Ir al contenido principal

Multivariable Calculus 1: Vectors and Derivatives

We live in a multivariable world. Explore the derivative in higher dimensions and learn how to apply it to solve real world problems. Part 1 of 3.

Multivariable Calculus 1: Vectors and Derivatives

Hay una sesión disponible:

Una vez finalizada la sesión del curso, será archivado.
Comenzó el 14 jul
Termina el 13 oct
13 semanas estimadas
4–6 horas por semana
Al ritmo del instructor
Dictado por un instructor según un cronograma
Gratis
Cambio opcional de categoría disponible

Sobre este curso

Omitir Sobre este curso

Variables are all around us: temperature, altitude, location, profit, color, and countless others. Multivariable Calculus is the tool of choice to shed light on complex relationships between 2, 3, or hundreds of variables simultaneously.

  • How does one control a robot whose motion depends on several variables at once?
  • How does an oceanographer understand carbon absorption of the ocean?
  • How can one assess if a prediction model matches data optimally?
  • How can one design policy to affect the behavior of consumers in order to better protect the planet?

All of these questions involve understanding vectors and derivatives of multivariable functions.

In this course, we begin our exploration of functions of several variables. We will start with learning to visualize multivariable functions, then move to computing and interpreting their derivatives. ​You will discover how to use linear approximations in several variables to simplify complex questions and will start to think about the world through multivariable dependencies.

---

Please note: edX Inc. has recently entered into an agreement to transfer the edX platform to 2U, Inc., which will continue to run the platform thereafter. The sale will not affect your course enrollment, course fees or change your course experience for this offering. It is possible that the closing of the sale and the transfer of the edX platform may be effectuated sometime in the Fall while this course is running. Please be aware that there could be changes to the edX platform Privacy Policy or Terms of Service after the closing of the sale. However, 2U has committed to preserving robust privacy of individual data for all learners who use the platform. For more information see the edX Help Center.

De un vistazo

  • Institución: MITx
  • Tema: Matemáticas
  • Nivel: Intermediate
  • Prerrequisitos:

    Single Variable Calculus (basic or undergraduate)

    • 18.01.1x
    • 18.01.2x (recommended)
    • 18.01.3x (recommended)
  • Idioma: English
  • Transcripción de video: English

Lo que aprenderás

Omitir Lo que aprenderás
  • How to visualize functions of 2 and 3 variables using level curves and level surfaces.
  • How to compute partial derivatives, directional derivatives, and gradients.
  • How to optimize multivariable functions subject to constraint equations.
  • How to represent the linear approximation of a multivariable function using vectors and matrices.

Plan de estudios

Omitir Plan de estudios

Unit 1: Functions of two variables

  • Graphing functions and slicing
  • Level curves
  • Partial derivatives
  • Tangent planes
  • Linear approximation

Unit 2: Geometry of derivatives

  • Vectors
  • Dot products
  • Gradients
  • Vector fields
  • Directional derivatives

Unit 3: Optimization

  • Critical points
  • Second derivative test
  • Constrained optimization
  • Lagrange multipliers
  • Least squares approximation

Unit 4: Matrices

  • Systems of equations
  • Matrix algebra
  • Undetermined and overdetermined systems
  • Linear functions as matrix maps

Unit 5: Curves

  • Parametric curves in 2 and 3 dimensions
  • Chain rule
  • Review
  • Vectors and derivatives in three dimensions and higher

Acerca de los instructores

¿Quién puede hacer este curso?

Lamentablemente, las personas residentes en uno o más de los siguientes países o regiones no podrán registrarse para este curso: Irán, Cuba y la región de Crimea en Ucrania. Si bien edX consiguió licencias de la Oficina de Control de Activos Extranjeros de los EE. UU. (U.S. Office of Foreign Assets Control, OFAC) para ofrecer nuestros cursos a personas en estos países y regiones, las licencias que hemos recibido no son lo suficientemente amplias como para permitirnos dictar este curso en todas las ubicaciones. edX lamenta profundamente que las sanciones estadounidenses impidan que ofrezcamos todos nuestros cursos a cualquier persona, sin importar dónde viva.

¿Te interesa este curso para tu negocio o equipo?

Capacita a tus empleados en los temas más solicitados con edX para Negocios.