Vector Functions

This course gives an overview of calculus with vector functions. It also covers the different rules of derivatives for vector functions. The next section introduces the topic of arc length and curvatures. It explains the method to determine the arc length and curvatures. The next section deals with the topic of motions of a particle along a curve. It introduces the concept of velocity and acceleration vectors. It also explains the meaning of the tangential component of acceleration and the normal component of acceleration. This section also covers the method to determine the velocity vectors, acceleration vectors, the tangential component of acceleration, and the normal component.

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

Vector Functions Lectures

Vector Functions

Vector Valued Functions - Intro

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x. The input of a function is called the argument and the output is called the value. The set of all permitted inputs is called the domain of the function. Similarly, the set of all permissible outputs is called the codomain. The most common symbols used to represent functions in mathematics are f and g. The set of all possible values of a function is called the image of the function, while the set of all functions from a set "A" to a set "B" is called the set of "B"-valued functions or the function space "B"["A"].

Matt Just

Vector Functions

Vector Valued Functions and Curves - Overview

In mathematics, vector calculus is an important part of differential geometry, together with differential topology and differential geometry. It is also a tool used in many parts of physics. It is a collection of techniques to describe and study the properties of vector fields. It is a broad and deep subject that involves many different mathematical techniques.

Matt Just

Vector Functions

Vector Valued Functions and Curves - Example 1

In mathematics, vector calculus is an important part of differential geometry, together with differential topology and differential geometry. It is also a tool used in many parts of physics. It is a collection of techniques to describe and study the properties of vector fields. It is a broad and deep subject that involves many different mathematical techniques.

Matt Just

Vector Functions

Vector Valued Functions and Curves - Example 2

In mathematics, vector calculus is an important part of differential geometry, together with differential topology and differential geometry. It is also a tool used in many parts of physics. It is a collection of techniques to describe and study the properties of vector fields. It is a broad and deep subject that involves many different mathematical techniques.

Matt Just

Vector Functions

Vector Valued Functions and Curves - Example 3

In mathematics, vector calculus is an important part of differential geometry, together with differential topology and differential geometry. It is also a tool used in many parts of physics. It is a collection of techniques to describe and study the properties of vector fields. It is a broad and deep subject that involves many different mathematical techniques.

Matt Just

Vector Functions

Vector Valued Functions and Curves - Example 4

In mathematics, vector calculus is an important part of differential geometry, together with differential topology and differential geometry. It is also a tool used in many parts of physics. It is a collection of techniques to describe and study the properties of vector fields. It is a broad and deep subject that involves many different mathematical techniques.

Matt Just

Vector Functions

Calculus of Vector Valued Functions - Overview

Calculus of Vector-Valued Functions is a branch of mathematics that deals with vector-valued functions of a single real variable, and their applications. It is the calculus of functions of a single variable, with vector valued arguments and results. It is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results.

Matt Just

Vector Functions

Calculus of Vector Valued Functions - Example 1

Calculus of Vector-Valued Functions is a branch of mathematics that deals with vector-valued functions of a single real variable, and their applications. It is the calculus of functions of a single variable, with vector valued arguments and results. It is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results.

Matt Just

Vector Functions

Calculus of Vector Valued Functions - Example 2

Calculus of Vector-Valued Functions is a branch of mathematics that deals with vector-valued functions of a single real variable, and their applications. It is the calculus of functions of a single variable, with vector valued arguments and results. It is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results.

Matt Just

Vector Functions

Calculus of Vector Valued Functions - Example 3

Calculus of Vector-Valued Functions is a branch of mathematics that deals with vector-valued functions of a single real variable, and their applications. It is the calculus of functions of a single variable, with vector valued arguments and results. It is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results.

Matt Just

Vector Functions

Calculus of Vector Valued Functions - Example 4

Calculus of Vector-Valued Functions is a branch of mathematics that deals with vector-valued functions of a single real variable, and their applications. It is the calculus of functions of a single variable, with vector valued arguments and results. It is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results. In particular, it is the study of vector functions of a single real variable, with vector valued arguments and results.

Matt Just

Vector Functions

Arc Length and Motion of a Particle - Overview

In mathematics, the arc length of a curve in a two-dimensional Euclidean space or in a Riemannian manifold is a measure of the size of the curve in the direction of its tangent vector. The concept of arc length can be generalized to higher dimensions and to more general manifolds.

Matt Just

Vector Functions

Arc Length and Motion of a Particle - Example 1

In mathematics, the arc length of a curve in a two-dimensional Euclidean space or in a Riemannian manifold is a measure of the size of the curve in the direction of its tangent vector. The concept of arc length can be generalized to higher dimensions and to more general manifolds.

Matt Just

Vector Functions

Arc Length and Motion of a Particle - Example 2

In mathematics, the arc length of a curve in a two-dimensional Euclidean space or in a Riemannian manifold is a measure of the size of the curve in the direction of its tangent vector. The concept of arc length can be generalized to higher dimensions and to more general manifolds.

Matt Just

Vector Functions

Arc Length and Motion of a Particle - Example 3

In mathematics, the arc length of a curve in a two-dimensional Euclidean space or in a Riemannian manifold is a measure of the size of the curve in the direction of its tangent vector. The concept of arc length can be generalized to higher dimensions and to more general manifolds.

Matt Just

Vector Functions

Arc Length and Motion of a Particle - Example 4

In mathematics, the arc length of a curve in a two-dimensional Euclidean space or in a Riemannian manifold is a measure of the size of the curve in the direction of its tangent vector. The concept of arc length can be generalized to higher dimensions and to more general manifolds.

Matt Just