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Calculus III Syllabus and Topical Outline: Multivariable Calculus and Vector Calculus

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Introduction to Functions

  • Percorso guidato
    Relations and Functions
    5:20
  • Introduction to Calculus Channel
    1:36
  • Percorso guidato
    Finding the Domain and Range of a Graph
    5:10

Properties of Functions

  • Percorso guidato
    Properties of Functions
    06:21

Introduction to Limits

  • Cases Where Limits Do Not Exist Example 2
    03:33
  • Finding Limits Numerically and Graphically
    6:47
  • Cases Where Limits Do Not Exist
    03:07

Tangent Lines and Derivatives

  • Percorso guidato
    Slopes of Tangent Lines
    05:13
  • Percorso guidato
    Determine Continuity Algebraically Example 1
    05:10
  • Percorso guidato
    Equations of Tangent Lines
    05:14

Derivatives as Functions

  • Percorso guidato
    Derivatives
    05:44

Basic Rules of Differentiation

  • The Power Rule: Negative & Rational Exponents
    04:09
  • The Power Rule: Negative & Rational Exponents Example 1
    03:37
  • The Power Rule
    04:02

Related Rates

  • Percorso guidato
    Intro To Related Rates
    04:16
  • Percorso guidato
    Real World Application
    06:16
  • Percorso guidato
    Changing Geometries
    06:35

Motion Analysis

  • Percorso guidato
    Derivatives Applied To Velocity
    06:29
  • Percorso guidato
    Derivatives Applied To Acceleration Example 2
    06:51
  • Percorso guidato
    Derivatives Applied To Acceleration
    06:15

Intro to Extrema

  • Finding Extrema Graphically Example 1
    04:45
  • Finding Extrema Graphically Example 2
    02:46
  • Finding Extrema Graphically
    05:58

Finding Global Extrema

  • Critical Points Example 2
    03:52
  • Finding Global Extrema (Extreme Value Theorem) Example 4
    03:34
  • Finding Global Extrema (Extreme Value Theorem) Example 3
    04:19

The First Derivative Test

  • The First Derivative Test: Finding Local Extrema Example 3
    11:22
  • The First Derivative Test: Finding Local Extrema Example 2
    04:00
  • The First Derivative Test: Finding Local Extrema Example 4
    05:00

Concavity

  • Determining Concavity Given a Function Example 3
    02:33
  • Determining Concavity from the Graph of f' or f''
    03:56
  • Determining Concavity Given A Function Example 2
    6:08

The Second Derivative Test

  • The Second Derivative Test: Finding Local Extrema
    06:02
  • The Second Derivative Test: Finding Local Extrema Example 1
    05:34

Curve Sketching

  • Summary of Curve Sketching
    11:41
  • Summary of Curve Sketching Example 3
    06:22
  • Summary of Curve Sketching Example 1
    13:20

Partial Fractions

  • Percorso guidato
    Integration Using Partial Fractions
    08:01
  • Percorso guidato
    Partial Fraction Decomposition: Repeated Linear Factors Example 5
    12:27
  • Percorso guidato
    Partial Fraction Decomposition: Distinct Linear Factors with Shortcut
    07:24

Fundamental Theorem of Calculus

  • Percorso guidato
    Fundamental Theorem of Calculus Part 2
    05:22
  • Percorso guidato
    Fundamental Theorem of Calculus Part 1
    06:11
  • Percorso guidato
    Fundamental Theorem of Calculus Part 1 Example1
    03:25

Work

  • Work Done On A Spring (Hooke's Law) Example 1
    06:02
  • Percorso guidato
    Pumping Liquids Example 5
    11:50
  • Percorso guidato
    Introduction To Work
    06:22