  
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, pathindependence, divergence and curl.


Course Objectives  
 The student will be able to:
 Demonstrate an Understanding of Integration of Functions of Several Variables
 Demonstrate an Understanding of Parameterization and Vector Fields, including equations of planes in vector form and using parametric equations, and computation of arc length
 Demonstrate an Understanding of Line Integrals
 Demonstrate an Understanding of Flux Integrals
 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
 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
 Discuss mathematical problems and write solutions in accurate mathematical language and notation
 Interpret mathematical solutions

Special Facilities and/or Equipment  
  Graphing Calculator.
 When taught hybrid: Four lecture hours per week in facetoface contact and one hour per week using CCC Confer. Students need internet access.

Course Content (Body of knowledge)  
  Integrating Functions of Several Variables
 The Definite Integral of a Function of Two Variables
 Iterated Integrals
 Triple Integrals
 Double Integrals in Polar Coordinates
 Integrals in Cylindrical and Spherical Coordinates
 Change of Variables in a Multiple Integral
 Applications
 Area
 Volume
 Center of Mass
 Moments of inertia
 Parameterization and Vector Fields
 Parameterized Curves
 Tangent vector
 Normal vector
 Binormal vector
 Parameterized Surfaces
 Planesin vector form and using parametric equations
 Nonlinear surfaces
 Motion, Velocity, and Acceleration
 Vector Fields
 Conservative
 Gradient
 The flow of a Vector Field
 Arc Length
 Curvature
 Line Integrals
 Parametric Equations
 The Idea of a Line Integral
 Computing Line Integrals Over Parameterized Curves
 Gradient Fields and PathIndependent Fields
 PathDependent Vector Fields and Green's Theorem
 Flux Integrals
 The Idea of a Flux Integral
 Flux Integrals for Graphs, Cylinders, and Spheres
 Flux Integrals Over Parameterized Surfaces
 Calculus of Vector Fields
 The Divergence of a Vector Field
 The Divergence Theorem
 The Curl of a Vector Field
 Stokes' Theorem
 Green's Theorem
 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.
 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
 Use appropriate technology to graph parameterized curves and surfaces in both 2 and 3dimensional space
 Discuss mathematical problems and write solutions in accurate mathematical language and notation
 Application problems from other disciplines
 Proper notation
 Use appropriate technology to graph parameterized curves and surfaces in both 2 and 3dimensional space
 Interpret mathematical solutions
 Explain the significance of solutions to application problems

Methods of Evaluation  
  Written homework
 Quizzes & tests
 Comprehensive final examination

Representative Text(s)  
 HughesHallet, 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 1621, with oddnumbered HW answers, index, Ready Reference, and endpapers taken from HughesHallett, Calculus: Single and Multivariable, 6th ed., 2014.

Disciplines  
 Mathematics


Method of Instruction  
  Lecture
 Discussion
 Cooperative learning exercises


Lab Content  
 Not applicable.


Types and/or Examples of Required Reading, Writing and Outside of Class Assignments  
  Homework Problems: Homework problems covering subject matter from text and related material ranging from 3060 problems per week. Students will need to employ critical thinking in order to complete assignments.
 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.
 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.
 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.
