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, p ...

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, mathematical structure, structure, space, Mathematica ...

and associate professor of

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

Drexel University Drexel University is a private university, private research university with its main campus in Philadelphia, Pennsylvania, United States. Drexel's undergraduate school was founded in 1891 by Anthony Joseph Drexel, Anthony J. Drexel, a financier ...

working on problems in moving surfaces in

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

(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 Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of f ...

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

physics Physics is the scientific study of matter, its Elementary particle, 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 whi ...

, and

engineering Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, s ...

Biography

Grinfeld received his

PhD A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

in Applied Mathematics from

MIT The Massachusetts Institute of Technology (MIT) is a private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of modern technology and sc ...

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, ...

. 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 matrix (mathemat ...

, Differential Equations, and

Tensor calculus In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other ...

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

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

on the instability of the 2S electron bubbles. 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, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in ...

and fluid films dynamics,

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

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