Introductory Calculus

 

Functions

• Introduction to Functions
  • Practice Problem 1 - Evaluating Functions with Constants and Variables
  • Practice Problem 2 - Evaluating Functions with Constants, Variables, & Equations
• Domain and Range
  • Practice Problem 1 - Finding the Domain and Range of Functions
• Combining Functions
  • Combining f(x)=2x and g(x)=1+x^2
  • Combining f(x)=3x-2 and g(x)=sqrt(x)
  • Combining f(x)=2*sqrt(x-1) and g(x)=sqrt(x-1)
  • Practice Problem - Splitting Up Functions
  • Combining f(x)=sqrt(x) and g(x)=1+x^3
  • Combining f(x)=pi-x and g(x)=cos(x)
  • Combining f(x)=1+x^2 for Various Equations
  • Combining f(x)=x, g(x)=x^2 for Various Equations
  • Combining f(x)=2x-1 and g(x)=x^2-x
  • Combining f(x)=2-x^2 and g(x)=x^3
  • Combining Complicated Functions 1
  • Combining Complicated Functions 2 - Part 1
  • Combining Complicated Functions 2 - Part 2
  • Combining Complicated Functions 3
  • Combining Complicated Functions 4
• Translating Functions
• Symmetry

Limits and Continuity

• Introduction to the Limit
• Directional Dependent Limits
• Evaluating Limits Algebraically
• Limit Rules
  • Limits Practice Problem Set 1
  • Limits Practice Problem Set 2
  • Limits Practice Problem Set 3
  • Limits Practice Problem Set 4
• Definition of Continuity

Derivatives

• The Definition of the Derivative
  • Practice Problem 1 - Finding Tangent Lines Using Points
  • Practice Problem 2 - Finding the Derivative of 3x^2 Rigorously
  • Practice Problem 3 - Finding the Derivative of x^3 Rigorously
  • Practice Problem 4 - Finding the Derivative of 2x^2+1 Rigorously
  • Practice Problem 5 - Finding the Derivative of sqrt(x+1) Rigorously
  • Practice Problem 6 - Finding the Derivative of 1/x Rigorously
  • Practice Problem 7 - Finding the Derivative of 1/(x+1) Rigorously
  • Practice Problem 8 - Finding the Derivative of ax^2+b Rigorously
    
• Basic Derivative Rules
• Derivative Power Rule
  • Derivative Power Rule Practive Problem Set 1
  • Derivative Power Rule Practive Problem Set 2
  • Derivative Power Rule Practive Problem Set 3
• Derivative Product Rule
  • Derivative Product Rule Practice Problem(s) 1
  • Derivative Product Rule Practice Problem(s) 2
  • Derivative Product Rule Practice Problem(s) 3
• Derivative Quotient Rule
  • Derivative Quotient Rule Practice Problem(s) 1
  • Derivative Quotient Rule Practice Problem(s) 2
  • Derivative Quotient Rule Practice Problem(s) 3
• Trigonometric Derivatives
  • Trigonometric Derivatives Practice Problem(s) 1
  • Trigonometric Derivatives Practice Problem(s) 2
  • Trigonometric Derivatives Practice Problem(s) 3
  • Trigonometric Derivatives Practice Problem(s) 4
  • Trigonometric Derivatives Practice Problem(s) 5
  • Trigonometric Derivatives Practice Problem(s) 6
  • Trigonometric Derivatives Practice Problem(s) 7 Part 1
  • Trigonometric Derivatives Practice Problem(s) 7 Part 2
  • Trigonometric Derivatives Practice Problem(s) 8
  • Trigonometric Derivatives Practice Problem(s) 9
  • Trigonometric Derivatives Practice Problem(s) 10
  • Trigonometric Derivatives Practice Problem(s) 11
  • Trigonometric Derivatives Practice Problem(s) 12
  • Trigonometric Derivatives Practice Problem(s) 13
  • Trigonometric Derivatives Practice Problem(s) 14
  • Trigonometric Derivatives Practice Problem(s) 15
• Derivative Chain Rule
  • Derivative Chain Rule Practice Problem(s) 1
  • Derivative Chain Rule Practice Problem(s) 2
  • Derivative Chain Rule Practice Problem(s) 3
  • Derivative Chain Rule Practice Problem(s) 4
  • Derivative Chain Rule Practice Problem(s) 5

Derivative Applications

• Introduction to Implicit Differentiation
  • Implicit Differentiation Introduction Practice Problem(s) 1 Part 1
  • Implicit Differentiation Introduction Practice Problem(s) 1 Part 2
• Implicit Differentiation with respect to Time
• Related Rates Introduction
  • Related Rates Practice – Depth of a Swimming Pool
    
  • Related Rates Practice – Volume of a Sphere
• First Derivative Test
• Second Derivative Test
  • Concavity Practice Problem 1
    
  • Concavity Practice Problem 2
    
  • Concavity Practice Problem 3
    
  • Concavity Practice Problem 4
    
  • Concavity Practice Problem 5
    
  • Concavity Practice Problem 6
    
  • Concavity Practice Problem 7
  • Concavity Practice Problem 8
  • Concavity Practice Problem 9
    
  • Concavity Practice Problem 10
    
  • Concavity Practice Problem 11
    
  • Concavity Practice Problem 12
    
  • Concavity Question 1 Part1 Split 1
    
  • Concavity Question 1 Part1 Split 2
    
  • Concavity Question 1 Part 2
    
  • Concavity Question 1 Part 3
    
  • Concavity Question 2
    
  • Concavity Question 3
    
  • Concavity Question 4
    
  • Min/Max/Inflection Points - User Submitted Part 1 of 2
    
  • Min/Max/Inflection Points - User Submitted Part 2 of 2
    
  • Complicated Concavity Problem - User Requested Part 1 of 2
    
  • Complicated Concavity Problem - User Requested Part 2 of 2
    
  • Using Calculus to Make Money on the Stock Market Problem - User Question
• Rectilinear Motion with Derivatives
• Absolute Max/Min, Rolle's Theorem, Mean Value Theorem
• Optimization Through Derivatives
  
  • Optimizing a Rain Gutter

Integration

• Understanding the Definite Integral Part 1
• Understanding the Definite Integral Part 2
  • Rectangular Practice Problem 1
    
  • Rectangular Practice Problem 2
    
  • Trapezoidal Practice Problem 1 Part 1
    
  • Trapezoidal Practice Problem 1 Part 2
• Introduction to the Definite Integral
• Definite Integral Properties
  
• Indefinite Integral
  
  • Indefinite Integral Practice Problem(s) 1
    
• Integral 'Power Rule'
  
  • Integral Power Rule Practice Problem(s) 1
    
  • Integral Power Rule Practice Problem(s) 2
    
  • Integral Power Rule Practice Problem(s) 3
    
• Trigonometric Integrals
  
  • Trigonometric Integrals Practice Problem(s) 1
    
  • Trigonometric Integrals Practice Problem(s) 2
    
• Introduction to U-Substitution
  
  • U-Substitution Practice Problem(s) 1
  • U-Substitution Practice Problem(s) 2
    U-Substitution Practice Problem(s) 3
    U-Substitution Practice Problem(s) 4
    
• U-Substitution for Trigonometric Integrals
  • U-Substitution for Trig Practice Problem(s) 1
    
  • U-Substitution for Trig Practice Problem(s) 2
    
  • U-Substitution for Trig Practice Problem(s) 3
  • Advanced U-Substitution Practice Problem(s) 1
    
  • Advanced U-Substitution Practice Problem(s) 2
    
  • Advanced U-Substitution Practice Problem(s) 3
    
  • Advanced U-Substitution Practice Problem(s) 4
    
• The Fundamental Theorem of Calculus
  • FToC Practice Problem(s) 1
    
  • FToC Practice Problem(s) 2
    
  • FToC Practice Problem(s) 3
    
  • FToC Practice Problem(s) 4
    
  • FToC Practice Problem(s) 5
    
  • FToC Practice Problem(s) 6
    
  • FToC Practice Problem(s) 7
    
  • FToC Practice Problem(s) 8
    
  • FToC Practice Problem(s) 9
    
  • FToC Practice Problem(s) 10
    
  • FToC Practice Problem(s) 11
    
• Integration by Parts
  • Integration by Parts Practice Problem(s) 1
    
  • Integration by Parts Practice Problem(s) 2
    

Integral Applications

• Calculating the Area Between Curves
  • Area Between Curves Practice Problem(s) 1
    
  • Area Between Curves Practice Problem(s) 2
    
  • Area Between Curves Practice Problem(s) 3
    
  • Area Between Curves Practice Problem(s) 4
    
  • Area Between Curves Practice Problem(s) 5
    
  • Area Between Curves Practice Problem(s) 6
    
  • Area Between Curves Practice Problem(s) 7
    
• Volumes of Revolution by Discs Part 1
  • Volumes of Revolution by Discs Practice 1
    
  • Volumes of Revolution by Discs Practice 2
    
• Volumes of Revolution by Discs Part 2
  • Volumes of Revolution by Discs Practice 3
    
  • Volumes of Revolution by Discs Practice 4
    
  • Volumes of Revolution by Discs Practice 5
    
• Volumes of Revolution by Shells
  • Volumes of Revolution by Shells Practice Problem 1
    
  • Volumes of Revolution by Shells Practice Problem 2
    
• Calculating Arc Length Using Integrals
  • Arc Length Practice Problem(s) 1
    
  • Arc Length Practice Problem(s) 2
    
• Calculating Surface Areas Using Integrals
  • Surface Area Practice Problem(s) 1
    
  • Surface Area Practice Problem(s) 2
    
• Work
  • Work Practice Problem 1
    

Integrals and Derivatives of Logs and Exponential

• Integrals and Derivatives of Logs and Exponentials
  
• Exponential Decay Problem

 

 

 

 

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Student Testimonials:

Lecture: Definition of the Derivative

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Lecture: Rigorous Derivative of Sin x

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Lecture: Definition of the Derivative

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Lecture: Question: Is Y a Function of X

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Lecture: Basic Derivative Rules

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Lecture: Problem 4 Solving 1/x Using the Definition of the Derivative

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Lecture: Definition of the Derivative

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Lecture: Rolle's Theorem / Mean Value Theorem

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Lecture: Definition of the Derivative

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Lecture: Definition of the Derivative

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Lecture: Trigonometric Derivatives

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