Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
Algebra II / E&I Algebra
Exponents & Polynomials Intermediate Algebra starts here!

Factoring Rational Expressions Rational Equations and Applications
Algebra III / Inter. Algebra
Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis

Course: Calculus III
Topic: Vectors and Geometry of Space
Subtopic: Vectors in 2D

Overview

A vector looks like a little ray, lies in two or three (or higher) dimensions, has length and direction, and can be used to represent things like velocity or force. You likely 2D vectors in a Precalculus math course. It may help to review particularly the list of objectives (to be sure that you know all that you should) listed in my College Trigonometry Lesson Notes TRIG #8.1, TRIG #8.2, TRIG #8.3, TRIG #8.4. Here in Calculus we will quickly re-introduce 2D vectors, vector terminology, vector operations, and some basic applications before expanding these concepts to 3D vectors, and ultimately moving to the Calculus of Vectors.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 13.1.1 Understand and use vector terminology
• 13.1.2 Perform vector operations including scalar multiplication and vector addition/subtraction algebraically, geometrically, and/or in terms of components
• 13.1.3 Algebraically determine if two vectors are equal or parallel
• 13.1.4 Compute a vector's components, magnitude, and direction
• 13.1.5 Find a unit vector in the direction of a given vector and determine if a given vector is a unit vector
• 13.1.6 Understand the properties of vectors from algebraic and geometric perspectives
• 13.1.7 Use vectors to analyze and solve STEM application problems involving velocities and forces

Terminology

Define: vector, magnitude, direction, equal vectors, zero vector, scalar, scalar multiple, position vectors, vector components, unit vector, standard basis vectors (a.k.a. coordinate unit vectors), equilibrium

Formulae to have in your notes: magnitude of a vector

Supplemental Resources (recommended)

Download: Briggs Calc for STEM's Multivariable Study Card If you print this it is only page 1 and half of page 2 that is used in this course. Most of the rest is used in Calc IV.

Supplemental Resources (optional)

Paul's OL Notes - Calc II: Vectors - The Basics and Vector Arithmetic

Patrick JMT Just Math video tutorials: PatrickJMT.com/#calculus
Scroll down the third column to videos starting with "An Introduction to Vectors, Part 1".

James Sousa's Math Is Power 4U video tutorials: MathIsPower4U - Calc II
Scroll down the third column to the "Vectors" category. All of the videos listed there are applicable to this unit.