-
AP CALCULUS RESOURCES !!!-copy01
-
1. Preliminary Review Topics
- Pythagorean Trigonometric Identity (1)
- Trig ID Movie (II)
- Trig ID Movie (III)
- Exponential Functions: Graphs
- Logarithmic Functions: Graphs
- Logarithmic Action!
- Logarithmic Action (2)!
- Logarithmic Action (3)!
- Logarithmic Action (4)!
-
2. Limits & Continuity
- Limits: Introductory Questions
- One CRAZY Limit !!!
- A tool to explore delta-epsilon understandings.
- Cont in uity
- IVT Dynamic Illustrator
- Continuity Questions
- Vertical Asymptote (Defined as a Limit)
- Horizontal Asymptote (Defined as a Limit)
- One Special Limit
-
3. Derivatives: Introduction & Intuition
- Average Velocity
- Average to Instantaneous (Intro)
- Sketch the Derivative (Warm Up)
- Drawing Derivatives
- Constructing Graphs of Derivative Functions (Intuitively)
- Average Rate of Change Intervals
- Average Rate of Change of a Function: Dynamic Illustration
- Average Rate of Change vs. Instantaneous Rate of Change
- Derivatives (Intro)-1
- Derivatives (Intro)-2
- Graphing The Derivative of a Function
- 3-Way Color-Changing Derivative Grapher
- When does f'(x) = f(x)?
- Mean Value Theorem
- Mean Value Theorem (Without Words)
-
4. Derivatives of Special Functions & Differentiation Techniques
- Derivative of a Product
- Important Trig Limits
- Derivative of Sine & Cosine Functions (Quick Investigation)
- Derivative of Tangent Function (Investigation)
- Implicit Differentiation: Intro
- Folium of Descartes
- Implicit Differentiation (Quick Check)
- Derivative of Arcsine Function
- Derivative of Arccosine Function
- Derivative of Arctangent Function
- Derivatives of Inverse Functions
- Derivative of Natural Log Function
-
5. Related Rates & Linearization of Functions
- Related Rates (1)
- Related Rates (2)
- Falling Ladder !!!
- Related Rates (3)
- Related Rates: Adjustable Cone with dh/dt Constant
- Related Rates (Rolling Carts Problem)
- Linearization Illustrator (Calculus)
- Linearization Checker (Calculus)
- Newton's Method: Illustrated
-
6. Closed Interval Method & Optimization Problems
- Critical Numbers & Critical Points of Functions (Intro)
- The Closed Interval Method (Application Problem)
- Optimization: Area of a Rectangle
- Minimizing the Area of a Triangle
- Optimization - Box
- Maximizing Trapezoid Area
- Optimization Challenge 1
- Optimization: Maximizing Area of a Rectangle Inside a Right Triangle
- Honeybee Population (Growth Rate Question)
- Oil Pipeline Optimization Problem
- Cylinder Inscribed Inside Sphere
- Cylinder Inscribed In Cone
- Distance From Point to Graph
- Optimization Problem: Isosceles Triangle Circumscribed about a Circle
-
7. Riemann Sums; Indefinite and Definite Integrals
- Definite Integral Illustrator (I)
- Trapezoid: Area (I)
- Definite Integral Illustrator (II)
- Definite Integrals: Sum
- What Makes a Function Even?
- What Makes a Function Odd?
- Odd Functions: Another Look (Take 2)!
- Accumulations
- All Sums (Riemann Sums)
-
8. Areas and Volumes; Solids of Revolution & Non-Revolution
- U-Substitution (Definite Integrals)
- Areas Between Curves (Intro)
- Area Between Curves
- Area Between 2 Curves
- Visualizing Volumes of Rotation
- Volume of Solid of Revolution about x-axis
- Disc Action!!!
- Solids of Revolution (Discs)
- Washer Action!!! (1)
- Washer Action !!! (2) - Calculus
- Cylindrical Shell Action!!! (1)
- Cylindrical Shell Action!!! (2)
- Parabola Around y-Axis
- Parabola Rotated Around y-Axis Wireframe
- Parabola Rotated Around x-Axis
- Parabola Rotated Around x-Axis
- Solids of Revolution: Around the x-Axis
- Solids of Revolution: Around the y-Axis
- Solids of Revolution: Around y=6
- Calculus Solids
- V. of Solid NOT of Revolution
- Cross-Sections Perpendicular to x-Axis: Squares
- Cross-Sections Perpendicular to x-Axis: Equilateral Triangle
- Cross-Sections Perpendicular to x-Axis: Right Triangles
- Cross-Sections Perpendicular to x-Axis: Rectangles
- Areas & Volumes: Culminating Activity
-
9. Average Value and Arc Length
- Average Value of a Function
- Arc Length (Calculus)
-
10. Integration Techniques
- Apex Section 6.1-Integration using substitution
- Sine & Cosine of a Sum: Discovery
- Partial Fraction Decomposition Calculator
-
11. Differential Equations
- Slope Field
- Copy of Slope Fields.
- Euler's Method
- Quiz: Writing Exponential Growth & Decay Functions
- Exponential Growth vs. Decay (Intro)
- Newton's Law of Cooling
- Logistic Growth Function
-
12. Sequences & Series
- Sequences (Dynamic Illustrator)
- Convergent or Divergent Series
- Sum of Infinite Geometric Series
- Partial Sums Alternating Series
- Integral Test for Series
- Taylor Polynomials
-
13. Parametric Equations
- Parametric Path on a Number Line
- Parametric Path
- Parametric Equations (I)
- Parametric Equations Grapher
- Parametric Equations: dy/dx (Ex 1)
- Cycloid Animation!
-
14. Polar Coordinates
- Trig Function Values (30 Degrees)
- Trig Function Values (45 Degrees)
- Trig Function Values (60 Degrees)
- Special Angles in Standard Position: Intro (V1)
- Special Angles in Standard Position: Intro (V2)
- Special Angles in Standard Position: Intro (V3)
- Polar Coordinates: Introduction
- Writing Equivalent Polar Coordinates: Quiz
- Polar Function Grapher
- Derivatives in Polar Coordintes
- Areas with Polar Coordinates
- Area Between 2 Polar Graphs
- Arc Length in Polar Coordintes
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AP CALCULUS RESOURCES !!!-copy01
Tim Brzezinski, 杖池 誠, Aug 3, 2017

Table of Contents
- Preliminary Review Topics
- Pythagorean Trigonometric Identity (1)
- Trig ID Movie (II)
- Trig ID Movie (III)
- Exponential Functions: Graphs
- Logarithmic Functions: Graphs
- Logarithmic Action!
- Logarithmic Action (2)!
- Logarithmic Action (3)!
- Logarithmic Action (4)!
- Limits & Continuity
- Limits: Introductory Questions
- One CRAZY Limit !!!
- A tool to explore delta-epsilon understandings.
- Cont in uity
- IVT Dynamic Illustrator
- Continuity Questions
- Vertical Asymptote (Defined as a Limit)
- Horizontal Asymptote (Defined as a Limit)
- One Special Limit
- Derivatives: Introduction & Intuition
- Average Velocity
- Average to Instantaneous (Intro)
- Sketch the Derivative (Warm Up)
- Drawing Derivatives
- Constructing Graphs of Derivative Functions (Intuitively)
- Average Rate of Change Intervals
- Average Rate of Change of a Function: Dynamic Illustration
- Average Rate of Change vs. Instantaneous Rate of Change
- Derivatives (Intro)-1
- Derivatives (Intro)-2
- Graphing The Derivative of a Function
- 3-Way Color-Changing Derivative Grapher
- When does f'(x) = f(x)?
- Mean Value Theorem
- Mean Value Theorem (Without Words)
- Derivatives of Special Functions & Differentiation Techniques
- Derivative of a Product
- Important Trig Limits
- Derivative of Sine & Cosine Functions (Quick Investigation)
- Derivative of Tangent Function (Investigation)
- Implicit Differentiation: Intro
- Folium of Descartes
- Implicit Differentiation (Quick Check)
- Derivative of Arcsine Function
- Derivative of Arccosine Function
- Derivative of Arctangent Function
- Derivatives of Inverse Functions
- Derivative of Natural Log Function
- Related Rates & Linearization of Functions
- Related Rates (1)
- Related Rates (2)
- Falling Ladder !!!
- Related Rates (3)
- Related Rates: Adjustable Cone with dh/dt Constant
- Related Rates (Rolling Carts Problem)
- Linearization Illustrator (Calculus)
- Linearization Checker (Calculus)
- Newton's Method: Illustrated
- Closed Interval Method & Optimization Problems
- Critical Numbers & Critical Points of Functions (Intro)
- The Closed Interval Method (Application Problem)
- Optimization: Area of a Rectangle
- Minimizing the Area of a Triangle
- Optimization - Box
- Maximizing Trapezoid Area
- Optimization Challenge 1
- Optimization: Maximizing Area of a Rectangle Inside a Right Triangle
- Honeybee Population (Growth Rate Question)
- Oil Pipeline Optimization Problem
- Cylinder Inscribed Inside Sphere
- Cylinder Inscribed In Cone
- Distance From Point to Graph
- Optimization Problem: Isosceles Triangle Circumscribed about a Circle
- Riemann Sums; Indefinite and Definite Integrals
- Definite Integral Illustrator (I)
- Trapezoid: Area (I)
- Definite Integral Illustrator (II)
- Definite Integrals: Sum
- What Makes a Function Even?
- What Makes a Function Odd?
- Odd Functions: Another Look (Take 2)!
- Accumulations
- All Sums (Riemann Sums)
- Areas and Volumes; Solids of Revolution & Non-Revolution
- U-Substitution (Definite Integrals)
- Areas Between Curves (Intro)
- Area Between Curves
- Area Between 2 Curves
- Visualizing Volumes of Rotation
- Volume of Solid of Revolution about x-axis
- Disc Action!!!
- Solids of Revolution (Discs)
- Washer Action!!! (1)
- Washer Action !!! (2) - Calculus
- Cylindrical Shell Action!!! (1)
- Cylindrical Shell Action!!! (2)
- Parabola Around y-Axis
- Parabola Rotated Around y-Axis Wireframe
- Parabola Rotated Around x-Axis
- Parabola Rotated Around x-Axis
- Solids of Revolution: Around the x-Axis
- Solids of Revolution: Around the y-Axis
- Solids of Revolution: Around y=6
- Calculus Solids
- V. of Solid NOT of Revolution
- Cross-Sections Perpendicular to x-Axis: Squares
- Cross-Sections Perpendicular to x-Axis: Equilateral Triangle
- Cross-Sections Perpendicular to x-Axis: Right Triangles
- Cross-Sections Perpendicular to x-Axis: Rectangles
- Areas & Volumes: Culminating Activity
- Average Value and Arc Length
- Average Value of a Function
- Arc Length (Calculus)
- Integration Techniques
- Apex Section 6.1-Integration using substitution
- Sine & Cosine of a Sum: Discovery
- Partial Fraction Decomposition Calculator
- Differential Equations
- Slope Field
- Copy of Slope Fields.
- Euler's Method
- Quiz: Writing Exponential Growth & Decay Functions
- Exponential Growth vs. Decay (Intro)
- Newton's Law of Cooling
- Logistic Growth Function
- Sequences & Series
- Sequences (Dynamic Illustrator)
- Convergent or Divergent Series
- Sum of Infinite Geometric Series
- Partial Sums Alternating Series
- Integral Test for Series
- Taylor Polynomials
- Parametric Equations
- Parametric Path on a Number Line
- Parametric Path
- Parametric Equations (I)
- Parametric Equations Grapher
- Parametric Equations: dy/dx (Ex 1)
- Cycloid Animation!
- Polar Coordinates
- Trig Function Values (30 Degrees)
- Trig Function Values (45 Degrees)
- Trig Function Values (60 Degrees)
- Special Angles in Standard Position: Intro (V1)
- Special Angles in Standard Position: Intro (V2)
- Special Angles in Standard Position: Intro (V3)
- Polar Coordinates: Introduction
- Writing Equivalent Polar Coordinates: Quiz
- Polar Function Grapher
- Derivatives in Polar Coordintes
- Areas with Polar Coordinates
- Area Between 2 Polar Graphs
- Arc Length in Polar Coordintes
Limits & Continuity
-
1. Limits: Introductory Questions
-
2. One CRAZY Limit !!!
-
3. A tool to explore delta-epsilon understandings.
-
4. Cont in uity
-
5. IVT Dynamic Illustrator
-
6. Continuity Questions
-
7. Vertical Asymptote (Defined as a Limit)
-
8. Horizontal Asymptote (Defined as a Limit)
-
9. One Special Limit
Derivatives: Introduction & Intuition
-
1. Average Velocity
-
2. Average to Instantaneous (Intro)
-
3. Sketch the Derivative (Warm Up)
-
4. Drawing Derivatives
-
5. Constructing Graphs of Derivative Functions (Intuitively)
-
6. Average Rate of Change Intervals
-
7. Average Rate of Change of a Function: Dynamic Illustration
-
8. Average Rate of Change vs. Instantaneous Rate of Change
-
9. Derivatives (Intro)-1
-
10. Derivatives (Intro)-2
-
11. Graphing The Derivative of a Function
-
12. 3-Way Color-Changing Derivative Grapher
-
13. When does f'(x) = f(x)?
-
14. Mean Value Theorem
-
15. Mean Value Theorem (Without Words)
Derivatives of Special Functions & Differentiation Techniques
-
1. Derivative of a Product
-
2. Important Trig Limits
-
3. Derivative of Sine & Cosine Functions (Quick Investigation)
-
4. Derivative of Tangent Function (Investigation)
-
5. Implicit Differentiation: Intro
-
6. Folium of Descartes
-
7. Implicit Differentiation (Quick Check)
-
8. Derivative of Arcsine Function
-
9. Derivative of Arccosine Function
-
10. Derivative of Arctangent Function
-
11. Derivatives of Inverse Functions
-
12. Derivative of Natural Log Function
Related Rates & Linearization of Functions
-
1. Related Rates (1)
-
2. Related Rates (2)
-
3. Falling Ladder !!!
-
4. Related Rates (3)
-
5. Related Rates: Adjustable Cone with dh/dt Constant
-
6. Related Rates (Rolling Carts Problem)
-
7. Linearization Illustrator (Calculus)
-
8. Linearization Checker (Calculus)
-
9. Newton's Method: Illustrated
Closed Interval Method & Optimization Problems
-
1. Critical Numbers & Critical Points of Functions (Intro)
-
2. The Closed Interval Method (Application Problem)
-
3. Optimization: Area of a Rectangle
-
4. Minimizing the Area of a Triangle
-
5. Optimization - Box
-
6. Maximizing Trapezoid Area
-
7. Optimization Challenge 1
-
8. Optimization: Maximizing Area of a Rectangle Inside a Right Triangle
-
9. Honeybee Population (Growth Rate Question)
-
10. Oil Pipeline Optimization Problem
-
11. Cylinder Inscribed Inside Sphere
-
12. Cylinder Inscribed In Cone
-
13. Distance From Point to Graph
-
14. Optimization Problem: Isosceles Triangle Circumscribed about a Circle
Riemann Sums; Indefinite and Definite Integrals
-
1. Definite Integral Illustrator (I)
-
2. Trapezoid: Area (I)
-
3. Definite Integral Illustrator (II)
-
4. Definite Integrals: Sum
-
5. What Makes a Function Even?
-
6. What Makes a Function Odd?
-
7. Odd Functions: Another Look (Take 2)!
-
8. Accumulations
-
9. All Sums (Riemann Sums)
Areas and Volumes; Solids of Revolution & Non-Revolution
-
1. U-Substitution (Definite Integrals)
-
2. Areas Between Curves (Intro)
-
3. Area Between Curves
-
4. Area Between 2 Curves
-
5. Visualizing Volumes of Rotation
-
6. Volume of Solid of Revolution about x-axis
-
7. Disc Action!!!
-
8. Solids of Revolution (Discs)
-
9. Washer Action!!! (1)
-
10. Washer Action !!! (2) - Calculus
-
11. Cylindrical Shell Action!!! (1)
-
12. Cylindrical Shell Action!!! (2)
-
13. Parabola Around y-Axis
-
14. Parabola Rotated Around y-Axis Wireframe
-
15. Parabola Rotated Around x-Axis
-
16. Parabola Rotated Around x-Axis
-
17. Solids of Revolution: Around the x-Axis
-
18. Solids of Revolution: Around the y-Axis
-
19. Solids of Revolution: Around y=6
-
20. Calculus Solids
-
21. V. of Solid NOT of Revolution
-
22. Cross-Sections Perpendicular to x-Axis: Squares
-
23. Cross-Sections Perpendicular to x-Axis: Equilateral Triangle
-
24. Cross-Sections Perpendicular to x-Axis: Right Triangles
-
25. Cross-Sections Perpendicular to x-Axis: Rectangles
-
26. Areas & Volumes: Culminating Activity
Polar Coordinates
-
1. Trig Function Values (30 Degrees)
-
2. Trig Function Values (45 Degrees)
-
3. Trig Function Values (60 Degrees)
-
4. Special Angles in Standard Position: Intro (V1)
-
5. Special Angles in Standard Position: Intro (V2)
-
6. Special Angles in Standard Position: Intro (V3)
-
7. Polar Coordinates: Introduction
-
8. Writing Equivalent Polar Coordinates: Quiz
-
9. Polar Function Grapher
-
10. Derivatives in Polar Coordintes
-
11. Areas with Polar Coordinates
-
12. Area Between 2 Polar Graphs
-
13. Arc Length in Polar Coordintes
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