Vector Fields

Celso Melchiades Doria ()
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Celso Melchiades Doria: Universidade Federal de Santa Catarina, Department of Mathematics, CFM

Chapter Chapter 4 in Differentiability in Banach Spaces, Differential Forms and Applications, 2021, pp 179-213 from Springer

Abstract: Abstract Vector fields arise naturally in physics where several variables are of a vectorial nature. We will look at examples in which a physical system is modeled by an ordinary differential equation (ODE). In Classical Mechanics, Newton’s 2nd law imposes the differential equation $$\vec {F}=m\frac{d\vec {v}}{dt}$$ F → = m d v → dt . An understanding of the analytical, algebraic and geometric properties of vector fields is the core of the study to understand the evolution of a system governed by an ODE.

Date: 2021
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DOI: 10.1007/978-3-030-77834-7_4

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