“Càlcul diferencial en diverses variables” és un breu curs introductori al càlcul diferencial en diverses variables. A l’estudiar problemes bàsics de les Ciències apareixen funcions de diverses variables. Per exemple, la temperatura d’un punt de l’aire depèn de la posició (tres coordenades reals) i del temps (una quarta variable real). La velocitat d’un mòbil a l’espai és un vector amb tres coordenades que depèn de la posició i del temps. Si ja heu seguit un curs de càlcul diferencial en una variable el nostre curs us pot servir per a començar a entendre les dificultats inherents al món de les diverses variables. Si esteu seguint ja un curs presencial sobre el tema el nostre curs us pot servir com a reforç i com a complement.
Càlcul en diverses variables
Gain insight into a topic and learn the fundamentals.
Intermediate level
Some related experience required
9 hours to complete
3 weeks at 3 hours a week
Flexible schedule
Learn at your own pace
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Recently updated!
February 2025
Assessments
5 assignments
Taught in Catalan
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There are 6 modules in this course
En aquest curs introduirem els fets bàsics del càlcul en diverses variables, insistint en les idees que el governen, però també en la tècnica. Presentarem demostracions dels resultats bàsics i discutirem exemples concrets per tal d’assolir una comprensió profunda del tema. Deixarem exercicis per tal que l’alumne avaluï el grau de comprensió assolit.
What's included
1 video6 readings
Amb aquest mòdul introduirem l’espai euclidià n-dimensional i en discutirem fets bàsics: desigualtats de Schwarz i Minkowski i la topologia.
What's included
7 videos1 assignment
Aquest mòdul introduirem la noció de límit i de continuïtat. També la noció de conjunt compacte i discutirem la propietat de Bolzano-Weierstrass. Veurem que les funcions contínues a un compacte són fitades i que els valors extrems (màxim i mínim) s’assoleixen.
What's included
7 videos1 assignment
En aquest mòdul introduïm les nocions de derivada parcial, direccional i de funció diferenciable. Definim el vector gradient i en fem una interpretació geomètrica.
What's included
7 videos1 assignment
En aquest mòdul s’explica com trobar els extrems (màxim i mínim) locals d’una funció de diverses variables mitjançant el gradient i la matriu hessiana. La fórmula de Taylor d'ordre 2 és un instrument tècnic per connectar la Matriu hessiana amb els extrems.
What's included
4 videos1 assignment
En aquest mòdul introduïm el teorema de la funció implícita i l’utilitzem per justificar el mètode de Lagrange per la determinació dels extrems d’una funció subjecta a una condició.
What's included
8 videos1 assignment
Instructor
Offered by
Recommended if you're interested in Math and Logic
Tecnológico de Monterrey
Tecnológico de Monterrey
Universidad de los Andes
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