Cambridge International AS & A Level Further Mathematics Further Pure Mathematics 2
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Description
Contents
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Language
English
ISBN
9781510422056
Cover
Title Page
Copyright
Contents
Introduction
How to use this book
The Cambridge International AS & A Level Mathematics 9709 syllabus
1 Hyperbolic functions
1.1 Hyperbolic functions
1.2 Inverse hyperbolic functions
2 Matrices
2.1 Important results relating to 2 × 2 matrices
2.2 Finding the inverse of a 3 × 3 matrix
2.3 Intersection of three planes
2.4 Eigenvalues and eigenvectors
3 Differentiation
3.1 Differentiating inverse trigonometric functions
3.2 Differentiating hyperbolic functions
3.3 Differentiating inverse hyperbolic functions
3.4 Finding the second derivative for relations given implicitly
3.5 Finding the second derivative for relations given parametrically
3.6 Polynomial approximations and Maclaurin series
3.7 Using the Maclaurin series for standard functions
4 Integration
4.1 Integration using the inverse sine function
4.2 Integrating hyperbolic functions
4.3 Integration using inverse hyperbolic functions
4.4 Integration using reduction formulae
4.5 Approximation of areas using rectangles
4.6 Using areas under curves to approximate series sums
4.7 The arc length of a curve
4.8 Surface area of a solid of revolution
5 Complex numbers
5.1 The modulus and argument of a complex number
5.2 De Moivre’s theorem
5.3 The nth roots of a complex number
5.4 Finding multiple angle identities using de Moivre’s theorem
5.5 The form z = re iθ
6 Differential equations
6.1 Integrating factors
6.2 Second order differential equations
6.3 Auxiliary equations with complex roots
6.4 Non-homogeneous differential equations
6.5 Use of substitutions to transform differential equations
Index
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