Author:
Ohio Open Ed Collaborative
Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Cac077, Vector-Valued Functions
Language:
English
Media Formats:
eBook, Interactive

Calculus and vector-valued functions module

Overview

With one input, and vector outputs, we work component-wise.

A question I’ve often asked myself is: “How do you know when you are doing a calculus problem?” The answer, I think, is that you are doing a calculus problem when you are computing: a limit, a derivative, or an integral. Now we are going to do calculus with vector-valued functions. To build a theory of calculus for vector-valued functions, we simply treat each component of a vector-valued function as a regular, single-variable function. Since we are currently thinking about vector-valued functions that only have a single input, we can work component-wise. Let’s see this in action.

Calculus and vector-valued functions

Ximera Module

With one input, and vector outputs, we work component-wise.