El Camino College - Division of Mathematical Sciences

Math 190
Single Variable Calculus and Analytic Geometry
5 units; 5 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 (prior to 7/92)

Prerequisite: Mathematics 180 with a minimum grade of C or qualification by testing (El Camino College Mathematics Placement Test) and assessment.

Catalog Description:
  Topics in this course include: limits; derivatives of algebraic, trigonometric and transcendental functions; differentials; graphing; applications; definite and indefinite integrals. Problem solving using a computer algebra system is integrated throughout the course.
Note: Mathematics 190 was formerly numbered Mathematics 5A.

 Course Objectives and Methods of Evaluation:

  1. Course objectives (list the major objectives stated as student outcomes in behaviorally measurable terms.)
    1.  Evaluate limits.
    2. Calculate derivatives of algebraic, trigonometric and transcendental functions (also by implicit differentiation).
    3. Calculate derivatives of inverse functions and calculate differentials.
    4. Graph functions including asymptotes, local extrema and inflection points.
    5. Solve application problems using differential calculus.
    6. Calculate definite and indefinite integrals (including the use of the method of substitution).
    7. Use computing software for solving calculus problems.
  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. Computer assisted problem assignments
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Outline of Subject Matter
 

Approximate Time

Major Topic

15 hours

I. Limits

  1. Definition of limit
  2. Two-sided and one-sided limits
  3. Limit laws
  4. Infinite limits
  5. Continuity
  6. Intermediate Value Theorem
  7. Limits at plus/minus infinity
  8. Problem solving using a computer algebra system

20 hours

II. Derivatives

  1.  Definition of derivative
  2. Differentiation rules (power, product, quotient)
  3. Derivatives and limits of trigonometric functions
  4. Chain Rule
  5. Implicit differentiation
  6. Related Rates
  7. Differentials
  8. Newton's Method
  9. Problem solving using a computer algebra system

15 hours

III. Derivatives of Inverse and Transcendental Functions

  1. Derivatives of exponential functions
  2. Inverse functions
  3. Logarithmic functions and their derivatives
  4. Exponential growth and decay
  5. Derivatives of inverse trigonometric functions
  6. Hyperbolic functions
  7. L'Hopital's Rule and indeterminate forms
  8. Problem solving using a computer algebra system

20 hours

IV.  Graphing

  1. Maxima and minima
  2. Extreme Value Theorem
  3. Mean Value Theorem
  4. Increasing/decreasing functions and the first derivative test
  5. Concavity and the second derivative test
  6. Curve sketching
  7. Applications
  8. Problem solving using a computer algebra system

15 hours

V. Integration

  1. Anti-derivatives and indefinite integrals
  2. Riemann Sums
  3. Area under curve
  4. The definite integral and its properties
  5. The Fundamental Theorem of Calculus
  6. The substitution rule
  7. Problem solving using a computer algebra system

 5 hours

Examinations

Total:

90 Hours

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Planned Instructional Activities:

Lecture, discussion, individual and computer assisted 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. Solve application problems at the Pre-Calculus level.
  2. Solve algebraic and trigonometric equations at the Pre-Calculus level
  3. Solve logarithmic and exponential equations at the Pre-Calculus level.

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Source of information: Course Outline of Record dated March, 2000



 Last Updated On: 4/20/06