{"id":"https://openalex.org/W4231746686","doi":"https://doi.org/10.1137/siread000049000002000301000001","title":"Education","display_name":"Education","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W4231746686","doi":"https://doi.org/10.1137/siread000049000002000301000001"},"language":"en","primary_location":{"id":"doi:10.1137/siread000049000002000301000001","is_oa":false,"landing_page_url":"https://doi.org/10.1137/siread000049000002000301000001","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025367520","display_name":"Andrew J. Bernoff","orcid":"https://orcid.org/0000-0001-9443-6320"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andrew J. Bernoff","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5025367520"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.25280184,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.59175351,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"49","issue":"2","first_page":"301","last_page":"301"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12250","display_name":"Experimental and Theoretical Physics Studies","score":0.10419999808073044,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12250","display_name":"Experimental and Theoretical Physics Studies","score":0.10419999808073044,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6313121914863586},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5684314966201782},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5320440530776978},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.4927957355976105},{"id":"https://openalex.org/keywords/laplaces-equation","display_name":"Laplace's equation","score":0.4820083677768707},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.4741377532482147},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4430710971355438},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42982104420661926},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3983131945133209},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.35803648829460144},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32780152559280396}],"concepts":[{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6313121914863586},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5684314966201782},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5320440530776978},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.4927957355976105},{"id":"https://openalex.org/C70615421","wikidata":"https://www.wikidata.org/wiki/Q339444","display_name":"Laplace's equation","level":3,"score":0.4820083677768707},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.4741377532482147},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4430710971355438},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42982104420661926},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3983131945133209},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.35803648829460144},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32780152559280396},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/siread000049000002000301000001","is_oa":false,"landing_page_url":"https://doi.org/10.1137/siread000049000002000301000001","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.4399999976158142}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3015584525","https://openalex.org/W2999616507","https://openalex.org/W4254213601","https://openalex.org/W2488373638","https://openalex.org/W2041486430","https://openalex.org/W2100299603","https://openalex.org/W4287241277","https://openalex.org/W963546583","https://openalex.org/W2897990565","https://openalex.org/W2905205127"],"abstract_inverted_index":{"Our":[0,43],"knowledge":[1],"in":[2,32,72,117,139,271,326,344],"mathematics":[3],"often":[4,70],"expands":[5],"by":[6,59,126,170,211],"taking":[7],"familiar":[8],"problems":[9,26,88,341],"and":[10,56,94,124,145,175,319,348,374],"revisiting":[11],"them":[12],"with":[13,351,367],"a":[14,40,66,85,100,108,127,153,179,187,195,199,220,238,248,283,295,323,327,352,361,368],"new":[15,41],"twist.":[16],"In":[17],"this":[18,320],"issue":[19],"we":[20,299],"have":[21],"two":[22],"papers":[23],"that":[24,27,69,112,215,274,331,342],"examine":[25],"are":[28],"usually":[29],"first":[30,44],"encountered":[31],"an":[33,63,140,157,381],"introductory":[34,73,141],"PDE":[35,74],"course,":[36],"though":[37],"shown":[38],"from":[39,53],"perspective.":[42],"contribution,":[45],"\u201cFundamental":[46],"Solutions":[47],"for":[48,84,102,107,152,166,190,384],"Some":[49],"Partial":[50],"Differential":[51],"Operators":[52],"Fluid":[54],"Dynamics":[55],"Statistical":[57],"Physics,\u201d":[58],"Jorge":[60],"Aar\u00e3o,":[61],"offers":[62],"answer":[64,316],"to":[65,137,182,224,340,364,379],"wearisome":[67],"question":[68],"arises":[71],"classes,":[75],"namely,":[76],"can":[77,298],"one":[78],"find":[79],"only":[80],"the":[81,91,104,146,150,167,183,212,225,228,231,234,254,258,264,276,279,288,291,301,312],"fundamental":[82,105],"solution":[83,106],"few":[86],"special":[87],"such":[89],"as":[90],"heat":[92],"equation":[93,192],"Laplace\u2019s":[95,191],"equation?":[96],"The":[97,130,161,315],"author":[98],"describes":[99],"method":[101],"computing":[103],"set":[109,235,306],"of":[110,185,198,227,230,236,307,334,354,371],"PDEs":[111],"arise,":[113],"among":[114],"other":[115,305],"places,":[116],"fluid":[118],"mechanics,":[119],"where":[120],"they":[121],"describe":[122],"diffusion":[123],"advection":[125],"linear":[128,349,372],"flow.":[129],"methodology":[131],"described":[132],"here":[133],"should":[134],"be":[135,380],"accessible":[136,363],"students":[138],"course":[142],"on":[143,247,278],"PDEs,":[144,345],"examples":[147],"could":[148],"form":[149],"foundation":[151],"supplemental":[154],"lecture":[155],"or":[156],"independent":[158],"research":[159],"project.":[160],"second":[162],"paper,":[163],"\u201cDetermining":[164],"Sets":[165],"Discrete":[168],"Laplacian,\u201d":[169],"Aviad":[171],"Rubinstein,":[172,174],"Jacob":[173],"Gershon":[176],"Wolansky,":[177],"adds":[178],"nice":[180],"twist":[181],"idea":[184,321],"solving":[186],"discrete":[188,196,243,292],"approximation":[189],"which":[193,309],"yields":[194],"analogue":[197],"harmonic":[200,204,244],"function.":[201,289],"A":[202,242],"continuous":[203],"function":[205,232,245,277,302,313],"$u":[206,250],"(x,":[207],"y)$":[208],"is":[209,222,260,268,317,358],"determined":[210],"mean\u2010value":[213],"property;":[214],"is,":[216],"its":[217],"value":[218],"at":[219,303,360],"point":[221],"equal":[223],"average":[226,259],"values":[229],"over":[233,263],"points":[237,308],"fixed":[239],"distance":[240],"away.":[241],"defined":[246],"lattice,":[249],"(i,":[251],"j)$,":[252],"has":[253,322,375],"same":[255],"property,":[256],"except":[257],"now":[261],"taken":[262],"nearest":[265],"neighbors.":[266],"It":[267],"well":[269],"known":[270],"both":[272],"cases":[273],"specifying":[275],"boundary":[280],"of,":[281],"say,":[282],"square":[284],"domain":[285],"uniquely":[286],"specifies":[287],"However,":[290],"problem":[293,330],"allows":[294],"fascinating":[296],"generalization:":[297],"specify":[300],"some":[304],"still":[310],"determines":[311],"uniquely?":[314],"yes,":[318],"natural":[324],"application":[325],"phase":[328],"detection":[329],"comes":[332],"out":[333],"optics.":[335],"This":[336],"paper":[337],"nicely":[338],"ties":[339],"arise":[343],"numerical":[346],"methods,":[347],"algebra":[350,373],"soup\u00e7on":[353],"physical":[355],"applications,":[356],"yet":[357],"written":[359],"level":[362],"any":[365],"student":[366],"solid":[369],"understanding":[370],"enough":[376],"open":[377],"questions":[378],"ideal":[382],"springboard":[383],"undergraduate":[385],"research.":[386]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-05-12T00:00:00"}
