Calculus III

Dr. Caldwell's Math 320 Syllabus
(This Math 320 syllabus and other courses resources are avaiable at


Dr. Caldwell, office 429 Humanities, office phone 7336.  Department office 7360.  E-mail:  Web page:

My main goal in this course is to teach you about this subject that I love.  It may not be obvious, but the way I teach this class (daily homework quizzes, tests, ...) are designed to help you succeed and to make sure all students are treated fairly. Come by my office anytime--too few students take advantage of office hours.  At UT Martin you can talk to and work with your teachers, take full advantage of that!

Catalog Description:

Math 320: Vectors and analytic geometric in space.  Vector-valued functions of several variables.  Differentials, gradients, and extrema of functions of several variables.  Multiple integrals and their applications.  Introductory vector analysis including line and surface integrals.


A grade of C or better in Mathematics 252.  (This means that you are expected to remember how to integrate and differentiate! You must recall basic trigonometry.)

Image of textbook


Calculus-Early Transcendentals (eighth edition), James Stewart, Cengage Learning, 2014. (Any format, e.g., ISBN-13: 978-1285741550.  We will have homework assigned from this text almost every day, so you will need access to the book in some readable form (hardback, loose-leaf, electronic, rented, ...).  We will not use webassign in my section(s) (just the textbook).  Look around and see if you can get it cheaper than at the UTM Bookstore.  The library has this textbook on reserve.


Letter grades will be assigned as follows:  90-100% A,  80-89% B,  70-79% C,  60-69% D,  0-59% F. The grade of I is given very rarely and only in cases of emergency.

The course grade will be determined as follows: 

  • 15 %   quizzes (daily five-minute) 
  • 65 %   tests (about five) 
  • 20 %   final (comprehensive) 


Homework will be evaluated through the quiz policy.  Go to this spot on the syllabus online to access the assignment list.

Homework will be evaluated through the quiz policy.  Click on the button(s) to the right for the list of daily assignments.

Tests & Final:

The homework, quizzes and classroom examples indicate the type of problems that will be on the tests and final (possibly changed to a multiple-choice format).  There are no make-up tests.  With an appropriate excuse, you can take a test early, but not late. If you miss a test, the missing grade wil be replaced by the average of the following tests and final.

The final will be a departmental comprehensive exam.  Review for the final by studying the hour tests, homework and quizzes.  There are usually practice final(s) online.   You may not leave the room (and phone, smart watches... must not be visible) during any test or final.


Learning is a biological process that requires your involvement.  In mathematics classes especially, you must do the homework.  To encourage you to do the homework, we will start most days with a brief "quiz" (usually less than five minutes).  This will be a problem similar to a problem from the previous night's homework.  You will be allowed to use your personal handwritten notes; but not your book, computer or printed notes.  If you have attended class and done all the homework, you should earn 100% on the quizzes.

These quizzes will be graded on a four-point scale: four points for the correct answer, three for a partially correct answer and two points if you just put your name.  If you are late, turn in a blank quiz after class for the two points. 

If you miss a class, then you will get a zero; however, the three lowest quizzes will be dropped.  At the end of the semester, all of your quiz points will be added, then converted into a percentage score.

Quizzes will be excused for appropriate excuses, but you must let me know (and provide documentation) within two weeks.  Being excused from a quiz does not excuse the next class' quiz (so if you miss class for any reason, you should still do your homework and be ready for the quiz--come see me if I can help).

Quizzes will usually be returned the next class meeting.  Those that are not picked up will be discarded after three class periods.

Learning Outcomes for Major:

Upon completion of his/her degree from the University of Tennessee at Martin with a major in mathematics, the graduate will be able to:

  1. apply mathematical concepts and principles to perform numerical and symbolic computations.
  2. use technology appropriately to investigate and solve mathematical and statistical problems.
  3. write clear and precise proofs.
  4. communicate effectively in both written and oral form.
  5. demonstrate the ability to read and learn mathematics and/or statistics independently.

Teaching Objectives:

The student will:

  1. Understand and use the basic ideas and concepts behind vectors and three dimensional analytic geometry.
  2. Use the basic calculus of vector-valued functions and apply this to solving problems concerning motion in space.
  3. Understand the concepts of limits and continuity of functions of several variables.
  4. Understand the concept of partial derivatives and work problems using chain rule, directional derivatives, and gradients of multivariate functions.
  5. Apply the calculus of several variables to finding tangents and normals, developing approximations, and locating extrema of functions of several variables.
  6. Set up and evaluate multiple integrals in the rectangular, cylindrical, and spherical coordinate systems.
  7. Apply multiple integration to finding areas, volumes, moments, and other situations.
  8. Understand and employ basic vector analysis techniques including line integrals, Green’s Theorem, surface integrals, Divergence Theorem, and Stokes’ Theorem.

Departmental Syllabus:

The Department of Mathematics and Statistics has a syllabus for each of it courses on line.


Attendance is required and will be assessed by the quiz policy.


A calculator is required for this course.  The use of the calculator will not be taught in the course itself.  Calculators capable of symbolic manipulation will not be allowed.

Canceled classes:

You (and the state) have paid well for the courses taught here so mathematics and statistics teachers very (very) rarely cancel classes. However, sometimes (especially in the spring) the university closes due to bad weather.  If this happens, I will contact you by Canvas and/or the e-mail address stored in the Banner system to let you know how we will make up the work.  I will also adjust the homework schedule on-line to reflect the change.


Academic dishonesty will not be tolerated and will result in at least a zero for the quiz, test or assignment.  Your Student Handbook clearly states "suspension from the university is the expected penalty" for "plagiarism, cheating, and academic integrity issues" and this includes submitting the work of another person as your own or permitting another to submit yours as his/her own.

Disability Services:

The University of Tennessee provides reasonable accommodations (academic adjustments and auxiliary aids) to ensure equal access to educational content and university programs for students with disabilities.  Any student eligible for and requesting accommodations due to a disability must provide instructors with a letter of accommodation from Disability Services.  For additional information, please contact the Disability Services office at 209 Clement Hall, (731) 881-7605.


If you have any questions: