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In this section we briefly touch upon the theory of vector-valued functions in several variables. To simplify matters we limit ourselves again to the case of two variables. First we define vector fields in the plane and extend the notions of continuity and differentiability to vector-valued functions. Then we discuss Newton’s method in two variables. As an application we compute a common zero of two nonlinear functions. Finally, as an extension of Sect. 15.1, we show how smooth surfaces can be described mathematically with the help of parameterisations.
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- Vector-Valued Functions of Two Variables
- Springer International Publishing
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- Chapter 16