Calculus I

Dr. Caldwell's Math 251 Syllabus
(This Math 251 syllabus and other courses resources are avaiable at


Dr. Caldwell, office 429 Humanities, office phone 7336.  Department office 7360.  E-mail:  Web page:  I will use your e-mail as stored in Banner, usually an account, to contact you (if the school closes, to send additional notes, ...) so please make sure that it is accurate.

Catalog Description:

Math 251-252: Limits and continuity.  Derivatives and integrals of polynomial, rational, exponential, logarithmic, trigonometric, and hyperbolic functions.  Techniques of integration.  Conics.  Parametric and polar equations.  Intermediate forms and improper integrals.  Infinite series, including Taylor series.  Must be taken in sequence.


Two units of high school algebra, one unit high school geometry, 1/2 unit high school trigonometry, and appropriate mathematics placement OR completion of EITHER Math 170 with a grade of C or better OR MATH 185 with a grade of C or better.

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 sections (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.  Click on the button to the right for the list of daily assignments.  Go to my web page to find this assignment list.

Homework will be evaluated through the quiz policy.  Click on the button to the right for the list of daily assignments.  Use these buttons to see the homework.

Tests & Final:

The homework, quizzes and classroom examples indicate the type of problems that will be on the tests, though some (probably the final) may be changed to a multiple-choice format.  No make-up tests.  If you miss a test, you will be given the average of the following tests and final.  The final will be comprehensive.  Review for the final by studying the hour tests, homework and quizzes.  (Check also to see if there is a practice final online.)   You may not leave the room (and your phone... must not be visible) during any test or final.


There is no way to pass a real mathematics class without doing the homework. So to help you focus on 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: one point for your name, four points for the correct answer, and two or three for a partially correct answer.  If you are late, you will get a one.  If you cheat, you may get a zero or negative score.  The four lowest quiz scores will be dropped (other than "earned" zero or negative scores, see above).  All of your remaining quiz points will be added, then converted into a percentage score.

If you miss the day, then you will get a zero.  Exceptions will be made for appropriate excuses, but you must miss, then let me know (and provide documentation) within two weeks.  Being excused from an absence does not excuse the next day's quiz.  If you miss class for any reason, you should still do your homework and be ready for the quiz.

Quizzes and tests will usually be returned the next class meeting.  Those that are not picked up will be discarded a week later.

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 apply the definitions and concepts of limit and continuity of functions.
  2. Understand and apply the definition of derivative, Rolle’s Theorem, and Mean Value Theorem.
  3. Differentiate both explicitly and implicitly algebraic, trigonometric, logarithmic, and exponential functions.
  4. Apply the basic differentiation rules to complex functions.
  5. Use derivatives in applications such as approximations, Newton’s Method, related rates, optimization, and L’Hopital’s Rule.
  6. Use derivatives to determine increasing-decreasing and concavity intervals for functions and use these results as an aid in curve sketching of these functions.
  7. Use the Fundamental Theorem of Calculus in definite integral evaluation.
  8. Integrate the basic functions including the use of basic substitution techniques.


The Department of Mathematics and Statistics publishes a syllabus for each of it courses which may be viewed in my office or on the departmental web pages.


Attendance is mandatory and will be enforced through the quiz policy.


A graphing 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.  You should check with your major advisor as to what calculator you might need in your major before you decide which calculator to use.

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 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 as needed.


Academic dishonesty will not be tolerated and will result in at least an F 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: