MATH141 Calculus II

Department of Science, Technology, Engineering & Mathematics: Mathematics

I. Course Number and Title
MATH141 Calculus II
II. Number of Credits
4 credits
III. Number of Instructional Minutes
IV. Prerequisites
MATH140 (C or better)
V. Other Pertinent Information
At least four one-hour tests, quizzes, and a two-hour comprehensive departmental final examination are given.
VI. Catalog Course Description
This course is a continuation of Math 140. Topics include differentiation and integration of transcendental functions, indeterminate forms, methods of integration, improper integrals, infinite series, parametric equations, and polar coordinates.
VII. Required Course Content and Direction
  1. Course Learning Goals

    Students will:

    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, integration by parts, and use a table of integrals;
    3. solve limit problems involving indeterminate forms with La'Hopital's Rule;
    4. evaluate improper integrals;
    5. determine convergence or divergence of positive term series using the ratio test, comparison test, limit comparison test or integral test; determine the convergence, absolute convergence, conditional convergence or divergence of alternating series; determine the interval of convergence of power series; and express a function as a series using Maclaurin or Taylor series; and
    6. convert parametric representation of curves to rectangular coordinates, represent a curve using polar coordinates, and 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. Trapezoidal Rule
      7. 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 Parametric Equations
      1. Plane Curves
      2. Parametric Equations
      3. Polar Coordinates
      4. Arc Length and Area
  3. Assessment Methods for Course Learning Goals

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

    A graphing calculator and a departmentally-selected textbook are used. Details are provided by the instructor of each course section. See course syllabus.

Review/Approval Date - 3/99; Revised 4/06; Revised 09/2013; New Core 8/2015