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Vector Analysis

In multivariable vector analysis, we discuss the differentiation and integration of the following functions:

  • Vector-valued functions f:RRn\mathbf{f} : \mathbb{R} \to \mathbb{R}^{n}
  • Multivariable functions f:RnRf : \mathbb{R}^{n} \to \mathbb{R}
  • Multivariable vector functions f:RnRm\mathbf{f} : \mathbb{R}^{n} \to \mathbb{R}^{m}

Real functions f:RRf : \mathbb{R} \to \mathbb{R} are covered in the Introduction to Analysis category.

Especially, 3D functions f:R3Rf : \mathbb{R}^{3} \to \mathbb{R} and f:R3R3\mathbf{f} : \mathbb{R}^{3} \to \mathbb{R}^{3} are discussed in the Mathematical Physics category, slightly less rigorously to suit the level of physics and engineering majors.

Euclidean Space

Vector-valued Functions

Covers content related to vector-valued functions f:RRn\mathbf{f} : \mathbb{R} \to \mathbb{R}^{n}.

Differentiation

Integration

Multivariable Functions

Covers content related to multivariable functions f:RnRf : \mathbb{R}^{n} \to \mathbb{R}.

Differentiation

Integration

Multivariable Vector Functions

Covers content related to f:RnRm\mathbf{f} : \mathbb{R}^{n} \to \mathbb{R}^{m}.

Differentiation

Integration

References

  • Walter Rudin, Principles of Mathmatical Analysis (3rd Edition, 1976)
  • William R. Wade, An Introduction to Analysis (4th Edition, 2010)
  • James Stewart, Daniel Clegg, and Saleem Watson, Calculus (early transcendentals, 9E)

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