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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.