Pavel Grinfeld (also known as Greenfield) is an

American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, pe ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and associate professor of

Applied Mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical s ...

Drexel University Drexel University is a private research university with its main campus in Philadelphia, Pennsylvania. Drexel's undergraduate school was founded in 1891 by Anthony J. Drexel, a financier and philanthropist. Founded as Drexel Institute of Art, S ...

working on problems in moving surfaces in

applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical s ...

(particularly

calculus of variations The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

, and

engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...

Biography

Grinfeld received his PhD in Applied Mathematics from

MIT The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the mo ...

in 20

followed by two years as a postdoctoral fellow at the MIT Department of Earth, Atmosphere and Planetary Sciences, conducting research in

geodynamics Geodynamics is a subfield of geophysics dealing with dynamics of the Earth. It applies physics, chemistry and mathematics to the understanding of how mantle convection leads to plate tectonics and geologic phenomena such as seafloor spreading, mo ...

. He joined the Department of Mathematics at Drexel University in 2005; currently teaching

Linear Algebra Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrices. ...

Differential Equations In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

, and

Tensor calculus In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime). Developed by Gregorio Ricci-Curbastro and his student Tullio Levi ...

. Grinfeld is the author of the dynamic fluid film equations. Grinfeld co-authored with Haruo Kojima of

Rutgers University Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's ...

on the instability of the 2S

electron bubble An electron bubble is the empty space created around a free electron in a cryogenic gas or liquid, such as neon or helium. They are typically very small, about 2 nm in diameter at atmospheric pressure. Electron bubbles in helium At room te ...

s. He is the author of a textbook on Tensor Calculus (201

as well as an e-workbook on Linear Algebra. He has recorded hundreds of video lectures; several dozen on Tensors (in a video course which may accompany his textbook) as well as over a hundred shorter videos on linear algebra. Many of these are available on YouTube as well as other sites.

Research interests

Hydrodynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and ...

and fluid films dynamics,

thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...

and phase transformations, minimal surfaces and

Other Activities

Grinfeld is the founder of Lemma, Inc. which has developed the online learning system also called Lemma (https://www.lem.ma)

Bibliography

* *

References

External links

Grinfeld's site at Drexel University
*
Grinfeld's Lemma site with videos, practice problems, and textbooks
* {{DEFAULTSORT:Grinfeld, Pavel 1974 births Living people 21st-century American mathematicians Massachusetts Institute of Technology School of Science alumni Drexel University faculty