BC Calculus

Vivian Donnelly, SAVAŞ ORHAN, 2018/03/15

Some activities to support class discussions.

目次

  1. Chapter 1 - Limits
    1. limit analyzer
    2. Limits: Introductory Questions
    3. Limits Example 1
    4. Limits Example 2
    5. Limits Example 3
    6. Limits Example 4
    7. Limits Example 5
    8. Limits Example 6
    9. Limits Example 7
    10. Cont in uity
    11. Continuity Questions
    12. Vertical Asymptote (Defined as a Limit)
    13. Horizontal Asymptote (Defined as a Limit)
    14. One Special Limit
  2. Chapter 2 - The Derivative
    1. Derivatives (Intro)-2
    2. When does f'(x) = f(x)?
    3. Important Trig Limits
    4. Graphical relationship between a function and its derivative
  3. Chapter 3 - Derivatives of Elementary Functions
    1. Derivatives of Inverse Functions
    2. Graphing The Derivative of a Function
    3. Derivative of Sine & Cosine Functions (Quick Investigation)
    4. Derivative of a Product
    5. Derivative of Tangent Function (Investigation)
    6. Implicit Differentiation: Intro
    7. Implicit Differentiation (Quick Check)
    8. Derivative of Arcsine Function
    9. Derivative of Arccosine Function
    10. Derivative of Arctangent Function
    11. Derivative of Natural Log Function
  4. Chapter4 Applications of the Derivative
    1. Derivative Definition
    2. tangent and derivative
    3. Existence of Derivative
    4. The rate of change of a shadow
    5. Mean Value Theorem (Without Words)
    6. Critical Points
    7. Critical Points of a function -Example
    8. Critical Numbers & Critical Points of Functions (Intro)
    9. Maximum/Minimum Videos
    10. Relative Extrema Illustrator
    11. Extrema on a Closed Interval
    12. Investigating the derivative at a cusp.
    13. Constructing Graphs of Derivative Functions (Intuitively)
    14. Sketch the Derivative (Warm Up)
    15. Quiz: Writing Exponential Growth & Decay Functions
    16. Exponential Growth vs. Decay (Intro)
    17. Newton's Law of Cooling
    18. Logistic Growth Function
  5. Chapter 5 The Integral
    1. Riemann Sums
    2. All Sums (Riemann Sums)
    3. Area between curves
    4. Area between curves
    5. Definite Integral Illustrator (II)
    6. Average Velocity
    7. Areas Between Curves (Intro)
    8. Area Between Curves
    9. Area Between 2 Curves
  6. Chapters 6 Antiderivatives
    1. Cross-Sections Perpendicular to x-Axis: Squares
    2. Region between two quadratics rotated about y=-3
    3. Definite Integrals: Sum
    4. What Makes a Function Even?
    5. What Makes a Function Odd?
    6. Odd Functions: Another Look (Take 2)!
    7. U-Substitution (Definite Integrals)
  7. Chapters 7 & 8 - Applications of Integral
    1. Volume of Rotation - Disk Method Visual
    2. Visualizing Volumes of Rotation
    3. 3D volume by rotation of a function
    4. Parabola Around y-Axis
    5. Parabola Rotated Around y-Axis Wireframe
    6. Parabola Rotated Around x-Axis
    7. Parabola Rotated Around x-Axis
    8. Cross sections are semi-circles.
    9. Cross sections are squares with one side in base.
    10. Volume: Circ base cross section isos rt triangle hyp in base
    11. Volume of revolution, donut shape, cylindrical shell method.
    12. Cylindrical Shell Action!!! (1)
    13. Cylindrical Shell Action!!! (2)
    14. Volume by Cylindrical Shells: Illustrated
    15. Volume of a Solid - Washer Method
    16. illustration of volume as a set of nested cylinders
    17. Arc length: Quick Investigation
    18. Disc Action!!!
    19. Washer Action!!! (1)
    20. Washer Action !!! (2) - Calculus
    21. V. of Solid NOT of Revolution
    22. Areas & Volumes: Culminating Activity
  8. Chapter 9 - Techniques of Integration
    1. Sine & Cosine of a Sum: Discovery
    2. Partial Fraction Decomposition Calculator
    3. Section 4.5-Integration using substitution
  9. Chapter 10 - Improper Integrals
    1. Gabriel's Horn
  10. Chapter 11 - Infinite Series
    1. Sequences (Dynamic Illustrator)
    2. lagrange error bound
    3. Calculus - Taylor Inequality (LaGrange Error Bound)
    4. Taylor Polynomials
    5. Taylor Series
  11. Chapter 12 - Differential Equations
    1. Slope Fields.
    2. Euler's Method of Function Approximation
    3. Euler's Method
  12. Chapter 13 - Polar
    1. Polar Grapher
    2. Section 10.4-Area in Polar Coordinates
    3. Areas with Polar Coordinates
    4. Arc Length in Polar Coordintes
    5. Derivatives in Polar Coordintes
    6. Area Between 2 Polar Graphs
  13. Review for AP EXAM

1.

Chapter 1 - Limits

  • 1. limit analyzer
  • 2. Limits: Introductory Questions
  • 3. Limits Example 1
  • 4. Limits Example 2
  • 5. Limits Example 3
  • 6. Limits Example 4
  • 7. Limits Example 5
  • 8. Limits Example 6
  • 9. Limits Example 7
  • 10. Cont in uity
  • 11. Continuity Questions
  • 12. Vertical Asymptote (Defined as a Limit)
  • 13. Horizontal Asymptote (Defined as a Limit)
  • 14. One Special Limit

1.1.

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1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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1.14.

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2.

Chapter 2 - The Derivative

  • 1. Derivatives (Intro)-2
  • 2. When does f'(x) = f(x)?
  • 3. Important Trig Limits
  • 4. Graphical relationship between a function and its derivative

2.1.

–

2.2.

–

2.3.

–

2.4.

–

3.

Chapter 3 - Derivatives of Elementary Functions

  • 1. Derivatives of Inverse Functions
  • 2. Graphing The Derivative of a Function
  • 3. Derivative of Sine & Cosine Functions (Quick Investigation)
  • 4. Derivative of a Product
  • 5. Derivative of Tangent Function (Investigation)
  • 6. Implicit Differentiation: Intro
  • 7. Implicit Differentiation (Quick Check)
  • 8. Derivative of Arcsine Function
  • 9. Derivative of Arccosine Function
  • 10. Derivative of Arctangent Function
  • 11. Derivative of Natural Log Function

3.1.

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3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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4.

Chapter4 Applications of the Derivative

  • 1. Derivative Definition
  • 2. tangent and derivative
  • 3. Existence of Derivative
  • 4. The rate of change of a shadow
  • 5. Mean Value Theorem (Without Words)
  • 6. Critical Points
  • 7. Critical Points of a function -Example
  • 8. Critical Numbers & Critical Points of Functions (Intro)
  • 9. Maximum/Minimum Videos
  • 10. Relative Extrema Illustrator
  • 11. Extrema on a Closed Interval
  • 12. Investigating the derivative at a cusp.
  • 13. Constructing Graphs of Derivative Functions (Intuitively)
  • 14. Sketch the Derivative (Warm Up)
  • 15. Quiz: Writing Exponential Growth & Decay Functions
  • 16. Exponential Growth vs. Decay (Intro)
  • 17. Newton's Law of Cooling
  • 18. Logistic Growth Function

4.1.

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4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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4.9.

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4.10.

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4.11.

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4.12.

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4.13.

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4.14.

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4.15.

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4.16.

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4.17.

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4.18.

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5.

Chapter 5 The Integral

  • 1. Riemann Sums
  • 2. All Sums (Riemann Sums)
  • 3. Area between curves
  • 4. Area between curves
  • 5. Definite Integral Illustrator (II)
  • 6. Average Velocity
  • 7. Areas Between Curves (Intro)
  • 8. Area Between Curves
  • 9. Area Between 2 Curves

5.1.

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5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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5.7.

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5.8.

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5.9.

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6.

Chapters 6 Antiderivatives

  • 1. Cross-Sections Perpendicular to x-Axis: Squares
  • 2. Region between two quadratics rotated about y=-3
  • 3. Definite Integrals: Sum
  • 4. What Makes a Function Even?
  • 5. What Makes a Function Odd?
  • 6. Odd Functions: Another Look (Take 2)!
  • 7. U-Substitution (Definite Integrals)

6.1.

–

6.2.

–

6.3.

–

6.4.

–

6.5.

–

6.6.

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6.7.

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7.

Chapters 7 & 8 - Applications of Integral

  • 1. Volume of Rotation - Disk Method Visual
  • 2. Visualizing Volumes of Rotation
  • 3. 3D volume by rotation of a function
  • 4. Parabola Around y-Axis
  • 5. Parabola Rotated Around y-Axis Wireframe
  • 6. Parabola Rotated Around x-Axis
  • 7. Parabola Rotated Around x-Axis
  • 8. Cross sections are semi-circles.
  • 9. Cross sections are squares with one side in base.
  • 10. Volume: Circ base cross section isos rt triangle hyp in base
  • 11. Volume of revolution, donut shape, cylindrical shell method.
  • 12. Cylindrical Shell Action!!! (1)
  • 13. Cylindrical Shell Action!!! (2)
  • 14. Volume by Cylindrical Shells: Illustrated
  • 15. Volume of a Solid - Washer Method
  • 16. illustration of volume as a set of nested cylinders
  • 17. Arc length: Quick Investigation
  • 18. Disc Action!!!
  • 19. Washer Action!!! (1)
  • 20. Washer Action !!! (2) - Calculus
  • 21. V. of Solid NOT of Revolution
  • 22. Areas & Volumes: Culminating Activity

7.1.

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7.2.

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7.3.

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7.4.

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7.5.

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7.6.

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7.7.

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7.8.

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7.9.

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7.10.

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7.11.

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7.12.

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7.13.

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7.14.

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7.15.

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7.16.

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7.17.

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7.18.

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7.19.

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7.20.

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7.21.

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7.22.

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8.

Chapter 9 - Techniques of Integration

  • 1. Sine & Cosine of a Sum: Discovery
  • 2. Partial Fraction Decomposition Calculator
  • 3. Section 4.5-Integration using substitution

8.1.

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8.2.

–

8.3.

–

9.

Chapter 10 - Improper Integrals

  • 1. Gabriel's Horn

9.1.

–

10.

Chapter 11 - Infinite Series

  • 1. Sequences (Dynamic Illustrator)
  • 2. lagrange error bound
  • 3. Calculus - Taylor Inequality (LaGrange Error Bound)
  • 4. Taylor Polynomials
  • 5. Taylor Series

10.1.

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10.2.

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10.3.

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10.4.

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10.5.

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11.

Chapter 12 - Differential Equations

  • 1. Slope Fields.
  • 2. Euler's Method of Function Approximation
  • 3. Euler's Method

11.1.

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11.2.

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11.3.

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12.

Chapter 13 - Polar

  • 1. Polar Grapher
  • 2. Section 10.4-Area in Polar Coordinates
  • 3. Areas with Polar Coordinates
  • 4. Arc Length in Polar Coordintes
  • 5. Derivatives in Polar Coordintes
  • 6. Area Between 2 Polar Graphs

12.1.

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12.2.

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12.3.

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12.4.

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12.5.

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12.6.

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13.

Review for AP EXAM


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