El Camino College - Division of Mathematical Sciences

Math 161
Calculus for the Biological, Management and Social Sciences II
3 units - 3 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 160 with a minimum grade of C.

Catalog Description:
  This course includes a study of techniques of integration, multi-variable calculus, differential equations and infinite series as well as topics such as probability and trigonometry.
Note: Mathematics 161 was formerly numbered Mathematics 9B.
Course Objectives and Methods of Evaluation:

  1. Course objectives (list the major objectives stated as student outcomes in behaviorally measurable terms.)
    1. Integrate using substitution, parts and numerical methods.
    2. Evaluate improper integrals.
    3. Apply integration to problems such as: finding the present value of an income stream; calculating the mean, variance and standard deviation of a continuously distributed random variable, and computing probabilities by integrating density functions.
    4. Solve separable differential equations and related applications in exponential growth and decay.
    5. Evaluate functions of several variables and graph functions of two variables.
    6. Computer and interpret partial derivatives and apply to problems such as marginal productivity of capital and optimization problems.
    7. Evaluate double integrals and apply to volume problems.
    8. Find the limit of a sequence and the sum of a geometric or telescoping series.
    9. Determine the convergence/divergence of an infinite series.
    10. Use Taylor Polynomials to approximate function values.
    11. Evaluate, differentiate, and integrate the trigonometric functions.
  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

9 hours

I. Techniques of Integration

  1. Substitution
  2. Integration by parts
  3. Numerical methods
  4. Improper integrals
  5. Applications: Present value of an income stream

6 hours

II. Probability and Statistics

  1. Mean, variance and standard deviation of a continuously distributed random variable
  2. Probabilities of density functions by integration

6 hours

III. Differential Equations

  1. Separation of variables
  2. Modeling of real world situations with different equations

9 hours

IV.  Multi-Variable Calculus

  1. Functions of Several Variables
  2. Graphs of functions of variables in three-dimensional Cartesian coordinate systems
  3. Cobb-Douglass production function
  4. Level curves
  5. Partial derivatives
  6. Marginal productivity of labor and capital
  7. Optimization problems
  8. Lagrange multipliers
  9. Method of least squares for finding a linear equation of set of data
  10. Double integrals and volume

9 hours

V. Indefinite Series

  1. Sequences and Series
  2. Limit of a Sequence
  3. Sum of a geometric or telescoping series
  4. Convergence of an infinite series: integral test, ratio test, comparison and limit comparison tests, and the alternating series test
  5. Taylor polynomials
9 hours

V. Trigonometry

  1. Radian and degree measure
  2. Definitions of trigonometric functions
  3. Graphs of trigonometric functions
  4. Derivatives of trigonometric functions
  5. Integrals of trigonometric functions

 6 hours

Exams

Total:

54 Hours

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Planned instructional activities:

Lecture, discussion, individual work, group work and/or computer-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, exponential and logarithmic functions and apply to graphing and optimization problems
  2. Integrate algebraic and exponential functions and apply to area problems..
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Source of information: Course Outline of Record dated November, 1998


 Last Updated On: 4/20/06