MAT 240 –Analytical Geometry and Calculus III

Mathematics Department

Semester: Spring 2012

Catalog Course Description:This course includes the following topics: multivariable calculus, including vectors; partial derivatives and their applications to maximum and minimum problems with and without constraints; line integrals; multiple integrals in rectangular and other coordinates; and Stokes' and Green's Theorems.

Prerequisite(s):MAT 141

Credit Hours:3.0 Credit Hours

Departmental Website:

Instructor: Patrick Harley

Telephone:738-7689

E-mail:

Campus Mailbox: 4th floor LET, Math Office

Personal Website:

Departmental Assistant:Mitzi Trigg – – 738-7689

Department Chair: Rick Bailey – – 738-7618

Program Coordinator:Rose Jenkins – – 822-3351

Class Schedule[s]:M W 5:25-7:25 LET 406

Textbook(s):Calculus, 9th Edition by Roland E. Larson and Bruce H. Edwards, Houghton Mifflin, 2010

Equipment: Graphing Calculator, TI-84 or TI-84+

Course Objectives:Upon completion of this course the student will be able to:

  1. Perform operations with vectors in space.
  2. Represent lines, planes and surfaces in space using rectangular, cylindrical and spherical Coordinates.
  3. Differentiate, integrate, and solve applied problems using vector-valued functions.
  4. Find partial derivatives, differentials, directional derivatives and gradients for functions of several variables.
  5. Determine extrema for functions of two variables.
  6. Evaluate double and triple integrals.
  7. Evaluate line integrals in vector fields.
  8. Solve problems by identifying what information is available and relevant to the problem.
  9. Solve problems by selecting or developing appropriate procedures and relationships.
  10. Solve problems by correctly applying the methods selected to the information available.
  11. Solve problems by verifying the validity and appropriateness of the solution.

Course Outcomes and Competencies:

Intended Course Outcome 3: Students should be able to solve more advanced mathematical application problems in programs that require mathematics knowledge beyond that included in the general education core competency of mathematics.

Course Competency 3: Students should be able to solve mathematical problems at the calculus and differential equation level by identifying what information is available and relevant to the problem; by selecting or developing appropriate procedures and relationships; by correctly applying the methods selected to the information available; and by verifying the validity and appropriateness of the solution.

Performance Measurement Instrument:Students will be given four applied mathematical problems to solve selected by the Mathematics Department to measure successful attainment of the competency. These problems will be embedded within student chapter tests and the final exam. A student scoring at least 3 out of 4 will be considered to have successfully attained the competency. The goal is for 80% of the students completing the assessment to successfully attain the competency.

Course Attendance:

ABSENCE -Failure to be present for a scheduled meeting of the class or arriving for the class more than ten minutes after the scheduled time for the class to begin.

TARDY --- Arrival to class after the instructor has called the roll and before ten minutes past the time scheduled for the class to begin.

  1. Absences are counted from the first day of classes.
  2. Five absences are allowed for a class that meets three times per week, and three absences are allowed for a class that meets two times per week.
  3. Three tardies are considered as one absence. The student must meet with the instructor at the end of the class to which he has been late to have the absence changed to a tardy.
  4. There are no "excused" absences; all absences are counted, regardless of the reason for the absence.
  5. A student missing class time by leaving early will also be counted absent.

Please note the following: You are responsible for all material and announcements presented, whether you are present or absent.

Withdrawal:Should the maximum allowable absences be exceeded prior to midterm, a "W" will be submitted to the registrar to be recorded on the student's transcript. Should the maximum allowable absences be exceeded after midterm, a "W" will be submitted to the registrar if the student was passing the course at the time of withdrawal OR a "WF" will be submitted if the student was failing the course at the time of withdrawal.

Tutoring: Tutoring services are provided through the AcademicSuccessCenter free of charge and are subject to availability. Please feel free to contact the AcademicSuccessCenter if you need additional assistance.

Course Requirements: This course will require the completion of homework and tests. Use will be made of internet resources. You will be required to obtain some assignments from the internet.

Course Grading:The course grading will consist of 4 tests and one cumulative homework grade. In addition, there will be a cumulative final exam. One test may be dropped, or the homework grade may be dropped. Thus, there will be 6 grades, equally weighted, at the conclusion of the course. The average of these grades will determine your grade following the scale below.

Grading Scale: 90-100ASuperior Work

80-89BGood Work

70-79CAverage Work

60-69DBelow Average Work

0- 59FUnsatisfactory Work

Classroom Rules/Other:The general routine of the class will move in three stages: (1) Instructor reviews some homework, (2) instructor lectures on new material, (3) students work problems.

There will be no makeup tests given for this course, unless there is a written doctor's excuse for the absence on the day of the test, and the instructor deems the illness to be serious enough to have warranted missing the test. Death or illness in the family is always a terrible thing, but does not qualify under the rule established here.

In the event of class disruption by a student - the MTC code considers such behavior, on the part of a student, an Honor Violation. According to college policy, the instructor is obligated to: (1) first warn the student that they are committing a violation, (2) ask the student to leave (calling in Campus Security if necessary). I am required, by contract, to remove all disruptive students from the class, and will follow this policy.

MTC policy forbids use of cell phones during class time, or disruption by a student who leaves class to make phone calls. I am required by contract to enforce this policy. If a cell phone is visible during the lecture, the student will be asked to leave class immediately.

Course Topic Outline/Course Calendar with Assignments:

WEEK / TOPIC / TEXT REF.
1 /

Vectors and the Geometry of Space

Vectors in the Plane / 11.1
Space Coordinates and Vectors in Space / 11.2
2 / The Dot Product of Two Vectors / 11.3
The Cross Product of Two Vectors in Space / 11.4
Lines and Planes in Space / 11.5
3 / Surfaces in Space / 11.6
Cylindrical and Spherical Coordinates / 11.7
4 /

TEST 1

Vector-Valued Functions

Vector-Valued Functions / 12.1
Differentiation and Integration of Vector-Valued Functions / 12.2
5 / Velocity and Acceleration / 12.3
Tangent Vectors and Normal Vectors / 12.4
6 / Arc Length and Curvature / 12.5

TEST 2

Functions of Several Variables

Introduction to Functions of Several Variables / 13.1
7 / Limits and Continuity / 13.2
Partial Derivatives / 13.3
8 / Differentials / 13.4
Chain Rules for Functions of Several Variables / 13.5
Directional Derivatives and Gradients / 13.6
9 / Tangent Planes and Normal Lines / 13.7
Extrema of Functions of Two Variables / 13.8
10 / Applications of Extrema of Functions of Two Variables / 13.9
Lagrange Multipliers / 13.10

TEST 3

11 /

Multiple Integration

Iterated Integrals and Area in the Plane / 14.1
Double Integrals and Volume / 14.2
12 / Change of Variables: Polar Coordinates / 14.3
Surface Area / 14.5
Triple Integrals and Application / 14.6
13 /

TEST 4

Vector Analysis

Vector Fields / 15.1
14 / Line Integrals / 15.2
Conservative Vector Fields and Independence of Path / 15.3
Green’s Theorem / 15.4

Comprehensive Final Examination

Academic Affairs Student Guidelines and Expectations

MTC Student Handbook:

Students are expected to read the MTC Student Handbook and abide by its policies. You can find the handbook online at copies are also available at various locations on campus. Some of the more important handbook policies that impact your academic success are listed below.

Academic Integrity:

  • The students of MTC have adopted the following Honor Code:

As a member of the MidlandsTechnicalCollege community, I will adhere to the college’s Student Code. I will act honorably, responsibly, and with academic integrity and honesty. I will be responsible for my own academic work and will neither give nor receive unauthorized or unacknowledged aid. I will behave courteously to all members of the MTC community and its guests and will respect college property and the property of others.

  • The Student Code(Appendix I of the MTC Student Handbook)defines academic dishonesty, which includes, but is not limited to, cheating on tests, plagiarism, collusion, and falsification. Such actions will result in discipline.
  • Cheating on tests includes:

.Copying from another student’s paper.

.Copying or presenting someone else’s work as your own.

.Using unauthorized materials during a test.

.Collaborating with any other person during a test without permission.

.Knowingly obtaining, using, buying, or selling in whole or part the contents of any test.

.Bribing any other person to obtain information about tests.

.Substituting for another student, or permitting another student to substitute for you.

  • Plagiarism is taking another person’s work and using it without giving the source credit in any graded assignment.
  • The use of cell phones or otherportable electronic devices for purposes of academic dishonesty in any form is strictly prohibited; students who violate this policy will be subject to the disciplinary procedures and sanctions outlined in the Student Code.
  • For more information about academic dishonesty, see the Student Code.

Class Attendance and Participation:

Students are responsible for meeting all attendance and participation requirements outlined in each course syllabus.

Portable Electronic Devices:

Cell phones and other portable electronic devices may be used in classrooms only for maintaining access to MTC Alerts!, the college’s emergency notification system. Other uses of portable electronic devices (for example, leaving class to make or receive phone calls, sending or reading text messages, accessing the internet, taking pictures or videos, listening to music, etc.) will be considered disruptive activities, and the student will be subject to disciplinary action.

Student Email Accounts (MyMTC Email):

  • All MTC students are assigned a college email account called MyMTC Email. For access, follow the link on the Enrolled Students page or go to
  • MyMTC Email is the primary way the college communicates with students. You are responsible for checking your college email regularly for important information and announcements about registration, financial aid, cancelled classes, emergencies, etc.
  • Students can use their college email accounts to communicate with faculty, staff, fellow students, and others, as well as to maintain personal calendars and task lists.
  • In addition to using MyMTC Email, students may also be required to communicate with instructors through Desire 2 Learn (D2L, the college-wide learning management system), or through course-specific software, such as MyMathLab.

MyMTC:

The college conducts business with students through MyMTC, which provides many services and resources, including access to transcripts, grades, and program evaluations; information about financial aid status; and how to search and register for courses. To accessMyMTC, follow the link on the Enrolled Students page or go to

Children on Campus:

Children are generally not permitted on campus except for special events. Children are not permitted in classes, labs, or advisors’ offices. Children can never be left unattended on campus, including in the library, the AcademicSuccessCenter, or parking lots.

Inclement Weather Policy:

  • If weather conditions or other emergencies cause the college to close or open late, announcements will be made over local radio and TV stations, on the MTC website, and on the college’s information line (803-738-8324).
  • Notices will be sent to students via MyMTC Email and MTC Alerts! when applicable.
  • Check for separate announcements for day and evening classes because weather conditions can change during the day.
  • Inclement weather schedules: In standard non-lab and non-clinical classes, if the college closing or reopening means that there is at least 30 minutes of a class remaining, plan to attend that class. For example, if the college opens at 10 a.m., classes that normally meet at 8 a.m. will not meet, but classes that normally begin at 9:35 a.m. will begin at 10 a.m. Similarly, if the college closes at 8 p.m., 6 p.m. classes will meet for their regular time, but 7:35 p.m. classes will not meet.
  • Check your syllabus for specific information about the inclement weather policy for that course.

Campus Emergency Protocol:

  • To report safety concerns or suspicious activities, call Campus Security at 7850 (on campus) or 738-7850 (cell phone or off campus).
  • To report a security emergency, call Campus Security at 738-7199 or dial local 911 immediately.
  • The college also provides emergency call boxes; look for these red call boxes in or near parking lots on all campuses.
  • If a college-wide emergency occurs, the college will communicate additional information and instructions in a number of ways, including the MTCInformationCenters, campus loud speakers, MyMTC Email, the MTC website, and MTCAlerts!.To sign up for MTC Alerts! and receive emergency notifications on your cell phone, go to:

Student Evaluation of Instruction:

Toward the end of the semester, students will be encouraged to participate in evaluating their courses. You can complete this confidential evaluation through MyMTC using your username and password. Announcements will be made during the term concerning how and when to complete the online evaluation.

Students Requiring Special Accommodations:

  • If a student with a disability requires special accommodations, the student should go to Counseling Services in the StudentCenter on Beltline or Airport Campus for assistance. Documentation regarding a specific disability is required in order for special arrangements to be made. All information received will remain confidential.
  • For more information, follow the Disability Resource Centers link under Online Resourceson the Enrolled Students page.

(Approved July 12, 2011)