MATH141 Calculus II

Department of Science, Technology, Engineering & Mathematics: Mathematics

  1. Course Number and Title

    MATH141 Calculus II

  2. Number of Credits

    4 credits

  3. Minimum Number of Instructional Minutes Per Semester

    3000 minutes

  4. Prerequisites

    MATH140 (C or better)

    Corequisites

    None

  5. Other Pertinent Information

    At least four one hour tests, and a two hour comprehensive departmental final examination will be given. Students who wish to continue with the course MATH242, Calculus III must complete MATH141 with a grade of C or better.

  6. Catalog Course Description

    This course is a continuation of MATH140. Topics include differentiation and integration of transcendental functions, indeterminate forms, methods of integration, improper integrals, infinite series, parametric equations, and polar coordinates.

  7. Required Course Content and Direction

    1. Learning Goals:

      The student will be able to:

      1. differentiate and integrate transcendental functions, including logarithms, exponential, trigonometry and inverse trigonometric, hyperbolic and inverse hyperbolic functions.
      2. apply methods of integration, such as algebraic substitution, trigonometric substitution, partial fractions, and integration by parts.
      3. use a table of integrals.
      4. solve limit problems involving indeterminate forms with L’hôpital’s rule.
      5. evaluate improper integrals.
      6. determine convergence or divergence of positive tem series using the ratio test, comparison test, limit comparison test, limit comparison test or integral test.
      7. determine the convergence, absolute convergence, conditional convergence or divergence of alternating series.
      8. determine the interval of convergence of power series.
      9. express a function as a series using Maclaurin or Taylor series.
      10. convert parametric representation of curves to rectangular coordinates.
      11. represent a curve using polar coordinates.
      12. integrate functions expressed in polar coordinates.

    2. Planned Sequence of Topics and/or Learning Activities:

      1. Differentiation and Integration of Transcendental Functions
        1. Logarithmic Functions
        2. Exponential Functions
        3. Trigonometric Functions
        4. Inverse Trigonometric Functions
        5. Hyperbolic Functions
      2. Methods of Integration
        1. Integration by Parts
        2. Trigonometric Integrals
        3. Trigonometric Substitution
        4. Partial Fractions
        5. Integral Tables
        6. Improper Integrals
      3. Infinite Series
        1. Sequences
        2. Convergence
        3. Integral Test and p- series
        4. Comparison Tests
        5. Ratio Test
        6. Root Test
        7. Power Series
        8. Taylor and Maclaurin Series
      4. Vectors and Parametic Equations
        1. Plane Curves
        2. Parametic Equations
        3. Polar Coordinates
        4. Arc Length and Area

    3. Assessment Methods for Core Learning Goals:

      All Discipline-Specific Course Objectives will be assessed as follows: The student will apply 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 will consist of open-ended questions reflecting theoretical and applied situations.

    4. Reference, Resource, or Learning Materials to be used by Students:

      Departmentally selected textbook. TI-83 graphing calculator is required. Details provided by the instructor of each course section. See Course Format.

  8. Teaching Methods Employed

    Lecture, recitation, discussion, and group work.

Review/Approval Date - 3/99; Revised 4/06