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Calculus with Analytic Geometry
Calculus of a Single Variable
Multivariable Calculus, Seventh Edition
Ron Larson - The Pennsylvania State University, The Behrend
College
Robert P. Hostetler - The Pennsylvania State University, The Behrend College
Bruce H. Edwards - University of Florida | | |
| | Chapter Summary
Chapter 14: Vector Analysis
14.1
- Understand the concept of a vector field.
- Determine whether a vector field is conservative.
- Find the curl of a vector field.
- Find the divergence of a vector field.
14.2
- Understand the use and concept of a piecewise smooth curve.
- Write and evaluate a line integral.
- Write and evaluate a line integral of a vector field.
- Write and evaluate a line integral in a differential form.
14.3
- Understand the use of the Fundamental Theorem of Line Integrals.
- Understand the concept of independence of path.
- Understand the concept of conservation of energy.
14.4
- Use Green’s Theorem to evaluate a line integral.
- Use alternative forms of Green’s Theorem.
14.5
- Understand the definition of a parametric surface.
- Find a set of parametric equations to represent a surface.
- Find a normal vector and a tangent plane to a parametric surface.
- Find the area of a parametric surface.
14.6
- Evaluate a surface integral as a double integral.
- Evaluate a surface integral for a parametric surface.
- Determine the orientation of a surface.
- Understand the concept of a flux integral.
14.7
- Understand and use the Divergence Theorem.
- Use the Divergence Theorem to calculate flux.
14.8
- Understand and use Stoke’s Theorem.
- Use curl to analyze the motion of a rotating liquid.
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