El Camino College - Division of Mathematical Sciences

Math 160
Calculus for the Biological, Management and Social Sciences I
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 130 or Mathematics 180  with a minimum grade of C in prerequisite, or qualification by testing (El Camino College Mathematics Placement Test) and assessment.

Catalog Description:
  This course includes a study of differentiation and integration of algebraic and exponential functions of one variable, definite integrals, and applications.
Note: Mathematics 160 was formerly numbered Mathematics 9A.
Course Objectives and Methods of Evaluation:

  1. Course objectives (list the major objectives stated as student outcomes in behaviorally measurable terms.)
    1.  Evaluate limits and determine the continuity of functions.
    2. Find the derivative of functions using the definition (limit of a quotient).
    3. Find the derivative of algebraic, exponential and logarithmic functions using basic rules of differentiation, the Product Rule, the Quotient Rule, and the Chain Rule.
    4. Find higher-order derivatives.
    5. Find derivatives using implicit differentiation.
    6. Graph functions using the first and second derivatives.
    7. Solve optimization and other application problems.
    8. Find indefinite integrals by using the basic rules of integration and integration by substitution.
    9. Use calculus to find areas under curves and areas between curves.
  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
      2. Homework problems
      3. Quizzes

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Outline of Subject Matter
 

Approximate Time

Major Topic

4 hours

I. Limits

  1. Limits of Functions
  2. Continuity of Functions

16 hours

II. Differentiation

  1. The derivative and the slope of a graph
  2. Differentiation rules
  3. Rates of change: Velocity and marginals
  4. The Chain Rule
  5. Higher-order derivatives
  6. Implicit differentiation

20 hours

III. Applications of the Derivative

  1. Curve sketching using the first and second derivatives
  2. Optimization problems
  3. Business and economics applications
  4. Asymptotes
  5. Differentials and marginal analysis

12 hours

IV.  Exponential and Logarithmic Functions

  1. Derivatives of exponential and logarithmic functions
  2. Exponential growth and decay

16 hours

V. Integration and its  Applications

  1. Antiderivatives and indefinite integrals
  2. Integrals of exponential and logarithmic functions
  3. Area and the Fundamental Theorem
  4. Area of a region bounded by two graphs
  5. The definite integral as the limit of a sum

 4 hours

Examinations

Total:

72 Hours

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Planned Instructional Activities:

Lecture, discussion, individual and group work

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. Perform operations on functions including: evaluation, addition, subtraction, multiplication, division, and composition..
  2. Manipulate functions including determination of: inverse, difference quotient, domain, and range.
  3. Graph quadratic, cubic, exponential, logarithmic, and rational functions.
  4. Solve a variety of application problems.
  5. Solve polynomial, radical, rational, exponential, and logarithmic equations.
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Source of information: Course Outline of Record dated January, 2001


 Last Updated On: 4/20/06