El Camino College - Division of Mathematical Sciences

Math 191
Single Variable Calculus and Analytic Geometry II
4 units; 4 hours lecture

Catalog Description Course Objectives and Methods of Evaluation
Outline of Subject Matter Planned Instructional Activities

Grading Method: Letter

Associate Degree Credit --- Transfers to CSU and Transfers to UC

Prerequisite: Mathematics 190 with a minimum grade of C.

Catalog Description:
This course includes a study of: methods of integration; applications; improper integrals; numerical integration; infinite sequences, series and power series; parametric equations, polar coordinates and conic sections.
Note: Mathematics 191 was formerly numbered Mathematics 5B.

 Course Objectives and Methods of Evaluation:

  1. Course objectives (list the major objectives stated as student outcomes in behaviorally measurable terms.)
    1.  Use integration to solve application problems involving: areas between curves; volumes by washers and cylindrical shells; arc length and areas of surfaces of revolution.
    2. Evaluate integrals using integration techniques including: integration by parts; trigonometric substitutions; partial fraction decomposition and tables of integrals.
    3. Use numerical techniques (both with and without technology) to approximate the values of integrals.
    4. Determine the convergence or divergence of sequences, series and power series.
    5. Solve problems using Taylor series.
    6. Solve problems involving parametric equations, polar coordinates and conic sections.
  1. Methods of Evaluation - Associate Degree Credit Course
    1. Substantial writing assignments are inappropriate for this degree applicable course because:
      1. The course is primarily computational in nature
      2. The course primarily involves skill demonstrations or problem solving.
    2. Computational or non-computational problem-solving demonstrations, including:
      1. Exam

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Outline of Subject Matter
 

Approximate Time

Major Topic

12 hours

I. Applications of Integration

  1. Areas between curves
  2. Volumes by Washers
  3. Volumes by Cylindrical Shells
  4. Average Value of a Function
  5. Arc Length
  6. Area of a Surface of Revolution

12 hours

II. Techniques of Integration

  1. Integration by Parts
  2. Trigonometric Integrals
  3. Trigonometric Substitution
  4. Integration of Rational Functions by Partial Fractions
  5. Numerical Integration (Simpson, Trapezoidal and Midpoint Rule)
  6. Improper Integrals

32 hours

III. Infinite Sequence and Series

  1. Sequences
  2. Series
  3. Integral and Comparison Tests
  4. Alternating Series
  5. Absolute Convergence; Ratio and Root Test
  6. Power Series and Representation of Functions as Power Series
  7. Taylor and Maclaurin Series; Applications
  8. Binomial Series

12 hours

IV.  Parametric Equations and Polar Coordinates

  1. Curves defined by Parametric Equations
  2. Tangents and Areas
  3. Arc Length and Surface Area
  4. Polar Coordinate
  5. Areas and lengths in Polar Coordinates
  6. Conic Sections

  4 hours

Examinations

Total:

72 Hours

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Planned Instructional Activities:

Lecture, discussion, individual assistance and technology aided instruction

Entrance Skills and Knowledge:

List the required skills and/or knowledge without which a student would be highly unlikely to receive a grade of A, B, C, or Credit (or for Health and Safety, would endanger self or others) in the Target Course.

  1. Differentiate algebraic, trigonometric, exponential and logarithmic functions.
  2. Determine tangent lines to the graphs of algebraic, trigonometric, exponential and logarithmic functions at specified points.
  3. Solve application problems using differential calculus.
  4. Integrate polynomials and other functions using substitution.
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Source of information: Course Outline of Record dated February, 2000


 Last Updated On: 4/20/06