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Effective: Winter 2015
MATH 1DCALCULUS5 Unit(s)

Prerequisites: Prerequisite: MATH 1C.
Advisory: Advisory: Demonstrated proficiency in English by placement as determined by score on the English placement test OR through an equivalent placement process OR completion of ESLL 25 & ESLL 249.
Grade Type: Letter Grade, the student may select Pass/No Pass
Not Repeatable.
FHGE: Non-GE Transferable: CSU/UC
5 hours lecture. (60 hours total per quarter)

Student Learning Outcomes -
  • A student will be able to perform various types of computations involving double and triple integrals, parameterization of curves and surfaces, and line and flux integrals.
  • A student will be able to demonstrate an understanding of the concepts of divergence and curl as well as key theorems related to these concepts (e.g., the Divergence Theorem and Stoke's theorem).
Description -
Introduction to integration of functions of more than one variable, including double, triple, flux and line integrals. Additional topics include polar, cylindrical and spherical coordinates, parameterization, vector fields, path-independence, divergence and curl.

Course Objectives -
The student will be able to:
  1. Demonstrate an Understanding of Integration of Functions of Several Variables
  2. Demonstrate an Understanding of Parameterization and Vector Fields, including equations of planes in vector form and using parametric equations, and computation of arc length
  3. Demonstrate an Understanding of Line Integrals
  4. Demonstrate an Understanding of Flux Integrals
  5. Demonstrate an Understanding of the Calculus of Vector Fields, including divergence and curl of a vector field, The Divergence Theorem, Stokes' Theorem, and Green's Theorem
  6. Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (E) above
  7. Discuss mathematical problems and write solutions in accurate mathematical language and notation
  8. Interpret mathematical solutions

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.

Course Content (Body of knowledge) -
  1. Integrating Functions of Several Variables
    1. The Definite Integral of a Function of Two Variables
    2. Iterated Integrals
    3. Triple Integrals
    4. Double Integrals in Polar Coordinates
    5. Integrals in Cylindrical and Spherical Coordinates
    6. Change of Variables in a Multiple Integral
    7. Applications
      1. Area
      2. Volume
      3. Center of Mass
      4. Moments of inertia
  2. Parameterization and Vector Fields
    1. Parameterized Curves
      1. Tangent vector
      2. Normal vector
      3. Binormal vector
    2. Parameterized Surfaces
      1. Planes--in vector form and using parametric equations
      2. Non-linear surfaces
    3. Motion, Velocity, and Acceleration
    4. Vector Fields
      1. Conservative
      2. Gradient
    5. The flow of a Vector Field
    6. Arc Length
    7. Curvature
  3. Line Integrals
    1. Parametric Equations
    2. The Idea of a Line Integral
    3. Computing Line Integrals Over Parameterized Curves
    4. Gradient Fields and Path-Independent Fields
    5. Path-Dependent Vector Fields and Green's Theorem
  4. Flux Integrals
    1. The Idea of a Flux Integral
    2. Flux Integrals for Graphs, Cylinders, and Spheres
    3. Flux Integrals Over Parameterized Surfaces
  5. Calculus of Vector Fields
    1. The Divergence of a Vector Field
    2. The Divergence Theorem
    3. The Curl of a Vector Field
    4. Stokes' Theorem
    5. Green's Theorem
  6. Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (E) above.
    1. Use appropriate technology to graph vector fields and use the graphs to solve various types of problems involving vector fields such as line integrals, flow lines, divergence and curl
    2. Use appropriate technology to graph parameterized curves and surfaces in both 2- and 3-dimensional space
  7. Discuss mathematical problems and write solutions in accurate mathematical language and notation
    1. Application problems from other disciplines
    2. Proper notation
    3. Use appropriate technology to graph parameterized curves and surfaces in both 2- and 3-dimensional space
  8. Interpret mathematical solutions
    1. Explain the significance of solutions to application problems
Methods of Evaluation -
  1. Written homework
  2. Quizzes & tests
  3. Comprehensive final examination
Representative Text(s) -
Hughes-Hallet, Et al Calculus: Single and Multivariable. 6th ed. John Wiley & Sons, Inc., 2013.
Math 1D: Foothill College Custom Edition (w/out Wiley Plus), ISBN 9781118971277. Chapters 16-21, with odd-numbered HW answers, index, Ready Reference, and endpapers taken from Hughes-Hallett, Calculus: Single and Multivariable, 6th ed., 2014.

Disciplines -
Mathematics
 
Method of Instruction -
  1. Lecture
  2. Discussion
  3. Cooperative learning exercises
 
Lab Content -
Not applicable.
 
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.