Cambridge International AS & A Level Mathematics Pure Mathematics 2 and 3 second edition
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Description
Contents
Reviews
Language
English
ISBN
9781510420816
Cover
Title Page
Copyright
Contents
Introduction
How to use this book
The Cambridge International AS & A Level Mathematics 9709 syllabus
1 Algebra
1.1 Operations with polynomials
1.2 Solution of polynomial equations
1.3 The modulus function
2 Logarithms and exponentials
2.1 Exponential functions
2.2 Logarithms
2.3 Graphs of logarithms
2.4 Modelling curves
2.5 The natural logarithm function
2.6 The exponential function
3 Trigonometry
3.1 Reciprocal trigonometrical functions
3.2 Compound-angle formulae
3.3 Double-angle formulae
3.4 The forms r cos(θ ± α ), r sin(θ ± α)
3.5 The general solutions of trigonometrical equations
4 Differentiation
4.1 The product rule
4.2 The quotient rule
4.3 Differentiating natural logarithms and exponentials
4.4 Differentiating trigonometrical functions
4.5 Differentiating functions defined implicitly
4.6 Parametric equations
4.7 Parametric differentiation
5 Integration
5.1 Integrals involving the exponential function
5.2 Integrals involving the natural logarithm function
5.3 Integrals involving trigonometrical functions
5.4 Numerical integration
6 Numerical solution of equations
6.1 Interval estimation − change-of-sign methods
6.2 Fixed-point iteration
6.3 Problems with the fixed-point iteration method
7 Further algebra
7.1 The general binomial expansion
7.2 Review of algebraic fractions
7.3 Partial fractions
7.4 Using partial fractions with the binomial expansion
8 Further calculus
8.1 Differentiating tan –1 x
8.2 Integration by substitution
8.3 Integrals involving exponentials and natural logarithms
8.4 Integrals involving trigonometrical functions
8.5 The use of partial fractions in integration
8.6 Integration by parts
8.7 General integration
9 Differential equations
9.1 Forming differential equations from rates of change
9.2 Solving differential equations
10 Vectors
10.1 Vectors in two dimensions
10.2 Vectors in three dimensions
10.3 Vector calculations
10.4 The angle between two vectors
10.5 The vector equation of a line
10.6 The intersection of two lines
10.7 The angle between two lines
10.8 The perpendicular distance from a point to a line
11 Complex numbers
11.1 Extending the number system
11.2 Working with complex numbers
11.3 Sets of points in an Argand diagram
11.4 The modulus−argument form of complex numbers
11.5 Sets of points using the polar form
11.6 Working with complex numbers in polar form
11.7 Complex exponents
11.8 Complex numbers and equations
Answers
Index
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