MATH1052-edX

Juan Carlos Ponce Campuzano, May 11, 2021

Applets for the edX version of MATH1052 Multivariate Calculus and ODEs from UQ

Table of Contents

  1. Chapter 1
    1. Sketch solution curves with slope fields
    2. Slope fields: Problem 1
    3. Slope fields: Problem 2
    4. Slope field and stable/unstable solutions
    5. Stable/Unstable equilibrium solutions
    6. Long term behaviour 1
    7. Long term behaviour 2
    8. Euler's method: General exploration
    9. Exploring errors in Euler's method
    10. ODEs: Linear or Non-linear?
    11. Logistic model
    12. The undamped spring
    13. Underdamping
    14. Critical damping
    15. Overdamping
    16. A simple undamped pendulum simulation
    17. Damped pendulum simulation
    18. Kinetic and Potential energy: Ball in free fall
    19. Conservation of energy: Undamped Spring
  2. Chapter 2
    1. Basic 3D plotter
    2. Conic sections
    3. Parabolas: Completing the square
    4. Generating a circle and ellipse
    5. Exploring Hyperbolas
    6. Contour Diagrams
    7. Cross-sections: Vibrating string guitar
    8. Problem 1: Cross sections
    9. Problem 2: Cross sections
  3. Chapter 3
    1. Geometric exploration of limits
    2. Partial derivatives
    3. Tangent line problems
    4. Vectors parallel to plane
    5. First-order approximation Zoom
    6. Gradients & Directional derivatives
  4. Chapter 4
  5. Chapter 5
    1. Parametric curves
    2. Parametric curves on intervals
    3. Parametric curves in 3D
    4. Position vector
    5. Position vector 3D
    6. Parametric straight line
    7. Arc Length parametric curves
    8. Polar curves
    9. Line Integrals: Work

1.

Chapter 1

  • 1. Sketch solution curves with slope fields
  • 2. Slope fields: Problem 1
  • 3. Slope fields: Problem 2
  • 4. Slope field and stable/unstable solutions
  • 5. Stable/Unstable equilibrium solutions
  • 6. Long term behaviour 1
  • 7. Long term behaviour 2
  • 8. Euler's method: General exploration
  • 9. Exploring errors in Euler's method
  • 10. ODEs: Linear or Non-linear?
  • 11. Logistic model
  • 12. The undamped spring
  • 13. Underdamping
  • 14. Critical damping
  • 15. Overdamping
  • 16. A simple undamped pendulum simulation
  • 17. Damped pendulum simulation
  • 18. Kinetic and Potential energy: Ball in free fall
  • 19. Conservation of energy: Undamped Spring

1.1.

Sketch solution curves with slope fields

1.2.1 Slope of y'=2y
– Juan Carlos Ponce Campuzano

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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1.15.

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1.16.

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1.17.

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1.18.

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1.19.

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2.

Chapter 2

  • 1. Basic 3D plotter
  • 2. Conic sections
  • 3. Parabolas: Completing the square
  • 4. Generating a circle and ellipse
  • 5. Exploring Hyperbolas
  • 6. Contour Diagrams
  • 7. Cross-sections: Vibrating string guitar
  • 8. Problem 1: Cross sections
  • 9. Problem 2: Cross sections

2.1.

Basic 3D plotter

2.1.1 to 2.1.2 Visualising functions, and topic main points
– Juan Carlos Ponce Campuzano

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.

Chapter 3

  • 1. Geometric exploration of limits
  • 2. Partial derivatives
  • 3. Tangent line problems
  • 4. Vectors parallel to plane
  • 5. First-order approximation Zoom
  • 6. Gradients & Directional derivatives

3.1.

Geometric exploration of limits

3.1.1 Limits & Continuity: review of the 1-variable case[br][br]This applet demonstrates left-hand, right-hand, and normal limits. Drag the red dot along the x-axis to show various inputs and outputs of this piecewise-defined function!
– Juan Carlos Ponce Campuzano

3.2.

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3.5.

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3.6.

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4.

Chapter 4


    This chapter does not contain any resources yet.

5.

Chapter 5

  • 1. Parametric curves
  • 2. Parametric curves on intervals
  • 3. Parametric curves in 3D
  • 4. Position vector
  • 5. Position vector 3D
  • 6. Parametric straight line
  • 7. Arc Length parametric curves
  • 8. Polar curves
  • 9. Line Integrals: Work

5.1.

Parametric curves

– Juan Carlos Ponce Campuzano

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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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