{"id":"https://openalex.org/W2083974706","doi":"https://doi.org/10.1109/te.2012.2227745","title":"Geometrical Approach to Vector Analysis in Electromagnetics Education","display_name":"Geometrical Approach to Vector Analysis in Electromagnetics Education","publication_year":2012,"publication_date":"2012-12-06","ids":{"openalex":"https://openalex.org/W2083974706","doi":"https://doi.org/10.1109/te.2012.2227745","mag":"2083974706"},"language":"en","primary_location":{"id":"doi:10.1109/te.2012.2227745","is_oa":false,"landing_page_url":"https://doi.org/10.1109/te.2012.2227745","pdf_url":null,"source":{"id":"https://openalex.org/S207741693","display_name":"IEEE Transactions on Education","issn_l":"0018-9359","issn":["0018-9359","1557-9638"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310322189","host_organization_name":"IEEE Education Society","host_organization_lineage":["https://openalex.org/P4310322189","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Education Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Education","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/A5027524682","display_name":"Branislav M. Notaro\u0161","orcid":"https://orcid.org/0000-0002-5755-961X"},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Branislav M. Notaros","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO, USA","[Department of Electrical and Computer Engineering,, Colorado State University, Fort Collins, CO, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO, USA","institution_ids":["https://openalex.org/I92446798"]},{"raw_affiliation_string":"[Department of Electrical and Computer Engineering,, Colorado State University, Fort Collins, CO, USA]","institution_ids":["https://openalex.org/I92446798"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5027524682"],"corresponding_institution_ids":["https://openalex.org/I92446798"],"apc_list":null,"apc_paid":null,"fwci":0.4945,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.74166209,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"56","issue":"3","first_page":"336","last_page":"345"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11283","display_name":"Experimental Learning in Engineering","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11283","display_name":"Experimental Learning in Engineering","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13682","display_name":"Engineering Education and Pedagogy","score":0.9556000232696533,"subfield":{"id":"https://openalex.org/subfields/2216","display_name":"Architecture"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/electromagnetics","display_name":"Electromagnetics","score":0.7661275863647461},{"id":"https://openalex.org/keywords/vector-calculus","display_name":"Vector calculus","score":0.5373014807701111},{"id":"https://openalex.org/keywords/computational-electromagnetics","display_name":"Computational electromagnetics","score":0.5237088799476624},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.522406816482544},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4583245515823364},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.45814934372901917},{"id":"https://openalex.org/keywords/electromagnetic-field","display_name":"Electromagnetic field","score":0.42461445927619934},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.41756927967071533},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.41457176208496094},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3816315829753876},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2522680163383484},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17665508389472961},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15434014797210693},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15242090821266174}],"concepts":[{"id":"https://openalex.org/C2909720056","wikidata":"https://www.wikidata.org/wiki/Q11406","display_name":"Electromagnetics","level":2,"score":0.7661275863647461},{"id":"https://openalex.org/C5408677","wikidata":"https://www.wikidata.org/wiki/Q200802","display_name":"Vector calculus","level":2,"score":0.5373014807701111},{"id":"https://openalex.org/C206844423","wikidata":"https://www.wikidata.org/wiki/Q5157313","display_name":"Computational electromagnetics","level":3,"score":0.5237088799476624},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.522406816482544},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4583245515823364},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.45814934372901917},{"id":"https://openalex.org/C28843909","wikidata":"https://www.wikidata.org/wiki/Q177625","display_name":"Electromagnetic field","level":2,"score":0.42461445927619934},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.41756927967071533},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.41457176208496094},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3816315829753876},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2522680163383484},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17665508389472961},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15434014797210693},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15242090821266174},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C61696701","wikidata":"https://www.wikidata.org/wiki/Q770766","display_name":"Engineering physics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/te.2012.2227745","is_oa":false,"landing_page_url":"https://doi.org/10.1109/te.2012.2227745","pdf_url":null,"source":{"id":"https://openalex.org/S207741693","display_name":"IEEE Transactions on Education","issn_l":"0018-9359","issn":["0018-9359","1557-9638"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310322189","host_organization_name":"IEEE Education Society","host_organization_lineage":["https://openalex.org/P4310322189","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Education Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Education","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5400000214576721,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W132479975","https://openalex.org/W565036307","https://openalex.org/W600103790","https://openalex.org/W1482123173","https://openalex.org/W1500697756","https://openalex.org/W1525984517","https://openalex.org/W1527190934","https://openalex.org/W1530384264","https://openalex.org/W1534361212","https://openalex.org/W1557628067","https://openalex.org/W2007256490","https://openalex.org/W2099065488","https://openalex.org/W2141673608","https://openalex.org/W2155461616","https://openalex.org/W2160191010","https://openalex.org/W2168039037","https://openalex.org/W2724356358","https://openalex.org/W3107508789","https://openalex.org/W3210211137","https://openalex.org/W4211015257","https://openalex.org/W4230457749","https://openalex.org/W4301018393","https://openalex.org/W6605464025"],"related_works":["https://openalex.org/W2136883852","https://openalex.org/W1604556474","https://openalex.org/W639500893","https://openalex.org/W1980866748","https://openalex.org/W1596145689","https://openalex.org/W4213211651","https://openalex.org/W4200038534","https://openalex.org/W2995254544","https://openalex.org/W4289713616","https://openalex.org/W2896301116"],"abstract_inverted_index":{"A":[0],"geometrical":[1,62,115,187],"approach":[2,170,188],"to":[3,13,52,60,68,73,76,110,129,138,165,171,206,218],"teaching":[4],"and":[5,9,38,56,72,92,104,117,133,144,184,196,198,210,215,221,231,237,245],"learning":[6],"vector":[7,50,101,172,213],"calculus":[8],"analysis":[10,51,173,214],"as":[11,158,199],"applied":[12],"electromagnetic":[14,53,135,219],"fields":[15],"is":[16,27,46,177,189,225],"proposed":[17],"for":[18],"junior-level":[19],"undergraduate":[20,24],"electromagnetics":[21,26],"education.":[22],"For":[23],"students,":[25],"typically":[28],"the":[29,34,39,44,47,61,64,70,82,90,97,106,131,134,166,186,240],"most":[30,40],"challenging":[31,41],"subject":[32,45],"in":[33,174,239],"Electrical":[35],"Engineering":[36],"curriculum,":[37],"component":[42],"of":[43,49,87,154,212,233],"application":[48,217],"field":[54],"theory":[55,220],"problem":[57,222],"solving.":[58,223],"According":[59],"approach,":[63],"students":[65,107],"are":[66,108],"taught":[67,109],"\u201cread\u201d":[69],"figure":[71],"\u201ctranslate\u201d":[74,130],"this":[75],"equations":[77],"at":[78,247],"all":[79],"times":[80],"throughout":[81],"computation":[83],"or":[84,146],"derivation,":[85],"instead":[86,153],"their":[88],"\u201ccrunching\u201d":[89],"formulas":[91,157],"numbers":[93],"without":[94],"even":[95],"visualizing":[96],"structure.":[98],"In":[99],"performing":[100],"manipulations,":[102],"integrals,":[103],"derivatives,":[105],"always":[111],"deal":[112,205],"with":[113],"real":[114],"entities":[116],"quantities":[118],"(arrows,":[119],"lengths,":[120],"angles,":[121],"points,":[122],"lines,":[123],"surfaces,":[124],"volumes,":[125],"etc.).":[126],"They":[127],"learn":[128],"geometry":[132],"physics":[136],"attached":[137],"it":[139],"into":[140],"mathematical":[141,151],"models":[142],"(equations":[143],"symbolic":[145],"numerical":[147],"values)":[148],"using":[149],"\u201cfirst":[150],"principles\u201d":[152],"just":[155],"\u201cblack-box\u201d":[156],"a":[159,203],"computer":[160],"would":[161],"do.":[162],"As":[163],"opposed":[164],"traditional":[167],"formal":[168],"algebraic":[169],"electromagnetics,":[175],"which":[176],"very":[178,182],"general":[179],"but":[180,191],"also":[181,192],"abstract":[183],"dry,":[185],"problem-dependent":[190],"much":[193],"more":[194],"intuitive":[195],"visual,":[197],"such":[200],"can":[201],"do":[202],"great":[204],"increase":[207],"students'":[208],"understanding":[209],"appreciation":[211],"its":[216],"This":[224],"confirmed":[226],"by":[227],"preliminary":[228],"class":[229],"testing":[230],"assessment":[232],"student":[234],"learning,":[235],"success,":[236],"satisfaction":[238],"courses":[241],"Electromagnetic":[242],"Fields":[243],"I":[244],"II":[246],"Colorado":[248],"State":[249],"University.":[250]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}