Further Maths A Level 2017

Nicola Trubridge, Oct 19, 2017

Table of Contents

  1. Matrix Transformation 2D
    1. Matrix Transformations 2x2
    2. 2x2 Matrix Transformation
    3. Matrix Transformations
    4. Linear Transformations v2
  2. Determinants and Inverses
    1. Determinants and inverse matrices
  3. Matrix Transformation 3D
    1. Matrix transformations 3D
  4. Invariant lines
    1. Invariant lines of Matrix Transformations
    2. Eigenvalues & Eigenvectors
    3. Eigenvalues & Eigenvectors calculator
    4. Eigenvalues & Eigenvectors (3 by 3)
  5. Series
    1. Maclaurin series approximations
    2. Maclaurin polynomials
    3. Maclaurin series for sinx
    4. Maclaurin polynomials
  6. A2 Ch 8.Series and Limits
    1. Finding and using Maclaurin series
    2. L'Hopital's Rule Visual
    3. Verification of L'Hopital's Rule
    4. Visual Demo of L'Hopitals Rule
    5. Visualizing L'Hopital's Rule
  7. A2 Ch 12. First order DE
    1. Slope Field Ex 12.3
    2. Slope Field Ex 12.4
  8. A2 Ch13. Numerical Methods
    1. Definite Integral Illustrator
    2. Simpsons Rule
    3. Comparing Numeric Integration Methods
    4. Numerical Integration
    5. Numeric Integration
    6. Numeric Integration LR
    7. Simpson's Rule Example 2
    8. Euler's Method
    9. Euler's Method
    10. Euler's Method
  9. A2 Ch 16. Differential Equations
    1. The (linearly) damped motion of a spring
    2. Free Vibrations with Damping
    3. Forced Vibrations With Damping
    4. Damped harmonic oscillator (small screens)
    5. Second Order Linear DE solver
    6. 2nd order differential equations
    7. EX16.3 Further SHM Calculations
    8. Simple Harmonic Motion

1.

Matrix Transformation 2D

  • 1. Matrix Transformations 2x2
  • 2. 2x2 Matrix Transformation
  • 3. Matrix Transformations
  • 4. Linear Transformations v2

1.1.

Matrix Transformations 2x2

What stays the same, what is different when the sliders are changed?[br]What effect does the determinant have on the area?[br]What happens if the determinant is 0?[br]What does it mean if there is a negative determinant?
– Nicola Trubridge

1.2.

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1.3.

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1.4.

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2.

Determinants and Inverses

  • 1. Determinants and inverse matrices

2.1.

Determinants and inverse matrices

– Nicola Trubridge

3.

Matrix Transformation 3D

  • 1. Matrix transformations 3D

3.1.

Matrix transformations 3D

– Nicola Trubridge, Juan Carlos Ponce Campuzano

4.

Invariant lines

  • 1. Invariant lines of Matrix Transformations
  • 2. Eigenvalues & Eigenvectors
  • 3. Eigenvalues & Eigenvectors calculator
  • 4. Eigenvalues & Eigenvectors (3 by 3)

4.1.

Invariant lines of Matrix Transformations

– Nicola Trubridge, GeoGebra Institute of MEI

4.2.

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4.3.

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4.4.

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5.

Series

  • 1. Maclaurin series approximations
  • 2. Maclaurin polynomials
  • 3. Maclaurin series for sinx
  • 4. Maclaurin polynomials

5.1.

Maclaurin series approximations

The diagram shows the Maclaurin series approximation to degree n for the exponential function. The exponential function is shown in red and the Maclaurin series approximation function is shown in blue. Move point A to see the error in the approximation at different points.[br][br]Use the slider to change the value of n.[br][br]You can use the toolbar to zoom in and out, or move the drawing pad to look at different parts of the graph.[br][br]Click the checkbox to look at the values of the derivatives at point A. In particular, compare the values when A has x-coordinate 0.
Maclaurin series approximations
– Integral Resources

5.2.

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5.3.

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5.4.

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6.

A2 Ch 8.Series and Limits

  • 1. Finding and using Maclaurin series
  • 2. L'Hopital's Rule Visual
  • 3. Verification of L'Hopital's Rule
  • 4. Visual Demo of L'Hopitals Rule
  • 5. Visualizing L'Hopital's Rule

6.1.

Finding and using Maclaurin series

1. Construct a straight line [math]y=a+bx[/math] which is a good approximation at the point where [math]x=0[/math][br][br]2. Find a quadratic [math]y=a+bx+cx^2[/math] which is a good approximation to [math]y=e^x[/math] [br][br][i]It should go through (0,1), in addition it should have the same derivative at (0,1) and the same second derivative at (0,1)[/i]
– Nicola Trubridge

6.2.

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6.3.

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6.4.

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6.5.

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7.

A2 Ch 12. First order DE

  • 1. Slope Field Ex 12.3
  • 2. Slope Field Ex 12.4

7.1.

Slope Field Ex 12.3

Enter your derivative. Use the sliders to change the length and density of the segments in the slope field.
– Nicola Trubridge, Steve Phelps

7.2.

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8.

A2 Ch13. Numerical Methods

  • 1. Definite Integral Illustrator
  • 2. Simpsons Rule
  • 3. Comparing Numeric Integration Methods
  • 4. Numerical Integration
  • 5. Numeric Integration
  • 6. Numeric Integration LR
  • 7. Simpson's Rule Example 2
  • 8. Euler's Method
  • 9. Euler's Method
  • 10. Euler's Method

8.1.

Definite Integral Illustrator

[b]Note: [/b][color=#0000ff]This applet only generates non-negative areas. [br]Thus, incorrect values will be displayed for any areas underneath the [i]x[/i]-axis. [/color]
– Nicola Trubridge, Tim Brzezinski

8.2.

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8.3.

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8.4.

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8.5.

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8.6.

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8.7.

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8.8.

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8.9.

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8.10.

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9.

A2 Ch 16. Differential Equations

  • 1. The (linearly) damped motion of a spring
  • 2. Free Vibrations with Damping
  • 3. Forced Vibrations With Damping
  • 4. Damped harmonic oscillator (small screens)
  • 5. Second Order Linear DE solver
  • 6. 2nd order differential equations
  • 7. EX16.3 Further SHM Calculations
  • 8. Simple Harmonic Motion

9.1.

The (linearly) damped motion of a spring
– A. G. Gomez (agg29@ou.ac.uk)

9.2.

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9.3.

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9.4.

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9.5.

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9.6.

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9.7.

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9.8.

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