COLLEGE OF ALAMEDA COURSE OUTLINE

COLLEGE: STATE APPROVAL DATE: 04/06/2016
ORIGINATOR: Michael J. Valdez STATE CONTROL NUMBER: CCC000351057
BOARD OF TRUSTEES APPROVAL DATE: 01/26/2016
CURRICULUM COMMITTEE APPROVAL DATE: 11/17/2015
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 003A   Calculus I
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:
  Meets AS degree and transfer requirements.
8. COURSE/CATALOG DESCRIPTION
  Theorems on limits and continuous functions, derivatives, differentials, and applications: Fundamental theorems of calculus and applications; properties of exponential, logarithmic, and inverse trigonometric functions, and hyperbolic functions.
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: MATH 201 Expiration Date:

  9. Are there prerequisites/corequisites/recommended preparation for this course? Yes
    Date of last prereq/coreq validation: 03/17/2015
  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. Diagram and compute limits of functions
  2. Prove and determine whether functions are continuous
  3. Compute the derivative of a function as a limit
  4. Compute derivatives of sums, differences, products, quotients, roots, powers and compositions of functions
  5. Compute derivatives of trigonometric, exponential and logarithmic functions
  6. Examine uses of the derivative such as to find the slope of a line tangent to a function
  7. Examine uses differentiation to solve real world problems (related rates, optimization, etc.)
  8. Solve problems by implicit differentiation
  9. Diagram and analyze the graph of a function by the use of differentiation.
  10. Calculate the area under a curve by the use Riemann Sums to approximate the area under a curve
  11. Calculate and evaluate a definite integral as a limit
  12. Apply and use the Fundamental Theorem of Calculus to evaluate integrals
  13. Set up and use integrals to find area
  14. Apply the substitution rule to solve integration problems
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. Functions (10%)


a. Essential functions
b. Constructing new functions from existing functions
c. Composite functions
d. One-to-one functions
e. Exponential functions
f. Inverse functions and logarithms

2. Limits and Continuous Functions (20%)


a. Introduction to limits by the tangent and velocity problems
b. Limit of a function
c. Calculating limits using various approaches: tables, graphs, limit laws, and algebra
d. The Squeeze Theorem
e. The precise definition of a limit
f. Continuity
g. The Intermediate Value Theorem
h. Limits at infinity; horizontal asymptotes

3. The Derivative (30%)


a. Definition of the derivative and its interpretation of as the slope of tangent line
b. The derivative as a function
c. Higher order derivatives
d. Derivatives of polynomial and exponential functions
e. The product and quotient rules
f. Derivatives of trigonometric functions
g. The Chain Rule
h. Implicit differentiation
i. Derivatives of inverse functions: Inverse trigonometric and logarithmic functions
j. Applications of the derivative: Rates of change, exponential growth and decay, related rates
k. Linear approximations and differentials
l. Hyperbolic functions

4. Applications of the Derivative (25%)


a. Maxima and minima of a function
b. The Mean-Value Theorem
c. Indeterminate forms and L’Hospital’s Rule
d. Applying first and second derivatives to curve sketching (extrema, concavity, asymptotes)
e. Optimization problems
f. Antiderivatives

5. Integrals (15%)


a. Introduction to Reimann sums through the area under the curve and distance travelled problem
b. Reimann sums and the definite integral
c. Properties of the definite integral
d. The Fundamental Theorem of Calculus
e. Indefinite integrals
f. Applications of the definite integral: Area under the curve and the Net Change Theorem
g. The substitution rule

11B. LAB CONTENT:
None
12. METHODS OF INSTRUCTION (List methods used to present course content.)
  1. Discussion
  2. Distance Education
  3. Lecture
  4. Multimedia Content
  5. Other (Specify)

  6. 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: 0.00 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:
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. Caluclus: Early Transcendentals 7th. Thomson Brooks-Cole Publishing Co
    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?     Yes
  • 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:
    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 002
    or
  • PREREQUISITE:
  • MATH 001: Pre-Calculus
    and
  • PREREQUISITE:
  • MATH 050: Trigonometry