MATH 111 Calculus I (4)

Catalog Description:

Introduction to the differential and integral calculus with the associated analytic geometry. Meets General Education Mathematical Sciences requirement. (Offered each semester.)


Prerequisites:

Two years of high school algebra.

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


Required Course Materials:

Larson, Hostetler and Edwards, Calculus, 10th edition, Brooks/Cole, 2014 (ISBN: 9781285060286) Web Assign Online Homework Access Card

 

Course Coordinator:

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

 

Course Audience:

Students majoring in mathematics, information science, engineering, physics, chemistry, or economics, or any student wanting to take more than one semester of Calculus.


Course Objectives:

  1. To develop a rigorous understanding of functions and the concepts of differentiation and integration.
  2. To enhance learning by examining geometric, numerical, and algebraic aspects of each problem.
  3. To acquire an understanding of the breadth of mathematics by introducing applications in a wide variety of scientific fields.
  4. To use the tools of Calculus to formulate and solve multi-step problems and to interpret the numerical results.
  5. To develop the student’s ability to communicate mathematical concepts through a series of written laboratory assignments and classroom discussions.
  6. To select and use technology when appropriate in problem solving.
  7. To develop the process of making appropriate conjectures, finding suitable means to test those conjectures, and drawing conclusions about their validity.

General Education Objectives:

  1. To identify methods and assumptions of the mathematical sciences.
  2. To introduce students to at least one of the three mathematical sciences of computing, mathematics and statistics from a liberal arts perspective.
  3. To help students develop logical, analytical, and abstract thinking through quantitative problem solving activities.

Topics:

  1. Limits: a) finite and infinite, b) one-sided limits, and c) continuity of functions.
  2. The derivative: a) slope of a tangent line, b) difference quotient, c) derivative formulas,
    d) chain rule, e) critical points and relative extrema, f) concavity and inflection points, and g) implicit differentiation.
  3. Applications of the derivative: a) curve sketching, b) optimization, c) related rates, d) differentials, and e)
    Newton’s method.
  4. The integral: a) sigma notation, b) area bounded by curves, c) Riemann sums, d) the definite integral, e) The Fundamental Theorem of Calculus, f) indefinite integrals, and g) substitution.
  5. Transcendental functions: a) the natural log function, b) the exponential function, and c) the inverse trig functions.

 

Revised: October 2013 (textbook); December 2011

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