MATH2001 - Calculus & Linear algebra II

Topic:Vectors 2D (Two-Dimensional), Vectors 3D (Three-Dimensional), Algebra, Calculus, Solids or 3D Shapes

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!

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

Chapter-01: Example 1.1

MATH2001 - Calculus & Linear algebra II

Table of Contents

Chapter 1

Chapter 3

Chapter 7

Chapter 11

Chapter 12

Chapter 13

Chapter 15

Chapter 19

Chapter 23

Chapter 24

Chapter 25

Chapter 26

Chatper 28

Chapter 30

Chapter 31

Chapter 32

Chapter 33

Chapter 34

Chapter 35

Chapter 38

Chapter 39

Chapter 40

Chapter 41

Chapter 42

Chapter 43

Chapter 45

Chapter 46

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