Oxford University Press
Education & Teaching
Understanding Pure Mathematics
US\$ 69.02
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Description
Contents
Reviews

A classic single-volume textbook, popular for its direct and straightforward approach. Understanding Pure Mathematics starts by filling the gap between GCSE and A Level and builds on this base for candidates taking either single-subject of double-subject A Level.

Language
English
ISBN
9781382018203
Front Cover
IFC
Title Page
Preface
Contents
Introductory work
The number line
Inequalities
Basic algebraic manipulation
Surds
Trigonometric ratios of acute and obtuse angles
Solution of triangles
Three-dimensional trigonometry
1 Functions
Basic concepts
Composite functions
The inverse of a function
Ordered pairs
The graph of a function
Some further considerations
2 Vectors
Basic concepts
Position vectors and unit vectors
The scalar product
Geometrical proofs by vector methods
The vector equation of a straight line
3 Coordinate geometry I
Loci
Distance between two points
Mid-point of a line joining two points
Gradient of a line joining two points
Parallel and perpendicular lines
The equation y = mx + c
Finding the cartesian equation of a straight line
Relationships shown as linear graphs
Intersection of lines
4 Trigonometry I
Trigonometric ratios of any angle
Trigonometric graphs
Graph sketching
Solving trigonometric equations
Pythagorean relationships
Secant, cosecant and cotangent
Compound angles
Circular measure
5 Algebra I
Indices
Variation
Elementary theory of logarithms
Polynomials in general
6 Matrices
Basic Concepts
Transformations
Further considerations
General reflections and rotations
7 Permutations and combinations
Successive operations
Permutations
Combinations
Selections of any size from a group
Division into groups
8 Series and the binomial theorem
Arithmetic progressions
Geometric progressions
Summation of other series and proof by induction
The binomial theorem for a positive integral index
The binomial theorem for any rational index
9 Probability
Simple probability
Sum and product laws
Further conditional probability
Probability involving permutations and combinations
10 Calculus I: Differentiation
Differentiation of axn
Maximum, minimum and points of inflexion
Small changes
11 Sketching functions I
General methods
Further considerations
Simple transformations
1/f(x)
12 Calculus II: Integration
The reverse of differentiation
The area under a curve
Volume of revolution
Two applications
Mean value of a function
13 Calculus III: Further techniques
Function of a function
Integration of f’(x)[f(x)]n
Related rates of change
Parameters
Product rule
Quotient rule
Implicit functions
14 Sketching functions II
Rational functions
Inequalities
15 Trigonometry II
Sum and product formulae
a cos x + b sin x
Inverse trigonometric functions
General solutions
Small angles
Differentiation of trigonometric functions
Integration of trigonometric functions
Differentiation of inverse trigonometric functions
16 Coordinate geometry II
Angle between two straight lines
Distance of a point from a line
The circle
The parabola
The ellipse and the hyperbola
Polar coordinates
17 Three-dimensional work: vectors and matrices
Three-dimensional work
Differentiation and integration of vectors
Equations of a straight line in 3-D
Equations of a plane
3 x 3 Matrices
Sets of linear equations
18 Algebra II
Partial fractions
Partial fractions and series
Complex numbers
19 Exponential and logarithmic functions
Differentiating the exponential function
The logarithmic function
The exponential series
The logarithmic series
20 Calculus IV: Further integration
Change of variable
Integration by parts
General methods
Differential equations
21 Numerical methods
The trapezium rule
Simpson’s rule
Taylor’s theorem
Maclaurin’s theorem
Solution of equations
ez, cos z and sin z for complex z
Index
IBC
Back Cover
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