reading
12.1-12.7
12.8-12.9
12.10-12.11
12.12
Course notes
Course notes
Course notes
Course notes
Key dates
Ass’t 1 posted
Ass’t 1 due in tutorial
Ass’t 2 posted
Ass’t 2 due in tutorial
Wed, Oct 15th, 4:30pm
13.1, 13.2, 13.6
13.8, 13.9
Course notes
15.1, Course notes
15.2-15.3, Course notes
Course notes
15.4, Course notes
Course notes
Ass’t 3 posted
Ass’t 3 due in tutorial
Ass’t 4 posted
Ass’t 4 due in tutorial
Time and location TBA
Note on academic o¤ences: Cheating and plagiarism will not be tolerated; students are referred to
University Policy 71 on scholastic o¤ences. http://www.adm.uwaterloo.ca/infosec/Policies/policy71.htm
Note for students with disabilities: The O¢ ce for Persons with Disabilities (OPD), located in Needles
Hall, Room 1132, collaborates with all academic departments to arrange appropriate accommodations for
students with disabilities without compromising the academic integrity of the curriculum. If you require
academic accommodations to lessen the impact of your disability, please register with the OPD at the
beginning of each academic term.
2