Calculus

Ben Roth, 2020/08/19

目次

  1. Derivatives
    1. Difference Quotient
    2. Derivatives as Tangent Slopes
    3. f(x)=f'(x)
    4. f, f', f''
    5. Derivative Calculator
    6. Related Rates (Lighthouse)
    7. Related Rates (Ladder Fall)
    8. Optimization (CAS)
    9. Optimization Challenge
    10. Open-Top Box Optimization
  2. Integrals
    1. Trapezoidal Rule
    2. Reimann Sums
    3. Integral Calculator
    4. Integrals (Intro to Notation)
    5. Integrals as an Area
    6. Integral (Effects of Vertical Shifts)
    7. Volumes of Revolution
    8. Volume of Revolution Using Cylinders
    9. Arc Length of a Function
  3. Kinematics
    1. Kinematics (Particle Motion)
    2. Position From Velocity
    3. Displacement & Velocity
    4. Parametric Functions (Variable Motion)
  4. Differential Equations
    1. Euler's Method
    2. Eulers method visualised (AI HL 5.16)
    3. Phase Portraits
    4. Phase Plane Sketcher
    5. Coupled Differential Equations (Linear)
    6. Lotka-Volterra predator-prey model
    7. Foxes and Rabbits

1.

Derivatives

  • 1. Difference Quotient
  • 2. Derivatives as Tangent Slopes
  • 3. f(x)=f'(x)
  • 4. f, f', f''
  • 5. Derivative Calculator
  • 6. Related Rates (Lighthouse)
  • 7. Related Rates (Ladder Fall)
  • 8. Optimization (CAS)
  • 9. Optimization Challenge
  • 10. Open-Top Box Optimization

1.1.

Difference Quotient

– Ben Roth

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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2.

Integrals

  • 1. Trapezoidal Rule
  • 2. Reimann Sums
  • 3. Integral Calculator
  • 4. Integrals (Intro to Notation)
  • 5. Integrals as an Area
  • 6. Integral (Effects of Vertical Shifts)
  • 7. Volumes of Revolution
  • 8. Volume of Revolution Using Cylinders
  • 9. Arc Length of a Function

2.1.

Trapezoidal Rule

– Ben Roth

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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3.

Kinematics

  • 1. Kinematics (Particle Motion)
  • 2. Position From Velocity
  • 3. Displacement & Velocity
  • 4. Parametric Functions (Variable Motion)

3.1.

Kinematics (Particle Motion)

– Ben Roth

3.2.

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3.3.

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3.4.

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4.

Differential Equations

  • 1. Euler's Method
  • 2. Eulers method visualised (AI HL 5.16)
  • 3. Phase Portraits
  • 4. Phase Plane Sketcher
  • 5. Coupled Differential Equations (Linear)
  • 6. Lotka-Volterra predator-prey model
  • 7. Foxes and Rabbits

4.1.

Euler's Method

– Ben Roth

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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