Multivariable Optimization

In this course, the 3-dimensional space and functions of several variables are introduced. The course discusses the theory of differentiation for functions of several variables, and discusses applications to optimization and finding local extreme points. The course includes the brief discussion of the Gradient Vector and Tangent Planes, Lagrange Multipliers.

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

Multivariable Optimization Lectures

Multivariable Optimization

Multivariable Optimization - Intro

In mathematics, optimization is the process of finding the best element of a set of choices. The best element is often defined as the element that has the largest value of some property. The set of choices is usually referred to as the domain of the optimization problem. The most general problem is to find the element which maximizes a given function. The set of choices is called the domain of the function.

Matt Just

Multivariable Optimization

The Gradient Vector and Tangent Planes - Overview

In mathematics, the gradient of a function is a vector field that describes the direction and magnitude of the greatest rate of change of the function. The gradient of a function of two or more variables is a vector field in the Cartesian plane whose components are the partial derivatives of the function of multiple variables with respect to each of the variables. The gradient is often denoted by a small letter, such as "d" (or "?") for a scalar function, partial derivative, or gradient vector, or "D" for a matrix of partial derivatives, or tensor gradient.

Matt Just

Multivariable Optimization

The Gradient Vector and Tangent Planes - Example 1

In mathematics, the gradient of a function is a vector field that describes the direction and magnitude of the greatest rate of change of the function. The gradient of a function of two or more variables is a vector field in the Cartesian plane whose components are the partial derivatives of the function of multiple variables with respect to each of the variables. The gradient is often denoted by a small letter, such as "d" (or "?") for a scalar function, partial derivative, or gradient vector, or "D" for a matrix of partial derivatives, or tensor gradient.

Matt Just

Multivariable Optimization

The Gradient Vector and Tangent Planes - Example 2

In mathematics, the gradient of a function is a vector field that describes the direction and magnitude of the greatest rate of change of the function. The gradient of a function of two or more variables is a vector field in the Cartesian plane whose components are the partial derivatives of the function of multiple variables with respect to each of the variables. The gradient is often denoted by a small letter, such as "d" (or "?") for a scalar function, partial derivative, or gradient vector, or "D" for a matrix of partial derivatives, or tensor gradient.

Matt Just

Multivariable Optimization

The Gradient Vector and Tangent Planes - Example 3

In mathematics, the gradient of a function is a vector field that describes the direction and magnitude of the greatest rate of change of the function. The gradient of a function of two or more variables is a vector field in the Cartesian plane whose components are the partial derivatives of the function of multiple variables with respect to each of the variables. The gradient is often denoted by a small letter, such as "d" (or "?") for a scalar function, partial derivative, or gradient vector, or "D" for a matrix of partial derivatives, or tensor gradient.

Matt Just

Multivariable Optimization

The Gradient Vector and Tangent Planes - Example 4

In mathematics, the gradient of a function is a vector field that describes the direction and magnitude of the greatest rate of change of the function. The gradient of a function of two or more variables is a vector field in the Cartesian plane whose components are the partial derivatives of the function of multiple variables with respect to each of the variables. The gradient is often denoted by a small letter, such as "d" (or "?") for a scalar function, partial derivative, or gradient vector, or "D" for a matrix of partial derivatives, or tensor gradient.

Matt Just

Multivariable Optimization

Extrema of Functions - Overview

In mathematics, a local maximum of a function (or point of inflection) is a value of the function in a neighborhood of which the function has a local maximum value (or local minimum value). Local extrema of functions of several variables are also called critical points.

Matt Just

Multivariable Optimization

Extrema of Functions - Example 1

In mathematics, a local maximum of a function (or point of inflection) is a value of the function in a neighborhood of which the function has a local maximum value (or local minimum value). Local extrema of functions of several variables are also called critical points.

Matt Just

Multivariable Optimization

Extrema of Functions - Example 2

In mathematics, a local maximum of a function (or point of inflection) is a value of the function in a neighborhood of which the function has a local maximum value (or local minimum value). Local extrema of functions of several variables are also called critical points.

Matt Just

Multivariable Optimization

Extrema of Functions - Example 3

In mathematics, a local maximum of a function (or point of inflection) is a value of the function in a neighborhood of which the function has a local maximum value (or local minimum value). Local extrema of functions of several variables are also called critical points.

Matt Just

Multivariable Optimization

Extrema of Functions - Example 4

In mathematics, a local maximum of a function (or point of inflection) is a value of the function in a neighborhood of which the function has a local maximum value (or local minimum value). Local extrema of functions of several variables are also called critical points.

Matt Just

Multivariable Optimization

Lagrange Multipliers - Overview

In mathematics, Lagrange multipliers are a generalization of the idea of a derivative to functions of several variables. They are used in the calculus of variations, optimization, and control theory. The Lagrangian is defined as the difference between the kinetic and potential energy of the system. The Lagrangian is a function of the generalized coordinates and the generalized velocities. The Lagrangian is a function of the position, velocity, and acceleration of a system. The Lagrangian is the function of the generalized coordinates and the generalized velocities. The Lagrangian is the function of the generalized coordinates and the generalized velocities.

Matt Just

Multivariable Optimization

Lagrange Multipliers - Example 1

In mathematics, Lagrange multipliers are a generalization of the idea of a derivative to functions of several variables. They are used in the calculus of variations, optimization, and control theory. The Lagrangian is defined as the difference between the kinetic and potential energy of the system. The Lagrangian is a function of the generalized coordinates and the generalized velocities. The Lagrangian is a function of the position, velocity, and acceleration of a system. The Lagrangian is the function of the generalized coordinates and the generalized velocities. The Lagrangian is the function of the generalized coordinates and the generalized velocities.

Matt Just

Multivariable Optimization

Lagrange Multipliers - Example 2

In mathematics, Lagrange multipliers are a generalization of the idea of a derivative to functions of several variables. They are used in the calculus of variations, optimization, and control theory. The Lagrangian is defined as the difference between the kinetic and potential energy of the system. The Lagrangian is a function of the generalized coordinates and the generalized velocities. The Lagrangian is a function of the position, velocity, and acceleration of a system. The Lagrangian is the function of the generalized coordinates and the generalized velocities. The Lagrangian is the function of the generalized coordinates and the generalized velocities.

Matt Just

Multivariable Optimization

Lagrange Multipliers - Example 3

In mathematics, Lagrange multipliers are a generalization of the idea of a derivative to functions of several variables. They are used in the calculus of variations, optimization, and control theory. The Lagrangian is defined as the difference between the kinetic and potential energy of the system. The Lagrangian is a function of the generalized coordinates and the generalized velocities. The Lagrangian is a function of the position, velocity, and acceleration of a system. The Lagrangian is the function of the generalized coordinates and the generalized velocities. The Lagrangian is the function of the generalized coordinates and the generalized velocities.

Matt Just

Multivariable Optimization

Lagrange Multipliers - Example 4

In mathematics, Lagrange multipliers are a generalization of the idea of a derivative to functions of several variables. They are used in the calculus of variations, optimization, and control theory. The Lagrangian is defined as the difference between the kinetic and potential energy of the system. The Lagrangian is a function of the generalized coordinates and the generalized velocities. The Lagrangian is a function of the position, velocity, and acceleration of a system. The Lagrangian is the function of the generalized coordinates and the generalized velocities. The Lagrangian is the function of the generalized coordinates and the generalized velocities.

Matt Just