Foothill CollegeApproved Course Outlines

Physical Sciences, Mathematics & Engineering Division
MATH 1ACALCULUSSummer 2013
5 hours lecture.5 Units

Total Quarter Learning Hours: 60 (Total of All Lecture, Lecture/Lab, and Lab hours X 12)
 
 Lecture Hours: 5 Lab Hours: Lecture/Lab:
 Note: If Lab hours are specified, see item 10. Lab Content below.

Repeatability -
Statement: Not Repeatable.

Status -
 Course Status: ActiveGrading: Letter Grade with P/NP option
 Degree Status: ApplicableCredit Status: Credit
 Degree or Certificate Requirement: AS Degree,   Foothill GE
 GE Status: Communication & Analytical Thinking

Articulation Office Information -
 Transferability: BothValidation: 07/01/2005; 11/27/12

1. Description -
Introduction to differential calculus, including limits, derivatives and their applications to curve-sketching, families of functions, and optimization.
Prerequisite: Satisfactory score on the mathematics placement test or MATH 48C.
Co-requisite: None
Advisory: Demonstrated proficiency in English by placement into ENGL 1A as determined by score on the English placement test or through an equivalent placement process.

2. Course Objectives -
The student will be able to:
  1. Demonstrate an understanding of and calculate limits.
  2. Demonstrate an understanding of and calculate first and second derivatives.
  3. Graph using the derivative.
  4. Apply techniques of differentiation.
  5. Demonstrate an understanding of applications of the derivative.
  6. Define the antiderivative and determine antiderivatives of simple functions.
  7. Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (F) above.
  8. Discuss mathematical problems and write solutions in accurate mathematical language and notation.
  9. Interpret mathematical solutions.
3. Special Facilities and/or Equipment -
  1. Graphing Calculator.
  2. When taught hybrid: Four lecture hours per week in face-to-face contact and one hour per week using CCC Confer. Students need internet access.

4. Course Content (Body of knowledge) -
  1. Demonstrate an understanding of and calculate limits.
    1. One sided and two sided limits
    2. Finding limits graphically
    3. The limit laws
    4. Evaluating limits
    5. l'Hospital's Rule
    6. Formal definition of a limit
    7. Continuity
    8. Intermediate Value Theorem
  2. Demonstrate an understanding of and calculate first and second derivatives.
    1. Average and instantaneous rates of change
    2. Slopes of secant and tangent lines
    3. Equations of tangent lines
    4. Continuity and differentiability
    5. Optimization
    6. The derivative at a point
    7. The derivative function
    8. Interpretations of the derivative
    9. The second derivative and concavity
    10. Applications to velocity and acceleration
    11. Tangents to parametric and polar curves
  3. Graph using the Derivative
    1. Critical points
    2. Graphing polynomial functions using the derivative
    3. Relative extrema
    4. Global extrema
    5. Inflection points
    6. First and second derivative tests
    7. Families of curves
  4. Apply techniques of differentiation
    1. Power rule
    2. Product rule
    3. Quotient rule
    4. Chain rule
    5. Implicit differentiation
    6. Derivatives of exponential functions
    7. Derivatives of logarithmic functions
    8. Derivatives of trigonometric functions
    9. Derivatives of hyperbolic functions
  5. Demonstrate an understanding of applications of the derivative
    1. Local linearity and linear approximation
    2. Differentials
    3. Mean Value Theorem
    4. Related Rates
    5. Optimization
  6. Define the antiderivative and determine antiderivatives of simple functions.
    1. Find general antiderivatives
    2. Antiderivatives in the context of rectilinear motion
    3. Graphing antiderivatives
  7. Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (F) above.
    1. Calculator/computer utilities for evaluating derivatives
    2. Calculator/computer utilities for constructing graphs of derivatives
    3. Calculator/computer utilities for estimating limits numerically
    4. Calculator/computer utilities for verifying solutions to optimization problems
  8. Discuss mathematical problems and write solutions in accurate mathematical language and notation.
    1. Application problems from other disciplines
    2. Proper notation
  9. Interpret mathematical solutions.
    1. Explain the significance of solutions to application problems.
5. Repeatability - Moved to header area.
 
6. Methods of Evaluation -
  1. Written homework
  2. Quizzes & tests
  3. Proctored comprehensive final examination
7. Representative Text(s) -
Stewart, James Calculus: Concepts and Contexts. 4th ed. Belmont, CA: Brooks/Cole, Cengage Learning, 2010.

8. Disciplines -
Mathematics
 
9. Method of Instruction -
  1. Lecture
  2. Discussion
  3. Cooperative learning exercises
 
10. Lab Content -
Not applicable.
 
11. Honors Description - No longer used. Integrated into main description section.
 
12. Types and/or Examples of Required Reading, Writing and Outside of Class Assignments -
  1. Homework Problems: Homework problems covering subject matter from text and related material ranging from 30 - 60 problems per week. Students will need to employ critical thinking in order to complete assignments.
  2. Lecture: Five hours per week of lecture covering subject matter from text and related material. Reading and study of the textbook, related materials and notes.
  3. Projects: Student projects covering subject matter from textbook and related materials. Projects will require students to discuss mathematical problems,write solutions in accurate mathematical language and notation and interpret mathematical solutions. Projects may require the use of a computer algebra system such as Mathematica or MATLAB.
  4. Worksheets: Problems and activities covering the subject matter.
Such problems and activities will require students to think critically. Such worksheets may be completed both inside and/or outside of class.
13. Need/Justification -
This course is a required core course for the A.S. degree in Mathematics and satisfies the Foothill GE requirement for Area V, Communications and Analytical Thinking.


Course status: Active
Last updated: 2014-03-21 20:20:57


Foothill CollegeApproved Course Outlines