503609
Description
Mind Map by declanlarkins, updated more than 1 year ago
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Mathematics:
Further Pure 2
- Rational Functions and Graphs
- Relationship between y=f(x) and y-squared =f(x)
- Features
- Asymptotes
- Restrictions
- Turning points
- Points of intersection
- Asymptotes
- Partial fractions
Annotations:
- Includes top-heavy fractions and quadratics in the denominator which can't be factorised eg. (\(x^2\)+\(a^2\))
- Relationship between y=f(x) and y-squared =f(x)
- Polar Coordinates
- Identify features of polar curves
- Symmetry
- Max/min r values
- Tangents at pole
- Symmetry
- Sketch polar curves
- Relationship between
polar and cartesian
- Integrate to find area of a sector
Annotations:
- \(\frac{1}{2}\)\(\int\)\(r^2\)d\(\theta\)
- Identify features of polar curves
- Hyperbolic Functions
- Derive and use ientities
Annotations:
- \(cosh^2\)x-\(sinh^2\)x = 1 sinh2x=2sinhxcoshx
- Sketch graphs of hyperbolic functions
- Inverse hyperbolics
- Derive and use expressions
in terms of logarithm
- Derive and use expressions
in terms of logarithm
- Define hyperbolic
functions in terms
of exponentials
- Derive and use ientities
- Differentiation and Integration
- Use Maclaurin series of
e^x, sinx, cosx and ln(1+x)
- Derive and use the
derivatives of hyperbolics
- Derive and use derivatives of inverse trig
- Derive and use the first
few terms of the Maclaurin
series of simple functions
- Integrate given expressions
and use trip or hyperbolic
substitutions to integrate
Annotations:
- Integrate: \(\frac{1}{\sqrt(a^2-x^2)}\)\(\frac{1}{\sqrt(x^2-a^2)}\)\(\frac{1}{\sqrt(x^2+a^2)}\)\(\frac{1}{(a^2+x^2)}\)
- Derive and use reduction
formulae to integrate
- Approximate area under a
curve using rectangles and
use to set bounds for the area
- Use Maclaurin series of
e^x, sinx, cosx and ln(1+x)
- Numerical Methods
- Convergence (and failure) of iterative formulae
- Staircase
- Cobweb
- Staircase
- Errors
- The ratio of two errors is approximately F'(X)
- The subsequent
error is proportional
to the previous error
squared if F'(X) = 0
- The ratio of two errors is approximately F'(X)
- Newton-Raphson
- When does it fail?
- When does it fail?
- Derive and use Newton-Raphson iterations
- Convergence (and failure) of iterative formulae
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