MATH2001 - Calculus & Linear algebra II

Juan Carlos Ponce Campuzano, Jul 5, 2022

This book contains learning resources (activities and visualizations) for the course Calculus & Linear algebra II from the UQ workbook. [b]Online slides:[/b] https://www.dynamicmath.xyz/math2001/ [b]Note:[/b] Some applets are made with other open-source lybraries, such as p5js, MathBox and Threejs. Enjoy!

Table of Contents

  1. Chapter 1
    1. Chapter-01: Example 1.1
    2. Chapter-01: Example 1.2
    3. Chapter-01: Example 1.3
    4. Chapter-01: Example 1.6
    5. Chapter-01: Example 1.7
  2. Chapter 3
    1. Chapter-03: Example 3-3
  3. Chapter 7
    1. Chapter-07: Change of basis
  4. Chapter 11
    1. Chapter-11: Examples orthonormal basis
    2. Chapter-11: Gram-Schmidt process
  5. Chapter 12
    1. Chapter-12-1: Theorem
    2. Chapter-12-2: Fitting line
    3. Chapter-12-2: Least squares error
    4. Chapter-12-2: Column space A
    5. Chapter-12-2: Column space A image
    6. Chapter-12-5: Fitting curve to data
    7. Chapter-12-5: Quadratic fit
  6. Chapter 13
    1. Chapter-13-1: sinx fit curve
    2. Chapter-13: Fitting curve to data (Cat)
  7. Chapter 15
    1. Chapter-15: Geometry of eigenvalues & eigenvectors
  8. Chapter 19
    1. Diagonalization: Quadratic forms
  9. Chapter 23
    1. Chapter-23: Riemann Integral
    2. Chapter 23-1: Surface
    3. Chapter 23-1: Surface & prisms
    4. Chapter-23-3-2: Example
  10. Chapter 24
    1. Fubini's theorem: Rectangular regions
    2. Chapter-24-2: Example
    3. Chapter-24-5: Vertical slabs
    4. Chapter-24-5: Horizontal slabs
    5. Chapter-24-6: Example
  11. Chapter 25
    1. Chapter 25-1-1: Example
    2. Chapter-25-2-1: Example testing
    3. Chapter-25-2-1: Example
  12. Chapter 26
    1. Chapter-26-1: Find volume
    2. Chapter-26-2: Example
    3. Chapter-26: how can we find the volume of any solid?
  13. Chapter 27
  14. Chatper 28
    1. Chapter-28: Polar plane
    2. Polar transformation
    3. Chapter-28-1: Example
    4. Chapter-28-2: Example
    5. Chapter-28-3: Example
  15. Chapter 29
  16. Chapter 30
    1. Chapter-30-2: Example
    2. Chapter-30-3: Example
  17. Chapter 31
    1. Chapter-31: Cylindrical coordinates
    2. Chapter-31: Cylindrical region
    3. Chapter-31-2: Example
  18. Chapter 32
    1. Chapter-32: Spherical coordinates
    2. Chapter-32: Spherical region
    3. Chapter-32-1: Simple example
    4. Chapter-32-3: Ice cream
  19. Chapter 33
    1. Chapter-33-1: Moment and Moment of inertia
    2. Chapter-33-1: Moment of inertia image
    3. Chapter-33-2: Hemisphere
  20. Chapter 34
    1. Vector Fields in 2D
    2. 2D Velocity fields
    3. Vector fields 3D
    4. 3D Velocity field
  21. Chapter 35
    1. Chapter-35-1: Integral
    2. Chapter-35-4-1: Example
    3. Line integrals of vector fields: Work & Circulation
  22. Chapter 36
  23. Chapter 37
  24. Chapter 38
    1. Vortex Shedding
    2. Flow around circle
    3. 3D constant flow
    4. Chapter-38: The net with angle
    5. Chapter-38-1-1: normal vectors
    6. Line integrals of vector fields: Flux
  25. Chapter 39
    1. Chapter 39: Exercise 3.2
  26. Chapter 40
    1. Surface plotter
    2. Surface plotter
    3. Parametrization
    4. Chapter 40: Example 40.3.1 Tangent plane
  27. Chapter 41
    1. Chapter-41: Smooth surface
  28. Chapter 42
    1. Chapter-42-2: Transformation (u^2-v^2, 2uv)
    2. Chapter-42-4: Example
    3. Transformations from R² to R²
  29. Chapter 43
    1. Chater-43-1: Normal unit vector on orientable surface
    2. Chapter-43-1: Non orientable surface - Mobius strip
    3. Chapter-43-1: Non orientable surface - Klein bottle
    4. Chapter-43-2: Flux surface
    5. Chapter-43-2: Flux approximation
    6. Chapter-43-2-1: Net outward flux
    7. Surface integral of a vector field over a surface
  30. Chapter 44
  31. Chapter 45
    1. Curl animation
    2. Chapter-45: Curl detector
  32. Chapter 46
    1. Chapter-46-2-1: Relation to Green's theorem
    2. Chapter-46: Stokes' theorem example
    3. Stokes' Theorem

1.

Chapter 1

  • 1. Chapter-01: Example 1.1
  • 2. Chapter-01: Example 1.2
  • 3. Chapter-01: Example 1.3
  • 4. Chapter-01: Example 1.6
  • 5. Chapter-01: Example 1.7

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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2.

Chapter 3

  • 1. Chapter-03: Example 3-3

2.1.

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3.

Chapter 7

  • 1. Chapter-07: Change of basis

3.1.

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4.

Chapter 11

  • 1. Chapter-11: Examples orthonormal basis
  • 2. Chapter-11: Gram-Schmidt process

4.1.

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4.2.

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5.

Chapter 12

  • 1. Chapter-12-1: Theorem
  • 2. Chapter-12-2: Fitting line
  • 3. Chapter-12-2: Least squares error
  • 4. Chapter-12-2: Column space A
  • 5. Chapter-12-2: Column space A image
  • 6. Chapter-12-5: Fitting curve to data
  • 7. Chapter-12-5: Quadratic fit

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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6.

Chapter 13

  • 1. Chapter-13-1: sinx fit curve
  • 2. Chapter-13: Fitting curve to data (Cat)

6.1.

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6.2.

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7.

Chapter 15

  • 1. Chapter-15: Geometry of eigenvalues & eigenvectors

7.1.

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8.

Chapter 19

  • 1. Diagonalization: Quadratic forms

8.1.

–

9.

Chapter 23

  • 1. Chapter-23: Riemann Integral
  • 2. Chapter 23-1: Surface
  • 3. Chapter 23-1: Surface & prisms
  • 4. Chapter-23-3-2: Example

9.1.

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9.2.

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9.3.

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9.4.

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10.

Chapter 24

  • 1. Fubini's theorem: Rectangular regions
  • 2. Chapter-24-2: Example
  • 3. Chapter-24-5: Vertical slabs
  • 4. Chapter-24-5: Horizontal slabs
  • 5. Chapter-24-6: Example

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 25

  • 1. Chapter 25-1-1: Example
  • 2. Chapter-25-2-1: Example testing
  • 3. Chapter-25-2-1: Example

11.1.

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11.2.

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11.3.

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12.

Chapter 26

  • 1. Chapter-26-1: Find volume
  • 2. Chapter-26-2: Example
  • 3. Chapter-26: how can we find the volume of any solid?

12.1.

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12.2.

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12.3.

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13.

Chapter 27


    This chapter does not contain any resources yet.

14.

Chatper 28

  • 1. Chapter-28: Polar plane
  • 2. Polar transformation
  • 3. Chapter-28-1: Example
  • 4. Chapter-28-2: Example
  • 5. Chapter-28-3: Example

14.1.

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14.2.

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14.3.

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14.4.

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14.5.

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15.

Chapter 29


    This chapter does not contain any resources yet.

16.

Chapter 30

  • 1. Chapter-30-2: Example
  • 2. Chapter-30-3: Example

16.1.

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16.2.

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17.

Chapter 31

  • 1. Chapter-31: Cylindrical coordinates
  • 2. Chapter-31: Cylindrical region
  • 3. Chapter-31-2: Example

17.1.

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17.2.

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17.3.

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18.

Chapter 32

  • 1. Chapter-32: Spherical coordinates
  • 2. Chapter-32: Spherical region
  • 3. Chapter-32-1: Simple example
  • 4. Chapter-32-3: Ice cream

18.1.

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18.2.

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18.3.

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18.4.

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19.

Chapter 33

  • 1. Chapter-33-1: Moment and Moment of inertia
  • 2. Chapter-33-1: Moment of inertia image
  • 3. Chapter-33-2: Hemisphere

19.1.

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19.2.

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19.3.

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20.

Chapter 34

  • 1. Vector Fields in 2D
  • 2. 2D Velocity fields
  • 3. Vector fields 3D
  • 4. 3D Velocity field

20.1.

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20.2.

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20.3.

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20.4.

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21.

Chapter 35

  • 1. Chapter-35-1: Integral
  • 2. Chapter-35-4-1: Example
  • 3. Line integrals of vector fields: Work & Circulation

21.1.

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21.2.

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21.3.

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22.

Chapter 36


    This chapter does not contain any resources yet.

23.

Chapter 37


    This chapter does not contain any resources yet.

24.

Chapter 38

  • 1. Vortex Shedding
  • 2. Flow around circle
  • 3. 3D constant flow
  • 4. Chapter-38: The net with angle
  • 5. Chapter-38-1-1: normal vectors
  • 6. Line integrals of vector fields: Flux

24.1.

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24.2.

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24.3.

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24.4.

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24.5.

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24.6.

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25.

Chapter 39

  • 1. Chapter 39: Exercise 3.2

25.1.

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26.

Chapter 40

  • 1. Surface plotter
  • 2. Surface plotter
  • 3. Parametrization
  • 4. Chapter 40: Example 40.3.1 Tangent plane

26.1.

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26.2.

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26.3.

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26.4.

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27.

Chapter 41

  • 1. Chapter-41: Smooth surface

27.1.

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28.

Chapter 42

  • 1. Chapter-42-2: Transformation (u^2-v^2, 2uv)
  • 2. Chapter-42-4: Example
  • 3. Transformations from R² to R²

28.1.

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28.2.

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28.3.

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29.

Chapter 43

  • 1. Chater-43-1: Normal unit vector on orientable surface
  • 2. Chapter-43-1: Non orientable surface - Mobius strip
  • 3. Chapter-43-1: Non orientable surface - Klein bottle
  • 4. Chapter-43-2: Flux surface
  • 5. Chapter-43-2: Flux approximation
  • 6. Chapter-43-2-1: Net outward flux
  • 7. Surface integral of a vector field over a surface

29.1.

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29.2.

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29.3.

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29.4.

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29.5.

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29.6.

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29.7.

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30.

Chapter 44


    This chapter does not contain any resources yet.

31.

Chapter 45

  • 1. Curl animation
  • 2. Chapter-45: Curl detector

31.1.

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31.2.

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32.

Chapter 46

  • 1. Chapter-46-2-1: Relation to Green's theorem
  • 2. Chapter-46: Stokes' theorem example
  • 3. Stokes' Theorem

32.1.

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32.2.

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32.3.

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