{"title":"Infinitesimal Calculus","authors":"Vic Dannon","doi":"10.1002/9781119580164.ch2","DOIUrl":"https://doi.org/10.1002/9781119580164.ch2","url":null,"abstract":"Abstract The controversy surrounding the infinitesimals, obstructed the development of the Infinitesimal Calculus. Postulating infinitesimals, only revealed Logic’s inapplicability to Mathematical Analysis, where claims must be proved, and unproven claims are ignored. Recently we have shown that when the Real Line is represented as the infinite dimensional space of all the Cauchy sequences of rational numbers, the hyper-reals are spanned by the constant hyper-reals, a family of infinitesimal hyper-reals, and the associated family of infinite hyper-reals. The infinitesimal hyper-reals are smaller than any real number, yet bigger than zero. The reciprocals of the infinitesimal hyper-reals are the infinite hyper-reals. They are greater than any real number, yet strictly smaller than infinity.","PeriodicalId":263591,"journal":{"name":"Introductory Electrical Engineering with Math Explained in Accessible Language","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132056951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"RLC Circuits: Part 2","authors":"","doi":"10.1002/9781119580164.ch28","DOIUrl":"https://doi.org/10.1002/9781119580164.ch28","url":null,"abstract":"","PeriodicalId":263591,"journal":{"name":"Introductory Electrical Engineering with Math Explained in Accessible Language","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132128375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Appendix J: Simulation Tools","authors":"","doi":"10.1002/9781119580164.app10","DOIUrl":"https://doi.org/10.1002/9781119580164.app10","url":null,"abstract":"","PeriodicalId":263591,"journal":{"name":"Introductory Electrical Engineering with Math Explained in Accessible Language","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116168920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Appendix C: Root Mean Square (RMS) Value","authors":"","doi":"10.1002/9781119580164.app3","DOIUrl":"https://doi.org/10.1002/9781119580164.app3","url":null,"abstract":"","PeriodicalId":263591,"journal":{"name":"Introductory Electrical Engineering with Math Explained in Accessible Language","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128410324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
L. A B O R A T O R Y E L E C T R O N I C S I, E. R. F O R T N, Current Kirchhoff, Law
{"title":"Kirchhoff's Laws","authors":"L. A B O R A T O R Y E L E C T R O N I C S I, E. R. F O R T N, Current Kirchhoff, Law","doi":"10.1002/9781119580164.ch19","DOIUrl":"https://doi.org/10.1002/9781119580164.ch19","url":null,"abstract":"The sum of currents entering a junction is equal to the sum of currents leaving the junction. The sum of voltage increases around a closed loop of a circuit is equal to the sum of voltage drops around the loop. • Branch Method Label a current through each branch of the circuit. Set up a set of independent equations for the junctions (current law) and loops (voltage law) in the circuit. Label a current around each independent loop of the circuit. Set up an equation for each current loop (voltage law), counting all the currents in any given element.","PeriodicalId":263591,"journal":{"name":"Introductory Electrical Engineering with Math Explained in Accessible Language","volume":"992 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116230587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Instrumentation and Bench","authors":"","doi":"10.1002/9781119580164.ch31","DOIUrl":"https://doi.org/10.1002/9781119580164.ch31","url":null,"abstract":"","PeriodicalId":263591,"journal":{"name":"Introductory Electrical Engineering with Math Explained in Accessible Language","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122486763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Appendix A: International System of Units (SI)","authors":"","doi":"10.1002/9781119580164.app1","DOIUrl":"https://doi.org/10.1002/9781119580164.app1","url":null,"abstract":"","PeriodicalId":263591,"journal":{"name":"Introductory Electrical Engineering with Math Explained in Accessible Language","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129666906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Inductors","authors":"Ansys Simplorer","doi":"10.1002/9781119580164.ch10","DOIUrl":"https://doi.org/10.1002/9781119580164.ch10","url":null,"abstract":"Inductance is the property that determines a component’s capacity to store magnetic energy and directly affects system dynamics through its impedance, which determines how quickly changes in power flow can occur. The impedance of an inductor, or group of coupled inductors, can be calculated into a matrix, called the impedance matrix. The value of this matrix depends on the geometry, nonlinear magnetic materials and source frequency, which can make analytical solutions very difficult. The impedance matrix is used directly as the modeling tool when performing circuit simulations to predict the effect the inductor has on the rest of the power system.","PeriodicalId":263591,"journal":{"name":"Introductory Electrical Engineering with Math Explained in Accessible Language","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122261154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Electromagnetism","authors":"S. Viola Kusminskiy","doi":"10.1017/9781108592123.013","DOIUrl":"https://doi.org/10.1017/9781108592123.013","url":null,"abstract":"The association of electricity and magnetism is also shown by electromagnetic induction, in which a changing magnetic field sets up an electric field within a conductor and causes the charges to move in the conductor. See also: EDDY CURRENT ; ELECTRICITY ; ELECTROMAGNET ; ELECTROMAGNETIC INDUCTION ; FARADAY’S LAW OF INDUCTION ; HALL EFFECT ; INDUCTANCE ; LENZ’S LAW ; MAGNETISM ; MAXWELL’S EQUATIONS ; RELUCTANCE . Kenneth V. Manning","PeriodicalId":263591,"journal":{"name":"Introductory Electrical Engineering with Math Explained in Accessible Language","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125487545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Resistors","authors":"Adrian Waygood","doi":"10.1016/b978-075064416-7/50011-7","DOIUrl":"https://doi.org/10.1016/b978-075064416-7/50011-7","url":null,"abstract":"","PeriodicalId":263591,"journal":{"name":"Introductory Electrical Engineering with Math Explained in Accessible Language","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121822179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}