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Comprehensive Study Notes: College Algebra and Trigonometry (MATH1034A)

주석실무비디오 수업

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Graphs and Coordinates

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

Intro to Functions & Their Graphs

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

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

Linear Equations

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

Polynomials Intro

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

Factoring Polynomials

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

Two-Variable Equations

  • Graphing Equations of Two Variables by Plotting Points
    04:29
  • Graphing Intercepts
    04:08
  • Equations with Two Variables
    05:28

Quadratic Functions

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

Intro to Quadratic Equations

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

Choosing a Method to Solve Quadratics

  • Choosing a Method to Solve Quadratics
    04:03

The Quadratic Formula

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

Complex Numbers

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

The Imaginary Unit

  • Square Roots of Negative Numbers
    05:02

Powers of i

  • Higher Powers of i
    05:10
  • Powers of i
    04:10

Radical Expressions

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

Rational Equations

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

Rationalize Denominator

  • Rationalizing Denominators Using Conjugates
    03:42
  • Rationalizing Denominators
    02:58

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 Conic Sections

  • Geometries from Conic Sections
    3:08

Circles

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

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

Hyperbolas NOT at the Origin

  • Graph Hyperbolas NOT at the Origin
    5:59