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. Online slides: https://www.dynamicmath.xyz/math2001/ Note: 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. 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

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