Matches in SemOpenAlex for { <https://semopenalex.org/work/W4361767082> ?p ?o ?g. }
Showing items 1 to 75 of
75
with 100 items per page.
- W4361767082 endingPage "29" @default.
- W4361767082 startingPage "5" @default.
- W4361767082 abstract "The role of mathematics in scientific practice is too readily relegated to that of formulating equations that model or describe what is being investigated, and then finding solutions to those equations. I survey the role of mathematics in: 1. Exact solutions of differential equations, especially conformal mapping; and 2. Simulations of solutions to differential equations via numerical methods and via agent-based models; and 3. The use of experimental models to solve equations (a) via physical analogies based on similarity of the form of the equations, such as Prandtl’s soap-film method, and (b) the method of physically similar systems. Two major themes emerge: First, the role of mathematics in science is not well described by deduction from axioms, although it generally involves deductive reasoning. Creative leaps, the integration of experimental or observational evidence, synthesis of ideas from different areas of mathematics, and insight regarding analogous forms are required to find solutions to equations. Second, methods that involve mappings or transformations are in use in disparate contexts, from the purely mathematical context of conformal mapping where it is mathematical objects that are mapped, to the use of concrete physical experimental models, where one concrete thing is shown to correspond to another." @default.
- W4361767082 created "2023-04-04" @default.
- W4361767082 creator A5063647563 @default.
- W4361767082 date "2023-01-01" @default.
- W4361767082 modified "2023-09-27" @default.
- W4361767082 title "How Mathematics Figures Differently in Exact Solutions, Simulations, and Physical Models" @default.
- W4361767082 cites W1438737554 @default.
- W4361767082 cites W1567751821 @default.
- W4361767082 cites W2021121177 @default.
- W4361767082 cites W2021786390 @default.
- W4361767082 cites W2492050474 @default.
- W4361767082 cites W2505413831 @default.
- W4361767082 cites W2604388780 @default.
- W4361767082 cites W2765878455 @default.
- W4361767082 cites W3100717110 @default.
- W4361767082 cites W4206728567 @default.
- W4361767082 cites W4230736257 @default.
- W4361767082 cites W4231039736 @default.
- W4361767082 cites W4245119057 @default.
- W4361767082 doi "https://doi.org/10.1007/978-3-031-25686-8_2" @default.
- W4361767082 hasPublicationYear "2023" @default.
- W4361767082 type Work @default.
- W4361767082 citedByCount "0" @default.
- W4361767082 crossrefType "book-chapter" @default.
- W4361767082 hasAuthorship W4361767082A5063647563 @default.
- W4361767082 hasConcept C103278499 @default.
- W4361767082 hasConcept C115961682 @default.
- W4361767082 hasConcept C136119220 @default.
- W4361767082 hasConcept C151730666 @default.
- W4361767082 hasConcept C154945302 @default.
- W4361767082 hasConcept C167729594 @default.
- W4361767082 hasConcept C199343813 @default.
- W4361767082 hasConcept C202444582 @default.
- W4361767082 hasConcept C2524010 @default.
- W4361767082 hasConcept C2777686260 @default.
- W4361767082 hasConcept C2779343474 @default.
- W4361767082 hasConcept C28826006 @default.
- W4361767082 hasConcept C33923547 @default.
- W4361767082 hasConcept C41008148 @default.
- W4361767082 hasConcept C71924100 @default.
- W4361767082 hasConcept C86803240 @default.
- W4361767082 hasConceptScore W4361767082C103278499 @default.
- W4361767082 hasConceptScore W4361767082C115961682 @default.
- W4361767082 hasConceptScore W4361767082C136119220 @default.
- W4361767082 hasConceptScore W4361767082C151730666 @default.
- W4361767082 hasConceptScore W4361767082C154945302 @default.
- W4361767082 hasConceptScore W4361767082C167729594 @default.
- W4361767082 hasConceptScore W4361767082C199343813 @default.
- W4361767082 hasConceptScore W4361767082C202444582 @default.
- W4361767082 hasConceptScore W4361767082C2524010 @default.
- W4361767082 hasConceptScore W4361767082C2777686260 @default.
- W4361767082 hasConceptScore W4361767082C2779343474 @default.
- W4361767082 hasConceptScore W4361767082C28826006 @default.
- W4361767082 hasConceptScore W4361767082C33923547 @default.
- W4361767082 hasConceptScore W4361767082C41008148 @default.
- W4361767082 hasConceptScore W4361767082C71924100 @default.
- W4361767082 hasConceptScore W4361767082C86803240 @default.
- W4361767082 hasLocation W43617670821 @default.
- W4361767082 hasOpenAccess W4361767082 @default.
- W4361767082 hasPrimaryLocation W43617670821 @default.
- W4361767082 hasRelatedWork W2016189534 @default.
- W4361767082 hasRelatedWork W2017533684 @default.
- W4361767082 hasRelatedWork W2063488590 @default.
- W4361767082 hasRelatedWork W2090649758 @default.
- W4361767082 hasRelatedWork W2115419199 @default.
- W4361767082 hasRelatedWork W2173133624 @default.
- W4361767082 hasRelatedWork W2328147739 @default.
- W4361767082 hasRelatedWork W4230623537 @default.
- W4361767082 hasRelatedWork W4252133255 @default.
- W4361767082 hasRelatedWork W2460807834 @default.
- W4361767082 isParatext "false" @default.
- W4361767082 isRetracted "false" @default.
- W4361767082 workType "book-chapter" @default.