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- https://math.libretexts.org/Under_Construction/Purgatory/MAT-004A_-_Multivariable_Calculus_(Reed)/05%3A_Vector_Calculus/5.02%3A_Vector_FieldsVector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. Th...Vector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. They are also useful for dealing with large-scale behavior such as atmospheric storms or deep-sea ocean currents. In this section, we examine the basic definitions and graphs of vector fields so we can study them in more detail in the rest of this chapter.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/16%3A_Vector_Calculus/16.01%3A_Vector_FieldsVector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. Th...Vector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. They are also useful for dealing with large-scale behavior such as atmospheric storms or deep-sea ocean currents. In this section, we examine the basic definitions and graphs of vector fields so we can study them in more detail in the rest of this chapter.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_by_David_Guichard_(Improved)/16%3A_Vector_Calculus/16.01%3A_Vector_FieldsA two-dimensional vector field is a function that maps each point (x,y) in R2 to a two-dimensional vector ⟨u,v⟩, and similarly a three-dimensional vector field maps (x,y,z) to ⟨u,v,w⟩.
- https://math.libretexts.org/Bookshelves/Calculus/Supplemental_Modules_(Calculus)/Vector_Calculus/4%3A_Integration_in_Vector_Fields/4.6%3A_Vector_Fields_and_Line_Integrals%3A_Work%2C_Circulation%2C_and_Flux/Vector_FieldsA vector field is be a function where the domain is Rn and the range is n-dimensional vectors.
- https://math.libretexts.org/Bookshelves/Scientific_Computing_Simulations_and_Modeling/Introduction_to_the_Modeling_and_Analysis_of_Complex_Systems_(Sayama)/13%3A_Continuous_Field_Models_I__Modeling/13.03%3A_Visualizing_Two-Dimensional_Scalar_and_Vector_FieldPlotting scalar and vector fields in Python is straightforward, as long as the space is two-dimensional.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_IV%3A_Multivariable_Calculus/03%3A_Vector_Calculus/3.04%3A_Greens_TheoremGreen’s theorem is an extension of the Fundamental Theorem of Calculus to two dimensions. It has two forms: a circulation form and a flux form, both of which require region \(D\) in the double integra...Green’s theorem is an extension of the Fundamental Theorem of Calculus to two dimensions. It has two forms: a circulation form and a flux form, both of which require region \(D\) in the double integral to be simply connected. However, we will extend Green’s theorem to regions that are not simply connected. Green’s theorem relates a line integral around a simply closed plane curve \(C\) and a double integral over the region enclosed by \(C\).
- https://math.libretexts.org/Courses/SUNY_Geneseo/Math_223_Calculus_3/05%3A_Vector_Calculus/5.01%3A_Vector_FieldsVector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. Th...Vector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. They are also useful for dealing with large-scale behavior such as atmospheric storms or deep-sea ocean currents. In this section, we examine the basic definitions and graphs of vector fields so we can study them in more detail in the rest of this chapter.
- https://math.libretexts.org/Courses/Mission_College/Math_4A%3A_Multivariable_Calculus_(Kravets)/05%3A_Vector_Calculus/5.02%3A_Vector_FieldsVector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. Th...Vector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. They are also useful for dealing with large-scale behavior such as atmospheric storms or deep-sea ocean currents. In this section, we examine the basic definitions and graphs of vector fields so we can study them in more detail in the rest of this chapter.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/16%3A_Vector_Calculus/16.02%3A_Vector_FieldsVector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. Th...Vector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. They are also useful for dealing with large-scale behavior such as atmospheric storms or deep-sea ocean currents. In this section, we examine the basic definitions and graphs of vector fields so we can study them in more detail in the rest of this chapter.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_IV%3A_Multivariable_Calculus/03%3A_Vector_Calculus/3.01%3A_Vector_FieldsVector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. Th...Vector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. They are also useful for dealing with large-scale behavior such as atmospheric storms or deep-sea ocean currents. In this section, we examine the basic definitions and graphs of vector fields so we can study them in more detail in the rest of this chapter.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q4/03%3A_Vector_Calculus/3.02%3A_Vector_FieldsVector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. Th...Vector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. They are also useful for dealing with large-scale behavior such as atmospheric storms or deep-sea ocean currents. In this section, we examine the basic definitions and graphs of vector fields so we can study them in more detail in the rest of this chapter.
