MATH 109 Calculus I, Part I (4)

Catalog Description:

Introduction to differential calculus with the associated analytical geometry. Completion of both MATH 109 and MATH 110 will be equivalent of the completion of MATH 111. Meets General Education Mathematical Sciences requirements. (Offered fall semester only.) DISCONTINUED and replaced by MATH 103 (S13)


Prerequisites:

 

Two years of high school algebra.

  1. Algebraic skills needed to solve inequalities and equations involving rational polynomial expressions.
  2. Understanding the use of variables.
  3. Basic properties of the real number system, including rational and irrational numbers.
  4. The ability to use the Cartesian plane to plot and draw graphs including the conic sections.
  5. Understanding exponential, logarithmic and trigonometric functions.
  6. Ability to analyze functions and their graphs.

Required Course Materials:

Larson, Hostetler and Edwards, Calculus, 9th edition, Brooks/Cole, 2010


Course Coordinator:

 

Douglas C. Phillippy, Ph.D., Associate Professor of Mathematics

 


Course Audience:

Students majoring in mathematics, computer science, engineering, physics, chemistry, or economics. Intended for students who desire to have the course material for Calculus I presented at a slower pace.


Course Objectives:

  1. To develop a rigorous understanding of the concept of differentiation.
  2. To strengthen the studentís mathematics background by reviewing selected precalculus topics as they are needed in the calculus sequence.
  3. To enhance learning by examining geometric, numerical, and algebraic aspects of topics taught.
  4. To acquire an understanding of the breadth of mathematics by introducing applications in a wide variety of scientific fields.
  5. To use the tools of Calculus to formulate and solve multi-step problems and to interpret the numerical results.
  6. To develop the studentís ability to communicate mathematical concepts through a series of written laboratory assignments and classroom discussions.
  7. To select and use technology when appropriate in problem solving.
  8. To develop the process of making appropriate conjectures, finding suitable means to test those conjectures, and drawing conclusions about their validity.

Topics:

  1. Review and further development of precalculus material including analytic geometry, functions, and trigonometry.
  2. Limits: A) finite and infinite, B) one-sided limits, C) continuity of functions.
  3. The derivative: A) slope of a tangent line, B) difference quotient, C) derivative formulas, D) chain rule, E) implicit differentiation.
  4. Applications: A) rectilinear motion, B) optimization, C) related rates, D) differentials, E) Newtonís method, F) curve sketching and relative extrema G) concavity and inflection points.
 

Revised: August 2009

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