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MATH 151: Calculus I Syllabus and Course Overview

주석실무비디오 수업

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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

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

Derivatives as Functions

  • 가이드 코스
    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

Product and Quotient Rules

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

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

  • 가이드 코스
    Finding The Implicit Derivative
    05:14
  • 가이드 코스
    Finding The Implicit Derivative Example 1
    09:16

Related Rates

  • 가이드 코스
    Intro To Related Rates
    04:16
  • 가이드 코스
    Real World Application
    06:16
  • 가이드 코스
    Changing Geometries
    06:35

Motion Analysis

  • 가이드 코스
    Derivatives Applied To Velocity
    06:29
  • 가이드 코스
    Derivatives Applied To Acceleration Example 2
    06:51
  • 가이드 코스
    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

Applied Optimization

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

Linearization

  • 가이드 코스
    Linearization
    07:17

Differentials

  • 가이드 코스
    Finding Differentials
    05:53
  • 가이드 코스
    Determining Error and Relative Error
    04:57
  • 가이드 코스
    Determining Error and Relative Error Example 1
    04:46

Antiderivatives

  • 가이드 코스
    Antiderivatives
    05:50
  • 가이드 코스
    Finding a Particular Antiderivative
    05:13

Indefinite Integrals

  • 가이드 코스
    Additional Rules for Indefinite Integrals
    05:56
  • 가이드 코스
    Power Rule for Indefinite Integrals
    04:04
  • 가이드 코스
    Introduction to Indefinite Integrals
    05:04

Estimating Area with Finite Sums

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

Riemann Sums

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

Introduction to Definite Integrals

  • 가이드 코스
    Basic Rules for Definite Integrals
    06:07
  • 가이드 코스
    Definition of the Definite Integral
    05:43

Fundamental Theorem of Calculus

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

Average Value of a Function

  • 가이드 코스
    Average Value of a Function Example 1
    04:25
  • 가이드 코스
    Average Value of a Function
    06:37

Substitution

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

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

Kinematics

  • 가이드 코스
    Using The Velocity Function
    10:17
  • 가이드 코스
    Using The Acceleration Function Example 1
    08:56
  • 가이드 코스
    Using The Acceleration Function
    08:14

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

Work

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

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

Initial Value Problems

  • 가이드 코스
    Initial Value Problems Example 2
    05:59
  • 가이드 코스
    Initial Value Problems
    05:03
  • 가이드 코스
    Initial Value Problems Example 1
    06:46

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

Sequences

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

Series

  • 가이드 코스
    Intro to Series: Partial Sums
    06:45
  • 가이드 코스
    Intro to Series: Partial Sums Example 1
    04:33
  • 가이드 코스
    Geometric Series
    06:00

Convergence Tests

  • 가이드 코스
    Ratio Test
    05:35
  • 가이드 코스
    Direct Comparison Test
    09:25
  • 가이드 코스
    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