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Calculus I: Core Topics and Learning Objectives

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Introduction to Functions

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

Piecewise Functions

  • Guided course
    Piecewise Functions Example 1
    02:59
  • Guided course
    Piecewise Functions
    05:36

Properties of Functions

  • Guided course
    Properties of Functions
    06:21

Common Functions

  • Properties of Parabolas
    7:42
  • Graphing Logarithmic Functions Example 1
    4:30
  • Logarithms Introduction
    7:30

Transformations

  • Guided course
    Intro to Transformations
    5:25

Combining Functions

  • Guided course
    Evaluating Composed Functions
    4:26
  • Guided course
    Adding & Subtracting Functions
    5:56
  • Guided course
    Adding & Subtracting Functions Example 1
    4:46

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

Finding Limits Algebraically

  • Limits of Rational Functions with Radicals
    06:13
  • Limits of Rational Functions: Denominator = 0 Example 1
    03:17
  • Limits of Rational Functions with Radicals Example 3
    02:54

Continuity

  • Intro to Continuity
    05:34
  • Intro to Continuity Example 2
    00:57
  • Determine Continuity Algebraically
    05:25

Tangent Lines and Derivatives

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

Basic Graphing of the Derivative

  • Guided course
    Graphing The Derivative - Special Cases
    04:24
  • Guided course
    Graphing The Derivative
    06:15
  • Guided course
    Graphing The Derivative Example 1
    03:29

Differentiability

  • Determining Differentiability Graphically
    05:02
  • Determining Differentiability Without A Graph
    05:20

Motion Analysis

  • Guided course
    Derivatives Applied To Velocity
    06:29
  • Guided course
    Derivatives Applied To Acceleration Example 2
    06:51
  • Guided course
    Derivatives Applied To Acceleration
    06:15

Derivatives as Functions

  • Guided course
    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

Higher Order Derivatives

  • Higher Order Derivatives
    02:42
  • Higher Order Derivatives Example 1
    02:02
  • Higher Order Derivatives Example 2
    02:23

Product and Quotient Rules

  • The Product Rule Example 1
    04:21
  • The Product Rule
    05:18
  • The Quotient Rule
    06:43

Derivatives of Trig Functions

  • Derivatives of Sine & Cosine
    03:53
  • Derivatives of Other Trig Functions Example 1
    01:32
  • Higher Order Derivatives of Sine & Cosine
    03:51

The Chain Rule

  • Intro to the Chain Rule Example 2
    07:39
  • Intro to the Chain Rule Example 3
    03:52
  • Intro to the Chain Rule Example 1
    07:01

Implicit Differentiation

  • Guided course
    Finding The Implicit Derivative
    05:14
  • Guided course
    Finding The Implicit Derivative Example 1
    09:16

Derivatives of Exponential & Logarithmic Functions

  • Derivatives of General Logarithmic Functions
    06:32
  • Derivative of the Natural Logarithmic Function
    05:18
  • Derivative of the Natural Exponential Function (e^x) Example 3
    02:38

Logarithmic Differentiation

  • Logarithmic Differentiation Example 1
    02:27
  • Logarithmic Differentiation
    06:30

Derivatives of Inverse Trigonometric Functions

  • Derivatives of Other Inverse Trigonometric Functions
    06:35
  • Derivatives of Inverse Sine & Inverse Cosine Example 1
    03:36
  • Derivatives of Inverse Sine & Inverse Cosine
    07:26

Related Rates

  • Guided course
    Intro To Related Rates
    04:16
  • Guided course
    Real World Application
    06:16
  • Guided course
    Changing Geometries
    06:35

Linearization

  • Guided course
    Linearization
    07:17

Differentials

  • Guided course
    Finding Differentials
    05:53
  • Guided course
    Determining Error and Relative Error
    04:57
  • Guided course
    Determining Error and Relative Error Example 1
    04:46

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

Applied Optimization

  • Intro to Applied Optimization: Maximizing Area
    10:13
  • Example 5: Packaging Design
    08:29
  • Example 4: Norman Window
    13:49

Antiderivatives

  • Guided course
    Antiderivatives
    05:50
  • Guided course
    Finding a Particular Antiderivative
    05:13

Indefinite Integrals

  • Guided course
    Additional Rules for Indefinite Integrals
    05:56
  • Guided course
    Power Rule for Indefinite Integrals
    04:04
  • Guided course
    Introduction to Indefinite Integrals
    05:04

Estimating Area with Finite Sums

  • Guided course
    Estimating the Area Under a Curve with Right Endpoints & Midpoint
    05:59
  • Guided course
    Estimating the Area Under a Curve with Right Endpoints & Midpoint Example 1
    09:17
  • Guided course
    Estimating the Area Under a Curve Using Left Endpoints
    07:59

Riemann Sums

  • Guided course
    Sigma Notation
    04:22
  • Guided course
    Introduction to Riemann Sums
    06:11
  • Guided course
    Sigma Notation Example 1
    03:05

Introduction to Definite Integrals

  • Guided course
    Basic Rules for Definite Integrals
    06:07
  • Guided course
    Definition of the Definite Integral
    05:43

Fundamental Theorem of Calculus

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

Substitution

  • Indefinite Integrals Example 1
    04:40
  • Substitution With an Extra Variable
    04:27
  • Definite Integrals
    06:36

Integrals of Exponential Functions

  • Integrals of General Exponential Functions
    05:11
  • Integrals of General Exponential Functions Example 1
    03:57
  • Integrals of Natural Exponential Functions (e^x) Example 3
    05:36

Integrals Involving Logarithmic Functions

  • Integrals Resulting in Natural Logs Example 2
    01:53
  • Integrals Involving Natural Logs: Substitution Example 3
    01:54
  • Integrals Resulting in Natural Logs
    03:48

Integrals Involving Inverse Trigonometric Functions

  • Completing the Square to Rewrite the Integrand Example 6
    03:19
  • Integrals Resulting in Inverse Trig Functions Example 1
    01:55
  • Integrals Resulting in Inverse Trig Functions: Substitution Example 5
    03:18

Area Between Curves

  • Finding Area Between Curves on a Given Interval
    05:23
  • Finding Area When Bounds Are Not Given
    05:06
  • Finding Area Between Curves that Cross on the Interval Example 2
    06:21

Work

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

Average Value of a Function

  • Guided course
    Average Value of a Function Example 1
    04:25
  • Guided course
    Average Value of a Function
    06:37

Introduction to Volume & Disk Method

  • Finding Volume Using Disks Example 3
    04:53
  • Disk Method Using y-Axis Example 5
    02:27
  • Introduction to Cross Sections
    05:38

Integrals of Trig Functions

  • Guided course
    Integrals Resulting in Basic Trig Functions
    05:28
  • Guided course
    Integrals Resulting in Basic Trig Functions Example 1
    04:22

Integration by Parts

  • Guided course
    Integration by Parts for Definite Integrals Example 7
    08:12
  • Guided course
    Integration by Parts for Definite Integrals
    06:18
  • Guided course
    Repeated Integration by Parts Example 3
    08:03

Partial Fractions

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

Improper Integrals

  • Guided course
    Improper Integrals: Infinite Intervals Example 2
    04:06
  • Guided course
    Improper Integrals: Infinite Intervals Example 1
    05:43
  • Guided course
    Improper Integrals: Infinite Intervals
    11:11

Basics of Differential Equations

  • Verifying Solutions of Differential Equations Example 1
    03:17
  • Solutions to Basic Differential Equations Example 7
    02:50
  • Verifying Solutions of Differential Equations
    05:09

Slope Fields

  • Understanding Slope Fields Example 2
    04:09
  • Understanding Slope Fields
    05:45
  • Understanding Slope Fields Example 1
    01:56

Euler's Method

  • Euler's Method
    07:33
  • Euler's Method Example 1
    08:09

Separable Differential Equations

  • Newton's Law of Cooling
    10:44
  • Separation of Variables Example 1
    05:28
  • Solving Separable Differential Equations Example 2
    04:55

Parametric Equations

  • Parameterizing Equations
    08:02
  • Eliminate Parameter: Equations with Trig
    04:11
  • Eliminate Parameter: Equations with Trig Example 3
    04:39

Calculus with Parametric Curves

  • Guided course
    Differentiation of Parametric Curves Example 2
    06:38
  • Guided course
    Higher Order Derivatives of Parametric Curves
    06:40
  • Guided course
    Arc Length of Parametric Curves
    06:29

Polar Coordinates

  • Convert Points from Polar to Rectangular
    06:17
  • Convert Points from Rectangular to Polar Example 1
    2:21
  • Convert Equations from Polar to Rectangular Example 2
    3:03

Calculus in Polar Coordinates

  • Guided course
    Area of Polar Regions Example 2
    12:18
  • Guided course
    Slope of Polar Curves
    09:04
  • Guided course
    Slope of Polar Curves Example 1
    05:58

Conic Sections

  • Guided course
    Horizontal Parabolas
    5:28
  • Guided course
    Foci and Vertices of an Ellipse
    5:30
  • Guided course
    Graphing Hyperbolas at the Origin Example 1
    3:58

Sequences

  • Recursive Formulas
    5:59
  • Arithmetic Sequences - General Formula Example 2
    7:00
  • Geometric Sequences - Recursive Formula
    04:18

Review of Factorials

  • Factorials
    5:22

Series

  • Guided course
    Intro to Series: Partial Sums
    06:45
  • Guided course
    Intro to Series: Partial Sums Example 1
    04:33
  • Guided course
    Geometric Series
    06:00

Convergence Tests

  • Guided course
    Ratio Test
    05:35
  • Guided course
    Direct Comparison Test
    09:25
  • Guided course
    Ratio Test Example 1
    10:07

Introduction to Power Series

  • Intro to Power Series Example 1
    03:17
  • Representing Functions as Power Series Example 8
    07:19
  • Intro to Power Series
    05:58

Taylor Series & Taylor Polynomials

  • Taylor Polynomials
    07:00
  • Taylor Series
    08:42
  • Convergence of Taylor & Maclaurin Series
    08:26

Kinematics

  • Guided course
    Using The Velocity Function
    10:17
  • Guided course
    Using The Acceleration Function Example 1
    08:56
  • Guided course
    Using The Acceleration Function
    08:14

Initial Value Problems

  • Guided course
    Initial Value Problems Example 2
    05:59
  • Guided course
    Initial Value Problems
    05:03
  • Guided course
    Initial Value Problems Example 1
    06:46