MATHEMATICS DIVISION COURSE SYLLABUS
MATH 280-01 CALCULUS III (5 Credit Hours) FALL 2008
CATALOG DESCRIPTION: Topics covered include the calculus of vector-valued functions, the
differential
calculus
of functions of more than one variable, directional derivatives, gradients,
partial derivatives,
multiple integration, vector
fields and line integrals. Applications
are included throughout the course.
Numerical, graphical and
algebraic approaches are included throughout the course.
PREREQUISITE: A grade of C or better in Math 183.
INSTRUCTOR: Thomas
Kelley
CONTACT
INFORMATION: Office: A-223 (Instructional
Telephone: (313)
845-6492 E-Mail: tkelley@hfcc.edu
Office
Hours: MWR 11:15 AM - 1 PM & 2:45 – 3:30 PM, Tues 11AM – Noon and
Fri 10 – 11:30 AM. Learning Lab: Tuesday 12:08 – 1 PM
COURSE GOALS:
1. To carry forth the objectives listed in the course outlines for Math 180 and Math 183.
2. To present the calculus of vector-valued functions and functions of several variables.
3. To show applications involving multi-dimensional mathematical models.
MAJOR CORE OBJECTIVES: Upon successful completion of this course students should be able to:
1. Graph by hand and computer 3-dimensional surfaces and solids such as lines, planes, cylinders and quadric surfaces using rectangular, cylindrical and spherical coordinate systems.
2. Graph by hand and computer contour diagrams and level surfaces and use these sketches to “picture” functions of 2 and 3 variables.
3. Identify and solve problems involving vectors both geometrically and algebraically and interpret vector operations, such as dot and cross products, projections, geometrically.*
4. Find the derivatives and integrals of vector-valued functions and use them to describe motion in space via the vector components of velocity and acceleration.
5. Find the partial and directional derivatives of functions of several variables using numerical, algebraic and graphical means and interpret each geometrically.
6. Identify whether the solution to a problem requires the use of a partial derivative, a directional derivative or a gradient, describe what these concepts represent, and solve the problem.*
7. Find local and global extrema of multivariate functions.
8. Evaluate multiple integrals both numerically using Riemann Sums and the rules for antidifferentiation and the Fundamental Theorem of Calculus using rectangular, cylindrical and spherical coordinates.
9. Identify problem situations that use multiple integrals, describe graphically what the integral represents, and set up and solve these problems.*
10. Graphically illustrate what a line integral represents and evaluate these line integrals using appropriate techniques such as parameterization, Fundamental Theorem of Line integrals or Green’s Theorem.
*=fulfills HFCC General Education Outcome for critical thinking and problem solving
TEXTBOOK: Calculus, Early Transcendentals, 6th Ed. by Stewart
Optional: Multivariable Calculus - Student Solutions Manual
A graphing calculator is required of each student. The Mathematics Division recommends and uses
the TI-83(or 84) or
TI-83(or 84) Plus Graphing
Calculator. Students will be expected to use the DPGraph computer program. (It is on the HFCC network and students may
download it free on their home computers.)
CORE COURSE TOPICS:
Chapter 12 Vectors and the Geometry of Space Sections 12.1 – 12.7
Chapter 13 Vector Functions Sections 13.1 – 13.4
Chapter 14 Partial Derivatives Sections 14.1 – 14.8
Chapter 15 Multiple Integrals Sections
15.1 – 15.8
In Section 15.5, skip the Probability and
Expected Values subsections.
After Section 15.5 cover Surface
Area using pages 1019–1022 of the 5th edition, provided as a
handout.
Chapter 16 Vector Calculus Sections
16.1 – 16.4
INSTRUCTIONAL POLICIES:
Assignments: Routine
homework problems will be assigned at each class to be turned in at the next
class. Worksheet homework will be
distributed and is usually due one week from the distribution date. Homework will be graded and returned.
Suggested exercises will be given and the student is strongly encouraged to do
them. They are not handed in, but questions on them during class or office
hours are welcome.
Attendance: Attendance will be noted at
each class session. If you miss a class
you are responsible for finding out what you missed and making arrangements for
making up the work. Office hours are for
questions not answered in class; they are not
make-up classes.
Grading
Procedures: At least three “in-class” exams will be given
during the semester with at least one week’s notice given before the date of
the exam. The grade on homework will
count as 1 “in-class” exam. The Final
exam will be given as scheduled by the college and counts from 25 – 33% of your
course grade.
Grading
Policy: Grades are based on the scale:
90 – 100 = A range. 80 – 89 = B range. 67 – 79 = C range. 55 –
66 = D range. Less than 55 = E.
Missed
Examination: If you must miss an exam for a very good reason, let me know as soon
as possible. Arrangements may be made to
take an exam early, but do not expect to be able to make up an exam if you let
me know after the fact.
Drop Policy:
College Policy: Students
may officially drop a class and receive a DR grade anytime up until the end of
the day Thursday, November 6, 2008. If a
student stops attending without officially withdrawing, the instructor may
record either an E or a DR grade.
Instructor Policy:
Students may receive a DR grade if they make a request for the grade in
writing to the instructor before noon on Friday, December 5, 2008.
Academic
Dishonesty:
College Board of Trustees
Policy #8500 (adopted
3/17/97):
A...It shall be the policy of the College
that determination of the fact of academic dishonesty by a student shall be a
matter of individual judgment by the instructor. The instructor may administer a penalty up
to, and including, failure in the particular course...
Instructor Policy:
Academic dishonesty of any form will be grounds for immediate failure in
the course and the recording of a final grade of E in the course. To insure the integrity of test scores,
students are not allowed to leave the classroom during tests.
A registered student may only drop-down
(move-up) to another math class within the first three weeks of the Fall and Winter semesters. In the Spring and/or Summer semesters,
students have only one and one-half
weeks to drop-down (move-up) to another class.
In order to drop-down (move-up), a student must:
Obtain the written permission of his/her
current instructor stating that the student was misplaced, see the Mathematics
Division Director for assistance in finding open sections, and obtain the
written permission of the instructor in the new lower (higher) course.
The student must then officially file an
Add-Drop form at the Registration office.