Foothill CollegeApproved Course Outlines

Physical Sciences, Mathematics & Engineering Division
MATH 1ACALCULUSWinter 2015
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 compute limits of functions at real numbers.
  2. Determine if a function is continuous at a real number.
  3. Find the derivative of a function as a limit.
  4. Find the equation of a tangent line to a function.
  5. Compute derivatives using differentiation formulas.
  6. Use implicit differentiation.
  7. Graph and differentiate functions in polar and parametric form.
  8. Demonstrate an understanding of and calculate first, second and higher-order derivatives.
  9. Graph functions using methods of calculus.
  10. Use differentiation to solve applications such as related rate problems and optimization problems.
  11. Define the antiderivative and determine antiderivatives of simple functions.
  12. Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (K) above.
  13. Discuss mathematical problems and write solutions in accurate mathematical language and notation.
  14. 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 compute limits of functions at real numbers.
    1. One sided and two sided limits
    2. Finding limits graphically
    3. The limit laws
    4. Compute limits using numerical and algebraic approaches
    5. Indeterminate forms and l'Hospital's Rule
    6. Formal definition of a limit
  2. Determine if a function is continuous at a real number.
    1. Continuity
    2. Intermediate Value Theorem
    3. Continuity and differentiability
  3. Find the derivative of a function as a limit.
    1. Use the definition to find derivatives of functions at a point.
    2. Use the definition to find derivatives of functions.
  4. Find the equation of a tangent line to a function.
    1. Average and instantaneous rates of change
    2. Slopes of secant and tangent lines
  5. Compute derivatives using differentiation formulas.
    1. Power rule
    2. Product rule
    3. Quotient rule
    4. Chain rule
    5. Differentiation of exponential functions
    6. Differentiation of logarithmic functions
    7. Differentiation of inverse functions
    8. Differentiation of trigonometric functions
    9. Differentiation of hyperbolic functions
  6. Use implicit differentiation.
    1. Equations to tangent lines at points of implicit curves
    2. Use implicit differentiation to find the derivative of an equation of two variables.
  7. Graph and differentiate functions in polar and parametric form.
    1. Tangents to parametric and polar curves
  8. Demonstrate an understanding of and calculate first, second and higher-order derivatives.
    1. Calculate first derivatives
    2. Calculate second derivatives
    3. Calculate higher order derivatives
  9. Graph functions using methods of calculus.
    1. Critical points
    2. Graphing functions using the first and second derivatives
    3. Relative extrema
    4. Global extrema
    5. Inflection points
    6. First and second derivative tests
    7. Second derivative and concavity
    8. Asymptotes
  10. Use differentiation to solve applications such as related rate problems and optimization problems.
    1. Local linearity and linear approximation
    2. Differentials
    3. Mean Value Theorem
    4. Related Rates
    5. Optimization
    6. Velocity and Acceleration
    7. Extreme Value Theorem
  11. Define the antiderivative and determine antiderivatives of simple functions.
    1. Find general antiderivatives
    2. Antiderivatives in the context of rectilinear motion
    3. Graphing antiderivatives
    4. Families of curves
  12. Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (K) 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
  13. Discuss mathematical problems and write solutions in accurate mathematical language and notation.
    1. Application problems from other disciplines
    2. Proper notation
  14. Interpret mathematical solutions.
    1. Interpretations of the derivative.
    2. 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: 2014-11-03 11:01:51


Foothill CollegeApproved Course Outlines