MAT 240 – Analytical Geometry and Calculus III

Mathematics

Semester Spring 2017

Catalog Course Description:This course includes the following topics: continuation of calculus of one variable, including analytic geometry, techniques of integration, volumes by integration, and other applications; infinite series, including Taylor series; and improper integrals.

Prerequisite(s):MAT 141

Credit Hours:4.0 Credit Hours

D2L BrightspaceLogin Page:

Instructor:Patrick Harley

Telephone:738-7689

E-mail:

Campus Mailbox: 4th floor, LET

Personal Website:

Departmental Assistant:Mitzi Trigg – – 803-738-7689

Department Chair: Rick Bailey – – 803-738-7689

Program Coordinator:Rose Jenkins – – 803-822-3351

Class Schedule[s]: B55, Mon/Wed, 5:25-7:25pm LET 413

Textbook(s):):Calculus, Tenth Edition by Roland E. Larson and Bruce H. Edwards, Brooks/Cole, Cengage Learning, 2014

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

Note: Calculators with computer algebra systems such as the TI-92, TI-89 or TI-Nspire are not allowed unless allowed by the instructor.

Software:Web Assign may be required.

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.

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. Two absences are allowed for a class that meets once per week, three absences are allowed for a class that meets two times per week and five absences are allowed for a class that meets three times per week.
  3. Threetardies 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.

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 5 tests, and a cumulative HW grade. In addition, there will be a cumulative final exam. One test 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: 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

Current Week / Topics Covered / Section
Week 1 /

Vectors and the Geometry of Space

Vectors in the Plane / 11.1
Space Coordinates and Vectors in Space / 11.2
Week 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
Week 3 / Surfaces in Space / 11.6
Cylindrical and Spherical Coordinates / 11.7
Week 4 /

TEST 1

Vector-Valued Functions

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

TEST 2

Functions of Several Variables

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

TEST 3

Week 11 /

Multiple Integration

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

TEST 4

Vector Analysis

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

Comprehensive Final Examination

Note: Student Learning Outcome data will be collected on tests and/or other assessments during the fall semester of even numbered years.

PLEASE NOTE: Should change become necessary, the instructor reserves the right to adjust the requirements, pace, or scheduling of this course. Any change will be announced in class before it becomes effective.