Vectors & Space
Level: 0 1 2 3 4 5 6 7
MSC Classification: msc# (mscname)

Prerequisites: Algebra

Getting Oriented

Rough Guides to Analysis
Calculus
Real Analysis
Complex Analysis

This guide will discuss vectors and mathematical objects in 3-dimensional space. Vectors provide a significant portion of the language of multivariable calculus, and must be understood before adequately broaching that subject.

In early mathematics courses, one usually sees functions of one variable only. For example, the function f(x)=x2 represents a function that takes in any number x and returns the number x*x. General functions, on the other hand, might have several input (independent) variables and several output (dependent) variables. For example, your position in space might be a function of time, and at least three numbers are required to specify the position exactly. The body-mass index is a function with two independent variables, weight and height, and a single dependent variable.

In order to study these kinds of functions, one needs to understand how they are typically represented mathematically. The purpose of this guide is to move beyond the Euclidean plane, and beyond representing points in space by pairs of values (x,y).

The Basics

3-Dimensional Space

Vectors

Vector Functions

Functions of Two Variables

Implicit Functions and Surfaces

Vector Fields

Going Further

  • functions with more than two/three inputs and outputs

The Road Ahead

multivariable calculus

References

  • Reference
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