MATH140 Calculus I

Department of Science, Technology, Engineering & Mathematics: Mathematics

I. Course Number and Title
MATH140 Calculus I
II. Number of Credits
4 credits
III. Minimum Number of Instructional Minutes Per Semester
3000
IV. Prerequisites
Math Placement Test score of 11 or MATH125 (C or better)
Corequisites
None
V. Other Pertinent Information
At least four hours of testing, quizzes, and a two-hour comprehensive departmental final examination are given.
VI. Catalog Course Description
This is the first course in the calculus sequence for physical science, business, computer science, mathematics and engineering students. Topics include: limits, the rate of change of a function, derivatives of algebraic and trigonometric functions, applications of derivatives, integration, and applications of the definite integral.
VII. Required Course Content and Direction
  1. Learning Goals:

    1. Course
    2. Students will:
      1. explain the concepts of limit and continuity;
      2. evaluate limits, and derivatives of algebraic and trigonometric function;
      3. use implicit differentiation to find a derivative and apply concepts of differentiation to problems in curve sketching, related rates, straight-line motion, science, business and economics;
      4. find indefinite integrals;
      5. solve elementary differential equations; and
      6. apply the definition of the definite integral and its properties, evaluate definite integrals and use the definite integral for applications involving topics such as average values, areas, volumes of solids of revolution, lengths of plane curves.

    3. Core (if applicable)
    4. Category I:
      Mathematics or Science
      Students will be able to:
      1. accurately translate descriptive problems into mathematical formulas and solve them.
      Category III:
      Critical Thinking/Problem Solving
      Students will be able to:
      1. demonstrate an understanding of solving problems by:
        1. recognizing the problem
        2. reviewing information about the problem
        3. developing plausible solutions
        4. evaluating the results
  2. Planned Sequence of Topics and/or Learning Activities:

    The following is a list of the minimum amount of course material to be covered by the instructor. Accompanying each topic is an approximate number of lesions required to study the topic.

    1. Limits and Continuity (8 lessons)
      1. Geometric Interpretation of Limits
      2. Evaluating Limits
      3. Limit Theorems
      4. One-Sided Limits
      5. Continuity

    2. The Derivative (12 lessons)
      1. Geometric Interpretation - Tangent Line to a Curve
      2. Definition of Derivative
      3. Velocity, Acceleration, and Other Rates of Change
      4. Finding Derivatives, Using the Limit Definition
      5. Finding Derivatives, Using the Differentiation Formulas
      6. Product and Quotient Rules
      7. Derivatives of Basic Trigonometic Functions
      8. Chain Rule and Composite Functions
      9. Implicit Differentiation
      10. Higher-Order Derivatives

    3. Applications of the Derivative (12 lessons)
      1. Straight Line Motion
      2. Related Rates
      3. Increasing and Decreasing Functions
      4. Relative and Absolute Extrema
      5. Concavity and Inflection Points
      6. Second Derivative Test
      7. Optimization Problems
      8. Linear Approximation and Differentials
      9. Mean Value Theorem
      10. Antiderivatives

    4. Integration (9 lessons)
      1. Indefinite Integrals
      2. Differential Equations
      3. Summation Notation
      4. Finding Areas and the Definition of Definite Integral
      5. Fundamental Theorem of Calculus
      6. Properties of the Definite Integral
      7. Using Substitution to Evaluate Integrals

    5. Applications of Integration (7 lessons)
      1. Area Under a Curve
      2. Average Value of a Function
      3. Area Between Curves
      4. Volumes of Revolution - Disk and Shell Method
      5. Length of a Plane Curve
  3. Assessment Methods for Core Learning Goals:

    1. Course
    2. The student applies mathematical concepts and principles to identify and solve problems presented through informal assessment, such as oral communication among students and between teacher and students. Formal assessment consists of open-ended questions reflecting theoretical and applied situations.

    3. Core (if applicable)
    4. CORE Category I: Math and Science: The students apply mathematical and scientific concepts and principles to identify and solve problems presented through informal assessment such as oral communication among students and between teacher and students. Formal assessment for the core consists of open-ended questions reflecting theoretical and applied situations.

      CORE Category III: Critical Thinking: The students apply critical thinking skills to identify and solve problems presented through informal assessment such as oral communication among students and between teacher and students. Formal assessment for the core consists of open-ended questions reflecting theoretical and applied situations.
  4. Reference, Resource, or Learning Materials to be used by Students:

    A graphing calculator and a departmentally selected textbook are used. Details are provided by the instructor of each course section. See course format.
VIII. Teaching Methods Employed
Section VIII is not being used in new and revised syllabi as of 12/10/08.

Review/Approval Date - 3/06; Core Goals/Objectives added 12/04; Revised 09/2013