COLLEGE OF ALAMEDA COURSE OUTLINE

COLLEGE: STATE APPROVAL DATE: 09/27/2010
ORIGINATOR: Khalilah Beal STATE CONTROL NUMBER: CCC000366071
BOARD OF TRUSTEES APPROVAL DATE: 05/08/2008
CURRICULUM COMMITTEE APPROVAL DATE: 10/03/2017
CURRENT EFFECTIVE DATE:
 
DIVISION/DEPARTMENT:

1. REQUESTED CREDIT CLASSIFICATION:
  Credit - Degree Applicable
Course is not a basic skills course.
Program Applicable
2. DEPT/COURSE NO: 3. COURSE TITLE:
  MATH 003B   Calculus II
4. COURSE: COA Course Changes only in Non-Catalog Info   TOP NO. 1701.00
5. UNITS: 5.000   HRS/WK LEC: 5.00 Total: 87.50
  HRS/WK LAB:

6. NO. OF TIMES OFFERED AS SELETED TOPIC:       AVERAGE ENROLLMENT:
7. JUSTIFICATION FOR COURSE:
  Satisfies General Education Analytical Thinking requirement for Associate Degree. Provides foundation for more advanced courses in Mathematics, Physics, Chemistry and related fields. Satisfies the Quantitative Reasoning requirement for transfer to UC and CSU.
8. COURSE/CATALOG DESCRIPTION
  Applications of definite integral: Methods of integration, polar coordinates, parametric equations, infinite and power series.
9. OTHER CATALOG INFORMATION
 
  1. Modular: No     If yes, how many modules:
  2. Open entry/open exit: No
  3. Grading Policy: Letter Grade Only
  4. Eligible for credit by Exam: No
  5. Repeatable according to state guidelines: No
  6. Required for degree/certificate (specify):
    New - Mathematics AS-T
  7. Meets GE/Transfer requirements (specify):
    Acceptable for credit: UC/CSU. AA/AS area 4b, 4e. CSU area B4. IGETC area 2A.
  8. C-ID Number: Expiration Date:

  9. Are there prerequisites/corequisites/recommended preparation for this course? Yes
    Date of last prereq/coreq validation: 10/03/2017
  10. Acceptable for Credit: CSU/UC
10. LIST STUDENT PERFORMANCE OBJECTIVES (EXIT SKILLS): (Objectives must define the exit skills required of students and include criteria identified in Items 12, 14, and 15 - critical thinking, essay writing, problem solving, written/verbal communications, computational skills, working with others, workplace needs, SCANS competencies, all aspects of the industry, etc.)(See SCANS/All Aspects of Industry Worksheet.)

Students will be able to:
  1. differentiate inverse trigonometric, hyperbolic and inverse hyperbolic functions
  2. evaluate definite integrals using a variety of integration formulas and techniques
  3. find indefinite integrals using a variety of integration formulas and techniques
  4. apply integration to finding areas, volumes, surface areas and lengths of curves (arc length) and to solving work problems
  5. evaluate improper integrals
  6. apply convergence tests to sequences and series
  7. express functions as power series
  8. use power series representations to integrate and differentiate functions
  9. graph, differentiate and integrate functions in polar and parametric forms
11A. COURSE CONTENT: List major topics to be covered. This section must be more than listing chapter headings from a textbook. Outline the course content, including essential topics, major subdivisions, and supporting details. It should include enough information so that a faculty member from any institution will have a clear understanding of the material taught in the course and the approximate length of time devoted to each. There should be congruence among the catalog description, lecture and/or lab content, student performance objectives, and the student learning outcomes. List percent of time spent on each topic; ensure percentages total 100%.

LECTURE CONTENT:

1. Applications of Integration 16.6%
a. Areas between curves
b. Volumes
c. Volumes by cylindrical shells
d. Work
e. Average value of a function

2. Techniques of Integration 16.6%
a. Integration by parts
b. Trigonometric integrals
c. Trigonometric substitution
d. Integration of rational functions by partial fractions
e. Strategy for integration
f. Integration using tables of integrals
g. Numerical integration, Trapezoidal rule, Simpson’s rule
h. Improper integrals

3. Further Applications of Integration 16.6%
a. Arc length
b. Area of a surface of revolution
c. Applications in physics and engineering (including moments and centers of mass)
d. Applications in economics, biology, probability

4. Differential Equations 16.6%
a. Modeling with differential equations
b. Direction fields and Euler’s method
c. Separable equations
d. Growth and Decay
e. Linear equations

5. Parametric Equations and Polar Coordinates 16.6%
a. Curves defined by parametric equations
b. Calculus with parametric curves
c. Polar coordinates
d. Areas and lengths in polar coordinates
e. Conic sections
f. Conic sections in polar coordinates

6. Infinite Series 16.6%
a. Sequences
b. Series
c. The integral test
d. The comparison tests
e. Alternating series
f. Absolute convergence, the ratio test, the root test
g. Power series, radius of convergence, interval of convergence
h. Representations of functions as power series
i. Differentiation and integration of power series
j. Taylor and Maclaurin series
k. The binomial series

11B. LAB CONTENT:
N/A
12. METHODS OF INSTRUCTION (List methods used to present course content.)
  1. Discussion
  2. Distance Education
  3. Lecture
  4. Other (Specify)

  5. Other Methods:
    Instructor-focused lecture on theory and the language of calculus. Question and answer periods based on worksheets and in-class examples to encourage class discussion and demonstrations which emphasize alternative approaches to problem solving and their underlying rationales. Video demonstration of tools specific to this level of calculus. Distance Ed addendum for hybrid instruction use.
13. ASSIGNMENTS: 10.00 hours/week (List all assignments, including library assignments. Requires two (2) hours of independent work outside of class for each unit/weekly lecture hour. Outside assignments are not required for lab-only courses, although they can be given.)

Out-of-class Assignments:
Out-of-class Assignments: College-level textbook chapter readings that reinforce lecture material. Problem sets including computational problems equivalent in content and level of difficulty to those covered in the lectures. Additional problems that introduce supplemental concepts and formulas and require the synthesis and analysis of various concepts. Graphical representation and analysis specific to the study of calculus.


ASSIGNMENTS ARE: (See definition of college level):
Primarily College Level
14. STUDENT ASSESSMENT: (Grades are based on):
ESSAY (Includes "blue book" exams and any written assignment of sufficient length and complexity to require students to select and organize ideas, to explain and support the ideas, and to demonstrate critical thinking skills.)
COMPUTATION SKILLS
NON-COMPUTATIONAL PROBLEM SOLVING (Critical thinking should be demonstrated by solving unfamiliar problems via various strategies.)
SKILL DEMONSTRATION
OTHER (Describe):
Assess essay for understanding and application of concepts presented in classwork and supplemental material. Evaluate computation skills for accurate application of steps and correct answers. Evaluate students' ability to analyze given information and apply it in terms of the question.
15. TEXTS, READINGS, AND MATERIALS
  A. Textbooks:
 
  • James Stewart. 2015. Calculus: Early Transcendentals 8th. Cengage
 

*Date is required: Transfer institutions require current publication date(s) within 5 years of outline addition/update.

  B. Additional Resources:
 
  • Library/LRC Materials and Services:

    The instructor, in consultation with a librarian, has reviewed the materials and services of the College Library/LRC in the subject areas related to the proposed new course
  • Are print materials adequate?     Yes
  • Are nonprint materials adequate?     Yes
  • Are electronic/online resources available?     Yes
  • Are services adequate?     Yes
  • Specific materials and/or services needed have been identified and discussed. Librarian comments:
    Collection sufficient to support course. New book requests submitted as needed. Math Department to donate additional materials.
  C. Readings listed in A and B above are: (See definition of college level):
 

Primarily college level

16. DESIGNATE OCCUPATIONAL CODE:
E - Non-Occupational
17. LEVEL BELOW TRANSFER:
Y - Not Applicable
18. CALIFORNIA CLASSIFICATION CODE:
Y - Credit Course
19. NON CREDIT COURSE CATEGORY:
Y - Not Applicable
20. FUNDING AGENCY CATEGORY:
Not Applicable - Not Applicable
SUPPLEMENTAL PAGE

Use only if additional space is needed. (Type the item number which is to be continued, followed by "continued." Show the page number in the blank at the bottom of the page. If the item being continued is on page 2 of the outline, the first supplemental page will be "2a." If additional supplemental pages are required for page 2, they are to be numbered as 2b, 2c, etc.)

1a. Prerequisites/Corequisites/Recommended Preparation:
    PREREQUISITE:
  • MATH 003A: Calculus I