AMA1021: Mathematical Modelling

Andrew Brown, Dec 20, 2016

Table of Contents

  1. Taylor Expansion
    1. Taylor_Expansion
  2. Basis Expansion
    1. Basis_Expansion_0
    2. Basis_Expansion_1
    3. Basis_Expansion_2
  3. Partial Differentiation
    1. Partial Derivatives
    2. Illustrating Partial Derivatives
  4. Line Integrals
    1. Line Integrals

1.

Taylor Expansion

  • 1. Taylor_Expansion

1.1.

Taylor_Expansion

Add the terms in the Taylor Series one by one and comment on the agreement between f(x) and F(x)
– Andrew Brown

2.

Basis Expansion

Make the red line match the blue line, and work out what the sliders control!

  • 1. Basis_Expansion_0
  • 2. Basis_Expansion_1
  • 3. Basis_Expansion_2

2.1.

Basis_Expansion_0

Make the red vector match the blue vector- what do the sliders control?
– Andrew Brown

2.2.

–

2.3.

–

3.

Partial Differentiation

Work out what the sliders control!

  • 1. Partial Derivatives
  • 2. Illustrating Partial Derivatives

3.1.

Partial Derivatives

What is represented by the blue and green curves? how are they affected by the position of the sliders?
– Andrew Brown

3.2.

–

4.

Line Integrals

  • 1. Line Integrals

4.1.

Line Integrals

Work out using geometry and calculus the area of the green shaded area for the various positions of the sliders
– Andrew Brown

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