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Syllabus Overview and Core Topics for Calculus I (MATH 1210)

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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

Exponential Functions

  • Exponential Functions
    6:13
  • The Number e
    4:47
  • Graphs of Exponential Functions
    5:46

Logarithmic Functions

  • Logarithms Introduction
    7:30
  • The Natural Log
    2:51
  • Graphs of Logarithmic Functions
    5:26

Properties of Logarithms

  • Product, Quotient, and Power Rules of Logs
    3:49
  • Evaluate Logarithms
    5:14
  • Expand & Condense Log Expressions
    4:22

Exponential & Logarithmic Equations

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

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

  • 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

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

  • Percorso guidato
    Finding The Implicit Derivative
    05:14
  • Percorso guidato
    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

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

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

Intro to Extrema

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

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

  • Percorso guidato
    Linearization
    07:17

Differentials

  • Percorso guidato
    Finding Differentials
    05:53
  • Percorso guidato
    Determining Error and Relative Error
    04:57
  • Percorso guidato
    Determining Error and Relative Error Example 1
    04:46

Antiderivatives

  • Percorso guidato
    Antiderivatives
    05:50
  • Percorso guidato
    Finding a Particular Antiderivative
    05:13

Estimating Area with Finite Sums

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

Riemann Sums

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

Introduction to Definite Integrals

  • Percorso guidato
    Basic Rules for Definite Integrals
    06:07
  • Percorso guidato
    Definition of the Definite Integral
    05:43

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

Average Value of a Function

  • Percorso guidato
    Average Value of a Function Example 1
    04:25
  • Percorso guidato
    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

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