COLLEGE OF ALAMEDA COURSE OUTLINE

COLLEGE: COLLEGE OF ALAMEDA STATE APPROVAL DATE: 09/27/2010
ORIGINATOR: Vanson Nguyen STATE CONTROL NUMBER: CCC000380993
BOARD OF TRUSTEES APPROVAL DATE: 05/08/2008
CURRICULUM COMMITTEE APPROVAL DATE: 02/17/2015
CURRENT EFFECTIVE DATE:
 
DIVISION/DEPARTMENT: COA - Science, Technology, Engineering, Art, and Mathematics / A - MATHEMATICS
1. REQUESTED CREDIT CLASSIFICATION:
  D - Credit - Degree Applicable
N - Not Basic Skills
1 - Program Applicable
2. DEPT/COURSE NO: 3. COURSE TITLE:
  MATH 003C   Calculus III
4. COURSE: COA Course Changes only in Non-Catalog Info   TOP NO. 170100 - Mathematics, General
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 the General Education Analytical Thinking requirement for Associate Degrees. Provides foundation for more advanced study in mathematics and related fields, such as Physics. Intended to satisfy the Quantitative Reasoning component required for transfer to UC or CSU.
8. COURSE/CATALOG DESCRIPTION
  Partial differentiation: Jacobians, transformations, multiple integrals, theorems of Green and Stokes, differential forms, vectors and vector functions, geometric coordinates, and vector calculus.
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: 02/17/2015
  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. perform vector operations
  2. determine equations of lines and planes
  3. find the limit of a function of several variables at a given point
  4. evaluate derivatives of vector functions and real-valued functions in several variables
  5. find a tangent vector on a space curve
  6. find the equation of a tangent plane at a point
  7. determine the differentiability of a function
  8. test for saddle points and find local and global extrema
  9. use Lagrange multipliers to solve constraint problems
  10. compute arc length
  11. find the curl and divergence of a vector field
  12. compute multiple (two-and three-dimensional) integrals
  13. use multiple integrals to find area, volume, density, center of mass, moments of inertia, expected values
  14. compute and graph vector fields including gradient vector fields
  15. apply Green's Theorem, Stokes' Theorem and the Divergence Theorem
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. Vectors in Two and Three Dimensions 
a. Algebra of vectors in two and three dimensions
b. The dot product
c. Projections
d. The cross product
e. Triple products
f. Vector, parametric and rectangular equations of lines and planes
g. Cylinders and quadric surfaces

2. Vector Functions 
a. Vector functions and space curves
b. Derivatives and integrals of vector functions
c. Arc length and curvature
d. Tangent, normal, and binormal vectors
e. Velocity and acceleration


3. Partial Derivatives 
a. Real-valued functions of several variables
b. Graphs of functions of two variables
c. Level curves and surfaces
d. Limits and continuity
e. Partial derivatives
f. Tangent planes, linear approximations, differentials
g. The chain rule
h. Higher order derivatives
i. Directional derivatives and the gradient vector
j. Conservative fields
k. Critical points, saddle points, local and global extrema
l. Lagrange multipliers

4.  Multiple Integrals 
a. Double integrals over rectangles
b. Iterated integrals
c. Double integrals over general regions
d. Double integrals in polar coordinates
e. Applications of double integrals such as finding area, volume, density, center of mass, moments of inertia, expected values
f. Triple integrals in rectangular coordinates
g. Triple integrals in cylindrical coordinates
h. Triple integrals in spherical coordinates
i. Change of variables in multiple integrals; the Jacobian

5. Vector Calculus 
a. Vector fields including gradient vector fields
b. Line integrals
c. The Fundamental Theorem for Line Integrals
d. Green’s Theorem
e. Curl and divergence
f. Parametric surfaces; areas of parametric surfaces
g. Surface integrals
h. Stokes’ Theorem
i. The Divergence Theorem
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.)
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. 2011. Calculus, Early Transcendentals 7th. Thomson Brooks Cole Publishing Company
    Rationale: -
 

*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?     No
  • Are nonprint materials adequate?     No
  • Are electronic/online resources available?     Yes
  • Are services adequate?     Yes
  • Specific materials and/or services needed have been identified and discussed. Librarian comments:
    Library print resources are not adequate. Recommendations are necessary from faculty to update library collections. (DHS). Additional textbooks to be donated.
  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, Credit course
20. FUNDING AGENCY CATEGORY:
Y - Not Applicable (funding not used to develop course)
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 003B: Calculus II