Multivariable Calculus-This course covers vector and multi-variable calculus.

This course covers vector and multi-variable calculus.

Multivariable Calculus

This course covers vector and multi-variable calculus.

A brief summary

This course covers vector and multi-variable calculus. Topics include vectors and matrices, parametric curves, partial derivatives, double and triple integrals, and vector calculus in 2- and 3-space. 

Many things depend on more than one independent variable. Here are just a few:

  1. In thermodynamics pressure depends on volume and temperature.
  2. In electricity and magnetism, the magnetic and electric fields are functions of the three space variables (x,y,z) and one time variable t.
  3. In economics, functions can depend on a large number of independent variables, e.g., a manufacturer's cost might depend on the prices of 27 different commodities.
  4. In modeling fluid or heat flow the velocity field depends on position and time.

Instructor:

MIT

What you will learn

This course, designed for independent study, has been organized to follow the sequence of topics . The content is organized into four major units:

  1. Vectors and Matrices
  2. Partial Derivatives
  3. Double Integrals and Line Integrals in the Plane
  4. Triple Integrals and Surface Integrals in 3-Space

Course Fee: Free

Certification By: Millionlights

Vectors and Matrices

Vectors and Matrices, Vectors, Determinants and Planes, Matrices and Systems of Equations, Parametric Equations for Curves

Partial Derivatives

Partial Derivatives, Functions of Two Variables, Tangent Approximation and Opt, Chain Rule, Gradient and Directional Derivatives, Lagrange Multipliers and Constrained Differentials

Double Integrals and Line Integrals in the Plane

Double Integrals and Line Integrals in the Plane, Double Integrals, Vector Fields and Line Integrals, Green's Theorem

Triple Integrals and Surface Integrals in 3-Space

Triple Integrals and Surface Integrals in 3-Space, Triple Integrals, Flux and the Divergence Theorem, Line Integrals and Stokes' Theorem

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