Math Insight

Pages similar to: Testing if three-dimensional vector fields are conservative

• The gradient theorem for line integrals
  A introduction to the gradient theorem for conservative or path-independent line integrals.
• How to determine if a vector field is conservative
  A discussion of the ways to determine whether or not a vector field is conservative or path-independent.
• A path-dependent vector field with zero curl
  A counterexample showing how a vector field could have zero curl but still fail to be conservative or path-independent.
• A conservative vector field has no circulation
  How a conservative, or path-independent, vector field will have no circulation around any closed curve.
• Finding a potential function for conservative vector fields
  How to find a potential function for a given conservative, or path-independent, vector field.
• Finding a potential function for three-dimensional conservative vector fields
  How to find a potential function for a given three-dimensional conservative, or path-independent, vector field.
• A simple example of using the gradient theorem
  An example of using the gradient theorem to calculate the line integral of a conservative, or path-independent, vector field.
• An introduction to conservative vector fields
  An introduction to the concept of path-independent or conservative vector fields, illustrated by interactive graphics.
• The fundamental theorems of vector calculus
  A summary of the four fundamental theorems of vector calculus and how the link different integrals.

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