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DIDATTICO","\u003Ch1 class=\"fw-semibold text-uppercase\">Analisi \u003Cspan class=\"text-color-primary-400\">Matematica\u003C/span>\u003C/h1>\n","\u003Cp class=\"font-size-body-1 text-color-grey-800\">Viaggio nell’analisi matematica, dalle funzioni alla derivata.\u003C/p>\n","\u003Ch2>Descrizione\u003C/h2>\n\u003Cp class=\"font-size-body-1\">In questo modulo affronteremo un viaggio che ci accompagnerà passo passo nel mondo dell’analisi matematica e, soprattutto, delle funzioni matematiche. Incominceremo capendo che cosa è una funzione da un punto di vista più generico possibile, per poi estendere il nostro ragionamento su funzioni di numeri reali, fondamentali per moltissime applicazione pratiche della Data Science e del Machine Learning. Partendo così dalle funzioni in una variabile reale, ne capiremo bene il significato da un punto di vista formale e grafico, attraverso l’utilizzo di un software open source chiamato GeoGebra, che impareremo ad utilizzare passo passo durante il corso di questo modulo, costruendo insieme tutto quello che vedremo. Approfondiremo poi le funzioni lineari a una variabile, capendo bene sia da un punto di vista matematico che grafico, che cosa sono, cosa rappresentano e come i singoli componenti di cui è composta ne influenzano il comportamento sperimentando proprio attraverso GeoGebra, per poi capire cosa sono le funzioni non lineari e come si differenziano da quelle lineari. Passeremo poi a capire cosa sono le funzioni composte e cosa, invece, le combinazioni di funzioni, arrivando così a studiare alcune delle principali funzioni di attivazione, ampiamente utilizzate nel contesto del Machine Learning e della Data Science. A questo punto avremmo tutto il necessario per avventurarci nello studio dei limiti, del rapporto incrementale e mettendo assieme i pezzi del puzzle studieremo con quanta più cura possibile il limite del rapporto incrementale che ci introdurrà così ad uno dei componenti chiave dell’analisi matematica, soprattutto quando abbiamo a che fare con il Machine Learning: la derivata. Studieremo così la derivata, studiandola da diverse angolazioni: sia tramite la sua definizione formale ricavandocela proprio dal limite del rapporto incrementale tramite le formule e con l’utilizzo di GeoGebra, sia da un punto di vista geometrico, sia infine capendo bene attraverso lo studio visivo delle funzioni, la relazione che sussiste tra la derivata e la funzione di partenza. Questo ci porterà a capire cosa sono i punti stazionari e come sono collegati al concetto di derivata. Passeremo poi a studiare le funzioni a 2 variabili, capendo come si differenziano con le funzioni a una variabile e vedendo come tutto quello che abbiamo visto a una variabile si estende, con gli opportuni aggiustamenti, anche a due variabili. Questo ci porterà quindi a studiare la derivata a due variabili e, di conseguenza, a parlare di gradiente, oggetto matematico al cuore di una delle più importanti applicazioni del Machine Learning. Infine, capiremo come tutto quello che abbiamo studiato fino ad ora si estende e si generalizza non solo a funzioni a due variabili, ma in generale anche a funzioni a N variabili e capiremo l’importanza di imparare a generalizzare.\u003C/p>\n",{"title":789,"list":790,"link":783},"DOMANDE FREQUENTI",[791,794,797,800,803,806],{"title":792,"text":793},"Quali competenze sono necessarie per seguire il modulo Analisi Matematica?","\u003Cp class=\"fw-regular font-size-body-1\">\u003Cspan class=\"text-color-grey-800\" data-sheets-root=\"1\" data-sheets-value=\"{"1":2,"2":"Per seguire questo modulo non sono necessarie competenze preliminari specifiche."}\" data-sheets-userformat=\"{"2":4480,"10":2,"11":4,"15":"Arial"}\">Per seguire questo modulo non sono necessarie competenze preliminari specifiche.\u003C/span>\u003C/p>\n",{"title":795,"text":796},"Quali sono i principali argomenti trattati nel modulo Analisi Matematica?","\u003Cp>\u003Cspan data-sheets-root=\"1\" data-sheets-value=\"{"1":2,"2":"Il modulo Analisi Matematica copre i seguenti argomenti principali: Introduzione, Geogebra, Funzioni ad una variabile, Immagine e Pre-Immagine, Funzioni su insiemi numerici, Biettività e funzione inversa, Recap su funzioni, Piano cartesiano e rappresentazione di un punto su GeoGebra, Insieme di punti su Geogebra, Prime funzioni su GeoGebra, Disuguaglianze su GeoGebra, Funzioni lineari a una variabile, Funzioni non lineari a una variabile, Traslare una funzione sul piano, Funzioni composte, Combinazioni di funzioni e discontinuità, Principali funzioni di attivazione, Limiti, Rapporto Incrementale, Derivata, Derivata come retta tangente al grafico, Relazione tra derivata e funzione, Punti Stazionari, Funzioni a 2 variabili, Spazio 3D, Visualizzazione di funzioni a due variabili, Derivate a due variabili, Calcolo e significato delle derivate a due variabili, Piano tangente, Gradiente, Funzioni a N variabili."}\" data-sheets-userformat=\"{"2":4480,"10":2,"11":4,"15":"Arial"}\">Il modulo Analisi Matematica copre i seguenti argomenti principali: Introduzione, Geogebra, Funzioni ad una variabile, Immagine e Pre-Immagine, Funzioni su insiemi numerici, Biettività e funzione inversa, Recap su funzioni, Piano cartesiano e rappresentazione di un punto su GeoGebra, Insieme di punti su Geogebra, Prime funzioni su GeoGebra, Disuguaglianze su GeoGebra, Funzioni lineari a una variabile, Funzioni non lineari a una variabile, Traslare una funzione sul piano, Funzioni composte, Combinazioni di funzioni e discontinuità, Principali funzioni di attivazione, Limiti, Rapporto Incrementale, Derivata, Derivata come retta tangente al grafico, Relazione tra derivata e funzione, Punti Stazionari, Funzioni a 2 variabili, Spazio 3D, Visualizzazione di funzioni a due variabili, Derivate a due variabili, Calcolo e significato delle derivate a due variabili, Piano tangente, Gradiente, Funzioni a N variabili.\u003C/span>\u003C/p>\n",{"title":798,"text":799},"Quali nozioni principali posso apprendere al termine del modulo Analisi Matematica?","\u003Cp class=\"fw-regular font-size-body-1\">\u003Cspan class=\"text-color-grey-800\" data-sheets-root=\"1\" data-sheets-value=\"{"1":2,"2":"Al termine del modulo Analisi Matematica sarai in grado di comprendere e applicare concetti avanzati di analisi matematica e funzioni matematiche, utilizzando strumenti come GeoGebra per visualizzare e sperimentare con funzioni lineari e non lineari, composte e combinazioni di funzioni, limiti, rapporti incrementali e derivate, estendendo i concetti a funzioni a due e più variabili."}\" data-sheets-userformat=\"{"2":4480,"10":2,"11":0,"15":"Arial"}\">Al termine del modulo Analisi Matematica sarai in grado di comprendere e applicare concetti avanzati di analisi matematica e funzioni matematiche, utilizzando strumenti come GeoGebra per visualizzare e sperimentare con funzioni lineari e non lineari, composte e combinazioni di funzioni, limiti, rapporti incrementali e derivate, estendendo i concetti a funzioni a due e più variabili.\u003C/span>\u003C/p>\n",{"title":801,"text":802},"Al termine del modulo sono previsti un esame finale e una certificazione?","\u003Cp class=\"fw-regular font-size-body-1\">\u003Cspan class=\"text-color-grey-800\" data-sheets-root=\"1\" data-sheets-value=\"{"1":2,"2":"Sì, al termine del modulo Analisi Matematica sono previsti un esame finale e una certificazione."}\" data-sheets-userformat=\"{"2":4480,"10":2,"11":4,"15":"Arial"}\">\u003Cspan data-sheets-root=\"1\" data-sheets-value=\"{"1":2,"2":"L'esame finale e la certificazione sono previsti per i corsi Data Masters, non per i singoli moduli."}\" data-sheets-userformat=\"{"2":4995,"3":{"1":0},"4":{"1":2,"2":16750848},"10":2,"11":4,"12":0,"15":"Arial"}\">L’esame finale e la certificazione sono previsti per i corsi Data Masters, non per i singoli moduli.\u003C/span>\u003C/span>\u003C/p>\n",{"title":804,"text":805},"Il materiale del modulo è scaricabile? Posso rivedere le lezioni?","\u003Cp class=\"fw-regular font-size-body-1\">\u003Cspan class=\"text-color-grey-800\">Tutti i materiali (slide, materiale per esercitazioni, ecc.) sono scaricabili, mentre tutte le lezioni possono essere riviste in qualsiasi momento.\u003C/span>\u003C/p>\n",{"title":807,"text":808},"In caso di dubbi e domande, è disponibile assistenza da parte dei docenti?","\u003Cp class=\"fw-regular font-size-body-1\">\u003Cspan class=\"text-color-grey-800\" data-sheets-root=\"1\" data-sheets-value=\"{"1":2,"2":"Certamente, durante il modulo Analisi Matematica è disponibile assistenza continua da parte dei nostri docenti per qualsiasi dubbio o domanda."}\" data-sheets-userformat=\"{"2":4480,"10":2,"11":4,"15":"Arial"}\">Certamente, durante il modulo Analisi Matematica è disponibile assistenza continua da parte dei nostri docenti per qualsiasi dubbio o domanda.\u003C/span>\u003C/p>\n",[810,813,817,820],{"icon":811,"caption":71,"text":812},"icon-level","Da Beginner ad Advanced",{"icon":814,"caption":815,"text":816},"icon-round-check","PREREQUISITI","Nessun Prerequisito",{"icon":818,"caption":70,"text":819},"icon-calendar","8 ore",{"icon":821,"caption":822,"text":823},"icon-lessons","LEZIONI","100% on demand",[825],{"title":745,"items":826},[827,830,832,834,836,838,840,842,844,846,848,850,852,854,856,858,860,862,864,866,868,870,872,874,876,878,880,882,884,886,888,890,892,894,896,898,900,902],{"title":828,"text":829},"Introduzione","\u003Cp>\u003Cspan class=\"text-color-grey-700\">Nessun dettaglio\u003C/span>\u003C/p>\n",{"title":831,"text":829},"Geogebra",{"title":833,"text":829},"Funzioni ad una variable",{"title":835,"text":829},"Immagine e Pre-Immagine",{"title":837,"text":829},"Funzioni su insiemi numerici",{"title":839,"text":829},"Biettivita e funzione inversa",{"title":841,"text":829},"Recap su funzioni",{"title":843,"text":829},"Piano cartesiano e rappresentazione di un punto su GeoGebra",{"title":845,"text":829},"Insieme di punti su Geogebra",{"title":847,"text":829},"Prime funzioni su GeoGebra",{"title":849,"text":829},"Disuguaglianze su GeoGebra",{"title":851,"text":829},"Funzioni lineari a una variabile",{"title":853,"text":829},"Funzioni non lineari a una variabile",{"title":855,"text":829},"Traslare una funzione sul piano",{"title":857,"text":829},"Funzioni composte",{"title":859,"text":829},"Combinazioni di funzioni e discontinuità",{"title":861,"text":829},"Principali funzioni di attivazione",{"title":863,"text":829},"Limiti - Parte 1",{"title":865,"text":829},"Limiti - Parte 2",{"title":867,"text":829},"Limiti - Parte 3",{"title":869,"text":829},"Rapporto Incrementale - Definizione",{"title":871,"text":829},"Rapporto Incrementale - Interpretazione del segno",{"title":873,"text":829},"Rapporto Incrementale - Interpretazione del valore assoluto",{"title":875,"text":829},"Derivata - Limite Rapporto Incrementale",{"title":877,"text":829},"Derivata - Introduzione",{"title":879,"text":829},"Derivata come retta tangente al grafico",{"title":881,"text":829},"Relazione tra derivata e funzione",{"title":883,"text":829},"Punti Stazionari",{"title":885,"text":829},"Funzioni a 2 variabili - Introduzione",{"title":887,"text":829},"Funzioni a 2 variabili - Spazio 3D - Parte 1",{"title":889,"text":829},"Funzioni a 2 variabili - Spazio 3D - Parte 2",{"title":891,"text":829},"Visualizzazione di funzioni a due variabili - costante, lineare e non lineare",{"title":893,"text":829},"Derivate a due variabili - Introduzione",{"title":895,"text":829},"Derivate a due variabili - 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