Abstract
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 parametrisations.
For the required basic notions of vector and matrix algebra we refer to Appendices A and B.
This is a preview of subscription content, log in via an institution to check access.
References
Further Reading
A. Quarteroni, R. Sacco, F. Saleri: Numerical Mathematics. Springer, New York 2000.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer-Verlag London Limited
About this chapter
Cite this chapter
Oberguggenberger, M., Ostermann, A. (2011). Vector-Valued Functions of Two Variables. In: Analysis for Computer Scientists. Undergraduate Topics in Computer Science. Springer, London. https://doi.org/10.1007/978-0-85729-446-3_16
Download citation
DOI: https://doi.org/10.1007/978-0-85729-446-3_16
Publisher Name: Springer, London
Print ISBN: 978-0-85729-445-6
Online ISBN: 978-0-85729-446-3
eBook Packages: Computer ScienceComputer Science (R0)