Transcription of Scalar Fields and Vector fields - IIT Ropar
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Scalar Fields and Vector fields - IIT Ropar
Scalar Fields and Vector fieldsDefinition A Scalar field is an assignment of a Scalar toeach point in region in the space. thetemperature at a point on the earth is a scalarfield. A Vector field is an assignment of a Vector toeach point in a region in the space. thevelocity field of a moving fluid is a Vector fieldas it associates a velocity Vector to each pointin the A Scalar field is a map from D to , where D is a subset of n. A Vector field is a map from D to n, where D is a subset of a subset of n. For n=2: Vector field in plane, for n=3: Vector field in space Example: Gradient fieldLine integral Line integral in a Scalar field Line integral in a Vector fieldLINE INTEGRAL IN A Scalar FIELDMOTIVATIONA rescue team follows a path in a danger area where for eachposition the degree of radiation is defined.
• A scalar field is a map from D to ℜ, where D is a subset of ℜn. • A vector field is a map from D to ℜn, where D is a subset of ℜn. • For n=2: vector field in plane, • for n=3: vector field in space • Example: Gradient field
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