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College Algebra Syllabus and Course Structure – MATH 1513

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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

Graphs and Coordinates

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

Linear Equations

  • Solving Linear Equations with Fractions
    04:02
  • Introduction to Solving Linear Equtions
    07:48
  • Categorizing Linear Equations
    06:00

Complex Numbers

  • Dividing Complex Numbers
    04:22
  • Introduction to Complex Numbers
    03:31
  • Adding and Subtracting Complex Numbers
    03:18

Intro to Quadratic Equations

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

The Square Root Property

  • Imaginary Roots with the Square Root Property
    02:20
  • Solving Quadratic Equations by the Square Root Property
    06:12

Completing the Square

  • Solving Quadratic Equations by Completing the Square
    06:24

The Quadratic Formula

  • Solving Quadratic Equations Using The Quadratic Formula
    06:36
  • The Discriminant
    04:11

Rational Equations

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

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

Transformations

  • Stretches & Shrinks of Functions
    6:02
  • Shifts of Functions
    5:34
  • Domain & Range of Transformed Functions
    4:22

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

Circles

  • Circles in Standard Form
    5:18
  • Circles in General Form
    6:20
  • Circles in Standard Form Example 1
    3:40

Quadratic Functions

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

Understanding Polynomial Functions

  • Introduction to Polynomial Functions
    06:04
  • Maximum Turning Points of a Polynomial Function
    02:44
  • Finding Zeros & Their Multiplicity
    03:42

Graphing Polynomial Functions

  • Example 1
    09:43
  • Identifying Intervals of Unknown Behavior
    05:01
  • Graphing Polynomial Functions
    05:25

Dividing Polynomials

    Zeros of Polynomial Functions

      Introduction to Rational Functions

      • Intro to Rational Functions
        6:04

      Asymptotes

      • Introduction to Asymptotes
        6:24
      • Determining Horizontal Asymptotes
        4:48
      • Determining Removable Discontinuities (Holes)
        3:34

      Graphing Rational Functions

      • Graphing Rational Functions Using Transformations
        5:31
      • Example 1
        3:08
      • Example 1
        10:18

      Introduction to Exponential Functions

      • Exponential Functions
        6:13

      Graphing Exponential Functions

      • Transformations of Exponential Graphs Example 1
        4:12
      • Graphing Exponential Functions Example 1
        3:58
      • Transformations of Exponential Graphs
        6:16

      The Number e

      • The Number e
        4:47

      Introduction to Logarithms

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

      Graphing Logarithmic Functions

      • Graphing Logarithmic Functions
        4:30
      • Transformations of Logarithmic Graphs
        4:37
      • Graphs of Logarithmic Functions
        5:26

      Properties of Logarithms

      • Change of Base Property
        5:36
      • Product, Quotient, and Power Rules of Logs
        3:49
      • Expand & Condense Log Expressions
        4:22

      Solving Exponential and Logarithmic Equations

      • Solving Exponential Equations Using Logs
        5:47
      • Solving Exponential Equations Using Like Bases
        4:46
      • Solving Logarithmic Equations
        5:02

      Two Variable Systems of Linear Equations

      • Example 1
        3:09
      • Solving Systems of Equations - Elimination
        6:48
      • Example 2
        3:31

      Graphing Systems of Inequalities

      • Linear Inequalities
        7:02
      • Nonlinear Inequalities
        3:21
      • Example 2
        4:37

      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

      Determinants and Cramer's Rule

      • Determinants of 3×3 Matrices
        7:25
      • Cramer's Rule - 2 Equations with 2 Unknowns
        6:54
      • Determinants of 2×2 Matrices
        4:36

      Introduction to Conic Sections

      • Geometries from Conic Sections
        3:08

      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

      Hyperbolas NOT at the Origin

      • Graph Hyperbolas NOT at the Origin
        5:59

      Parabolas

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

      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