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Comprehensive Study Notes for College Algebra: Numbers, Functions, Trigonometry, Induction, Sigma Notation, and Conic Sections

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Linear Inequalities

  • Interval Notation
    05:18
  • Linear Inequalities with Fractions & Variables on Both Sides
    03:42
  • Linear Inequalities
    06:07

Intro to Functions & Their Graphs

  • Finding the Domain of an Equation
    3:43
  • Relations & Functions Example 1
    1:30
  • Relations and Functions
    5:20

Common Functions

  • Graphs of Common Functions
    5:57

Function Operations

  • Adding & Subtracting Functions
    5:56
  • Adding & Subtracting Functions Example 1
    4:46
  • Multiplying & Dividing Functions
    7:24

Function Composition

  • Evaluating Composed Functions
    4:26
  • Decomposition of Functions Example 1
    1:46
  • Domain Restrictions of Composed Functions
    3:51

Introduction to Matrices

  • Performing Row Operations on Matrices
    8:38
  • Example 1
    13:06
  • Solving Systems of Equations - Matrices (Reduced Row-Echelon Form)
    5:58

Intro to Quadratic Equations

  • Introduction to Quadratic Equations
    05:35
  • Solving Quadratic Equations by Factoring
    06:08

Graphs and Coordinates

  • Graphs and Coordinates - Example
    02:16
  • Graphs & the Rectangular Coordinate System
    05:10

Quadratic Functions

  • Converting Standard Form to Vertex Form
    04:34
  • Vertex Form
    08:07
  • Example 2
    7:49

Algebraic Expressions

  • Evaluating Algebraic Expressions
    03:11
  • Introduction to Algebraic Expressions
    05:09
  • Introduction to College Algebra Channel
    1:51

Exponents

  • Simplifying Exponential Expressions
    6:39
  • Introduction to Exponent Rules
    7:39
  • Zero and Negative Rules
    6:37

Radical Expressions

  • Square Roots
    05:49
  • Nth Roots
    06:56

Simplifying Radical Expressions

  • Adding & Subtracting Like Radicals
    03:50
  • Adding & Subtracting Unlike Radicals by Simplifying
    5:48
  • Radical Expressions with Variables
    06:44

Rational Exponents

  • Rational Exponents
    04:06

Polynomials Intro

  • Standard Form of Polynomials
    05:16
  • Introduction to Polynomials
    05:13
  • Adding and Subtracting Polynomials
    03:34

Multiplying Polynomials

  • Special Products - Cube Formulas
    03:41
  • Special Products - Square Formulas
    04:14
  • FOIL
    03:07

Factoring Polynomials

  • Factor Using the AC Method When a Is 1
    4:16
  • Factor by Grouping
    04:36
  • Introduction to Factoring Polynomials
    07:30

Introduction to Rational Functions

  • Intro to Rational Functions
    6:04

Rational Equations

  • Introduction to Rational Equations
    05:56
  • Restrictions on Rational Equations
    05:21

Introduction to Matrices

  • Performing Row Operations on Matrices
    8:38
  • Example 1
    13:06
  • Solving Systems of Equations - Matrices (Reduced Row-Echelon Form)
    5:58

Sequences

  • Example 2
    4:19
  • Example 1
    5:52
  • Introduction to Sequences
    8:22

Arithmetic Sequences

  • Example 2
    7:00
  • Example 1
    2:35
  • Arithmetic Sequences - Recursive Formula
    6:40

Geometric Sequences

  • Geometric Sequences - General Formula
    4:45
  • Geometric Sequences - Recursive Formula
    4:18

Factorials

  • Factorials
    5:22

Combinatorics

  • Permutations vs. Combinations
    3:18
  • Fundamental Counting Principle
    4:04
  • Permutations of Non-Distinct Objects
    6:37

Probability

  • Probability of Non-Mutually Exclusive Events Example
    2:57
  • Probability of Multiple Independent Events
    5:54
  • Probability of Non-Mutually Exclusive Events
    5:14

Introduction to Logarithms

  • Evaluate Logarithms
    5:14
  • Logarithms Introduction
    7:30
  • The Natural Log
    2:51

Introduction to Conic Sections

  • Geometries from Conic Sections
    3:08

Parabolas

  • Parabolas as Conic Sections Example 1
    7:12
  • Horizontal Parabolas
    5:28
  • Horizontal Parabolas Example 1
    7:18

Ellipses: Standard Form

  • Graph Ellipses NOT at Origin
    4:50
  • Foci and Vertices of an Ellipse
    5:30
  • Graph Ellipses at Origin
    5:12

Hyperbolas at the Origin

  • Asymptotes of Hyperbolas
    5:50
  • Graphing Hyperbolas at the Origin Example 1
    3:58
  • Introduction to Hyperbolas
    6:15