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Lagrangian Mechanics

David D. Nolte

in Introduction to Modern Dynamics: Chaos, Networks, Space, and Time

Published in print:
2019
Published Online:
November 2019
ISBN:
9780198844624
eISBN:
9780191880216
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198844624.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Dynamical systems follow trajectories for which the mechanical action integrated along the trajectory is an extremum. The action is defined as the time average of the difference between kinetic and ... More


Cellular Homology

Graham Ellis

in An Invitation to Computational Homotopy

Published in print:
2019
Published Online:
November 2019
ISBN:
9780198832973
eISBN:
9780191871375
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198832973.003.0002
Subject:
Mathematics, Computational Mathematics / Optimization, Geometry / Topology

This chapter introduces more basic concepts of algebraic topology and describes datatypes and algorithms for implementing them on a computer. The basic concepts include: chain complex, chain mapping, ... More


e: A very special number

Marcel Danesi

in Pythagoras' Legacy: Mathematics in Ten Great Ideas

Published in print:
2020
Published Online:
January 2020
ISBN:
9780198852247
eISBN:
9780191886959
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198852247.003.0006
Subject:
Mathematics, History of Mathematics, Educational Mathematics

The number e, which is equal to 2.71828…, might seem like something trivial—a play on numbers by mathematicians. Nothing could be further from the truth. It is defined as the limit of the expression ... More


The Consequences of Extensivity

Robert H. Swendsen

in An Introduction to Statistical Mechanics and Thermodynamics

Published in print:
2019
Published Online:
February 2020
ISBN:
9780198853237
eISBN:
9780191887703
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198853237.003.0013
Subject:
Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

While not all thermodynamic systems are extensive, those that are homogeneous satisfy the useful postulate of extensivity. In this chapter we return to the thermodynamic postulates and consider the ... More


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