MATH510-03 - Wentworth Institute of Technology

Wentworth Institute of Technology
Department Applied Math and Sciences
Fall 2010
Math 510 Calculus III
Department Office:
Dwight F. Horan
Location: IRALL 216
Location: Second Floor, Ira Allen 206
Phone: (617) 989-4358
Phone: (617) 989-4333
Email: [email protected]
Office hours
Monday, Tuesday and Thursday, 11:00 to 12:00. Other times are available by
appointment. Students should make appointment by contacting the instructor or
the Applied Mathematics and Science Department Administrative Assistant.
Credit Hours
4 hours
4 credit hours
Meeting Times
Class Type
From To
10:00 am
10:50 am
10:00 am
10:50 am
WAT 004
12:00 pm
12:50 pm
Section 03
Section 05
12:00 pm
12:50 pm
2:00 am
2:50 am
Section 09
Course Description
This course is designed to build on concepts developed in Calculus I and
II. Students will be exposed to Calculus concepts relating to engineering design,
inspection, and quality assurance. Skills developed in this course will be of value to
all majors.
Students must have successfully completed Calculus II in order to take this course
and have received an acceptable grade in Calculus II. Grades of "IC", "W", and "F" do
not satisfy prerequisites, nor does taking the prerequisite concurrent with this
Required Text (also available in online form)
Thomas’ Calculus Early Transcendentals Media Upgrade, 11/e, by Weir, Hass, and Giordano
The College Bookstore:
103 Ward Street Boston MA 02115
Telephone: 617-445-8814
Any scientific calculator may be used but a graphics or programmable calculator
would be best. Some exercises will be presented with these operations in mind.
Elementary programming may be required. Demonstrations will be done using the
Texas Instruments family of calculators. If you do not have a Ti then it is your
responsibility to know how to operate your own particular brand of calculator. A
virtual Ti family calculator is available on Blackboard.
Course Goals
After successful completion of this course students will have a working knowledge
of three dimensional vector applications, partial derivative applications and
multiple integral applications.
Course Learning Outcomes:
In addition, specific objectives are:
MATH 510 CALCULUS III: Learning Objectives
I. Vectors and Geometry of Space
Understand the three-dimensional coordinate system.
Find the distance between points.
Find the center and radius of a sphere.
Find the component form of a vector.
Express a vector as a product of its length and direction.
Find the direction of a vector and the midpoint of a line segment.
Find the dot product.
Find the projection of vectors.
Find the angle between vectors.
Find the length and direction of the cross product of vectors.
Find parametric equations of a line.
Find an equation of a plane.
Solve three dimension problems involving lines and planes.
Identify equations of cylinders.
Identify equations of quadric surfaces.
II. Vector-Valued Functions and Motion in Space
Find a particle’s position, velocity and acceleration vectors.
Find the angle between velocity and acceleration vectors.
Find parametric equations for the line tangent to a curve.
Find a curve’s unit tangent vector.
Find arc length.
III. Partial Derivatives
 Find domain and range of functions of several variables.
 Identify surface and level curves.
Find equations for level curves and level surfaces.
Find first-order partial derivatives.
Find higher order derivatives.
Find the gradient of a function.
Find the directional derivative of a function.
Find the greatest rate of change of a function and its direction.
Find equations of tangent planes and normal lines to surfaces.
Find local extrema.
Classify local extrema.
IV. Polar Coordinates
Understand the polar coordinate system.
Find the slope of a curve.
Graph in the polar system.
Find the area of regions.
V. Multiple Integrals
Evaluate an iterated integral.
Evaluate the double integral.
Evaluate a double integral over a given region.
Find the volume beneath a surface.
Reverse the order of integration.
Evaluate double integrals in polar coordinates.
Find the area of a region by double integration.
Evaluate a triple integral.
Find the volume of a solid using a triple integral.
Instructional Methodologies:
Lectures, Labs, and demonstrated examples.
Attendance Policy
Regular Attendance at every class is expected. If a student misses 10% of his/her
scheduled class sessions, he/she may be notified in writing by the instructor
through the instructor's department office, that continued absenteeism may result
in being withdrawn from the course. Students receiving this notice will be required
to consult with their instructor and advisor. If a student misses 15% of his/her
scheduled classes, he/she may be given a grade of WA in the course by the
instructor. This attendance policy will be in force each semester beginning on the
published "last day to add a course" date and continue through to the "last day to
drop a course" date.
Assignments/Submitted Work/Late Work
All written work submitted for this course must meet the Standards for English I.
Poorly written papers will be returned to you, without a grade, for revision. Students
are encouraged to utilize the Writing Center facility for help polishing their papers.
Work submitted late will be subject to a reduced grade. Assignments are listed on
the course outline and/or assigned by the instructor.
There will be three exams and a final. The dates will be announced in class
approximately one week in advance. Exams missed can be made up at the
discretion of the instructor. This is not to be confused with retests, which are not
usually given.
The homework will be online using MyMathLab. There will be lab assignments
throughout the course. The lab assignments will be done using MATLAB. The school
has a site license for the software so if you want to use your own laptop make sure
it's loaded on there. We will often revisit problems done in class using MATLAB.
There will also be a project done in MATLAB.
Grading and Student Evaluation System
Exams and final/project will count for 80% of your grade. Lab and homework
assignments will constitute the last 20%. Labs will be marked down 10% per class
day after the due date.
Wentworth Grading System:
Grade Definition
Student learning and accomplishment
far exceeds published objectives for the
course/test/assignment and student work
is distinguished consistently by its high
level of competency and/or innovation.
Student learning and accomplishment
goes beyond what is expected in the
published objectives for the course/test/
assignment and student work is frequently
characterized by its special depth of
understanding, development, and/or innovative
Student learning and accomplishment
meets all published objectives for the
course/test/assignment and student
work demonstrates the expected level of
understanding, and application of concepts
Student learning and accomplishment
based on the published objectives for
the course/test/assignment were met
with minimum passing achievement.
Student learning and accomplishment
based on the published objectives for than 60
the course/test/assignment were not
sufficiently addressed nor met
Grading and Student Evaluation System
Each exam will count for 20% of your grade. A final exam will be scheduled during
finals week. The final exam will have a weight of 20 %. Additional out-of-class
assignments will constitute the last 20%.
The drop/add period for day students ends on Friday of the first week of classes.
Dropping and/or adding courses is done online. Courses dropped in this period are
removed from the student’s record. Courses to be added that require written
permission, e.g. closed courses, must be done using a Drop/Add form that is
available in the Student Service Center. Non-attendance does not constitute
dropping a course. If a student has registered for a course and subsequently
withdraws or receives a failing grade in its prerequisite, then the student must
drop that course. In some cases, the student will be dropped from that course by
the Registrar. However, it is the student’s responsibility to make sure that he or she
meets the course prerequisites and to drop a course if the student has not
successfully completed the prerequisite. The student must see his or her academic
advisor or academic department head for schedule revision and to discuss the
impact of the failed or withdrawn course on the student’s degree status.
Make-up Policy:
Exams missed can be made up at the discretion of the instructor. This is not to be
confused with retests, which are not usually given.
Academic Support:
The Center for Teaching and Learning (CTL) assists all Wentworth students with
academic challenges in the areas of math, science, technical courses specific to
majors, and writing. The CTL is a supportive and safe learning environment for
students looking to improve or maintain their academic standing. In this studentbased learning environment, students can receive individual help with their studies,
meet and work in study groups, or go on-line to find resources to assist them in
meeting their goals for academic success. It includes tutors in many subjects,
online writing assistance and workshops. Make appointments at or through Lconnect.
Academic Honesty Statement:
“Students at Wentworth are expected to be honest and forthright in their academic
endeavors. Academic dishonesty includes cheating, inventing false information or
citations, plagiarism, tampering with computers, destroying other people’s studio
property, or academic misconduct” (Academic Catalog). See your catalogue for a full
Student Accountability Statement:
Students caught cheating or plagiarizing will receive a zero for that assignment. A
second infraction will result the student’s failure of the course.
Class Communication
If you are going to miss a class, please inform the instructor either by email or voice
mail, if possible. You are still responsible for material missed.
Disability Services Statment:
Any student who thinks s/he may require a disability-related accommodation for
this course should contact me privately to discuss your specific needs. Disability
Services coordinates reasonable accommodations for students with documented
disabilities. They are located in Watson Hall 003 (the Counseling Center) and can
be contacted at 617-989-4390 or [email protected] For more information on
acceptable documentation and the Disability Services process, visit the Disability
Services website at
Suggested Assignment (if online
assignments are unposted)
I. Vectors and Geometry of Space
Week 1
Sec 9.1
3-D Coordinate Systems
Pg. 504 1-51 every other odd
Sec 9.2
Pg. 513 1-29 odd
Week 2
Sec 9.3 The Dot Product
Pg. 520 1-12, 27-33
Sec 9.4
The Cross Product
Pg. 527 1-23 odd
Sec 9.5
Lines and Planes in Space
Pg. 535 1-69 every other odd
Sec 9.6
Cylinders and Quadric Surface
Pg. 542 1-43 odd
Week 3
II. Vector-Valued Functions and Motion in Space
Week 4
Sec 10.1
Vector Functions and Their Derivatives
Pg. 553 1-17 odd
Sec 10.3
Arc Length in Space
Pg. 564 1-9 odd
III. Partial Derivatives
Week 5
Sec 11.1
Functions of Several Variables
Pg. 588 1-43
Sec 11.2
Limits in Higher Dimensions
Pg. 597 1-11
Sec 11.3
Partial Derivatives
Pg. 607 1-19, 41-46
Sec 11.5
Directional Derivatives
and Gradient Vectors
Pg. 625 1-12,17,18,27-29
Sec 11.6
Tangent Planes
Pg. 632 1-17
Sec 11.7
Extreme Values and Saddle Points
Pg. 641 1-29 odd
Double and Iterated Integrals
over Rectangles
Pg. 661 1-19 odd, 23-27
Double Integrals over General Regions
Pg. 668 1-6, 11-43 odd
Area by Double Integration
Pg. 672 1-3 odd
Sec 8.2
Graphing in Polar Coordinates
Pg. 483 1-31
Sec 8.3
Areas and Lengths in Polar Coordinates
Pg. 487 1-25 odd
Double Integrals in Polar Form
Pg. 677 1-21
Triple Integrals in Rectangular
Pg. 684 1-19 odd
Week 6
Week 7
Week 8
Week 9
IV. Multiple Integrals
Week 10
Sec 12.1
Week 11
Sec 12.2
Week 12
Sec 12.3
Week 13
Week 14
Sec 12.4
Week 15
Sec 12.5
*Other topics as time permits
Moments and Center of Mass
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