Multiple Integrals

The course discusses the integral of a function of two variables over a region in a plane and the integral of a function of three variables over a region in space. These integrals are multiple integrals. It focuses only on the double and triple integrals. It includes the discussion on Polar, Cylindrical, and Spherical Coordinates. The course discusses the application of integrals i.e. how multiple integrals can be used to calculate quantities that vary over two or three dimensions such as the total mass or the angular momentum of an object of varying density and volumes of solid with general curved boundaries.

10 topics

121 lectures

Educators

Course Curriculum

6 videos

The Dot Product

5 videos

The Cross Product

5 videos

Lines and Planes in Space

5 videos

Vector Functions

16 videos

Functions of Several Variables

11 videos

Partial Derivatives

10 videos

Multivariable Optimization

16 videos

Multiple Integrals

21 videos

Vector Calculus

26 videos

Multiple Integrals Lectures

Multiple Integrals

Multiple Integrals - Intro

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data. Integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. The area above the x-axis adds to the total.

Matt Just

Multiple Integrals

Double Integrals - Overview

In mathematics, a double integral is an integral where the integrand is a function of two variables, and the integral is taken over some region in the Euclidean plane.

Matt Just

Multiple Integrals

Double Integrals - Example 1

In mathematics, a double integral is an integral where the integrand is a function of two variables, and the integral is taken over some region in the Euclidean plane.

Matt Just

Multiple Integrals

Double Integrals - Example 2

In mathematics, a double integral is an integral where the integrand is a function of two variables, and the integral is taken over some region in the Euclidean plane.

Matt Just

Multiple Integrals

Double Integrals - Example 3

In mathematics, a double integral is an integral where the integrand is a function of two variables, and the integral is taken over some region in the Euclidean plane.

Matt Just

Multiple Integrals

Double Integrals - Example 4

In mathematics, a double integral is an integral where the integrand is a function of two variables, and the integral is taken over some region in the Euclidean plane.

Matt Just

Multiple Integrals

Triple Integrals - Overview

In mathematics, a triple integral is a generalization of an ordinary definite integral to functions of three variables. It is a three-dimensional generalization of the two-dimensional definite integral.

Matt Just

Multiple Integrals

Triple Integrals - Example 1

In mathematics, a triple integral is a generalization of an ordinary definite integral to functions of three variables. It is a three-dimensional generalization of the two-dimensional definite integral.

Matt Just

Multiple Integrals

Triple Integrals - Example 2

In mathematics, a triple integral is a generalization of an ordinary definite integral to functions of three variables. It is a three-dimensional generalization of the two-dimensional definite integral.

Matt Just

Multiple Integrals

Triple Integrals - Example 3

In mathematics, a triple integral is a generalization of an ordinary definite integral to functions of three variables. It is a three-dimensional generalization of the two-dimensional definite integral.

Matt Just

Multiple Integrals

Triple Integrals - Example 4

In mathematics, a triple integral is a generalization of an ordinary definite integral to functions of three variables. It is a three-dimensional generalization of the two-dimensional definite integral.

Matt Just

Multiple Integrals

Polar, Cylindrical, and Spherical Coordinates - Overview

In mathematics, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the "x"-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the basis of analytic geometry.

Matt Just

Multiple Integrals

Polar, Cylindrical, and Spherical Coordinates - Example 1

In mathematics, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the "x"-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the basis of analytic geometry.

Matt Just

Multiple Integrals

Polar, Cylindrical, and Spherical Coordinates - Example 2

In mathematics, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the "x"-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the basis of analytic geometry.

Matt Just

Multiple Integrals

Polar, Cylindrical, and Spherical Coordinates - Example 3

In mathematics, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the "x"-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the basis of analytic geometry.

Matt Just

Multiple Integrals

Polar, Cylindrical, and Spherical Coordinates - Example 4

In mathematics, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the "x"-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the basis of analytic geometry.

Matt Just

Multiple Integrals

Applications of Integration - Overview

In mathematics, multiple integration is a generalization of single integration to functions of several variables.

Matt Just

Multiple Integrals

Applications of Integration - Example 1

In mathematics, multiple integration is a generalization of single integration to functions of several variables.

Matt Just

Multiple Integrals

Applications of Integration - Example 2

In mathematics, multiple integration is a generalization of single integration to functions of several variables.

Matt Just

Multiple Integrals

Applications of Integration - Example 3

In mathematics, multiple integration is a generalization of single integration to functions of several variables.

Matt Just

Multiple Integrals

Applications of Integration - Example 4

In mathematics, multiple integration is a generalization of single integration to functions of several variables.

Matt Just