Math 190—Analytic Geometry and Calculus I
Syllabus—Spring 2005

Catalog Description

Topics explore the foundations of calculus: limits, continuity, the derivative of a function, the chain rule, the Mean Value Theorem, Riemann sums, integration. Includes applications, optimization problems, derivatives and integrals of algebraic, trigonometric, exponential, and logarithmic functions.

Rationale

Calculus reaches out to a wide range of fields that use the principles to construct mathematical models that bring understanding of the world around us. Some of the fields of study that use calculus are economics, biology, medical research, space exploration, psychology, physics, engineering, physiology, education, computer science, and actuarial science. The material presented in this course is intended to provide students with the mathematical skills necessary to be successful not only in subsequent calculus courses and advanced math courses, but also in related areas. At the conclusion of the course the student will appreciate the derivative and the integral and their potential for application, as well as the Fundamental Theorem of Calculus, which provides an amazing connection between the derivative and the integral.

Goals

1. Further develop the student’s skill with algebra.
2. To introduce the fundamental concepts of the calculus.
3. Develop proficiency with the algorithmic processes of calculus including selecting appropriate techniques and their application in problem solving situations.
4. Develop problem solving skills, study habits, skill communicating using mathematical notation and vocabulary, and familiarity with the deductive nature of mathematics.

Competencies

1. Proficiency with the algebra of functions.

2. Proficiency in application of calculus to graphing functions and equations.

3. Ability to compute the slope of a tangent line to a curve at a point.

4. Compute derivatives and integrals for large classes of functions using definitions and standard algorithms.

5. Apply differentiation and integration to problems in optimization, geometry, approximation and the physical and life sciences.

6. Compute limits of various functions using basic properties of limits and/or l’Hopital’s rule.

7. Understand the basic mathematical development of the definite integral and the derivative.

8. Grasp the significance of a few major theorems of calculus (intermediate value theorem, mean value theorem, fundamental theorems of calculus, e.g.).

Performance indicators

These competencies shall be assessed primarily by means of written work and written examinations. Additional assessment may take place by means of observation of in-class activities and discussion.

Course Information

Text

Thomas, G. B., Finney, R. L., Weir, M. D., & Giordano, F. R. (2001). Thomas’ Calculus, (10^th ed.), Boston: Addison Wesley.

Calculators

It is recommended that you have a graphing calculator. A TI-85 may be used on occasion for demonstrations. Graphing devices vary greatly so you should have a manual and become familiar with your own calculator and its features.

Course Requirements and Evaluation

Final grades will be determined by the percentage of possible points earned from exams and homework according to the following scale:

Homework

Homework will be assigned on a regular basis. I recommend that you come to my office to see me about any homework problems that are causing you difficulty.

Reading

I expect you to read the text prior to our class meetings. This will help prepare you for the class presentation and class discussion.

Attendance

Attendance is expected. Attendance will be taken at the beginning of each class period.
Note: If you miss more than 50% of a class at any given point in the semester, you will be dropped from the class. This will be recorded as a withdraw/fail.

Miscellaneous

• If you are having difficulty with the course please come to my office to see me as soon as possible.
• Math tutors will be available in the Learning Center located in Baity Hall if you desire additional help.
• Keep up with homework. It is easier to keep up than catch up.

Tentative Schedule

A tentative schedule gives you a rough guideline of what to expect during the semester. However, changes invariably occur, and you will get this information in class.

Final Exam: 10 a.m., Tuesday, May 3

You must take the final exam at the time designated for your class. The final exam is mandatory. Make your travel arrangements accordingly.