Introducing Pure Mathematics

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Description

Contents

Reviews

Language

English

ISBN

9781382018173

Front Cover

Title Page

Contents

Preface

1 Algebra

Linear equations

Linear inequalities

Simutaneous linear equations

Quadratic equations

Completing the square

Quadratic formula

Discriminant of a quadratic equation

Disguised quadratic equations

Sketching the graph of a quadratic function

Maxima and minima

Quadratic inequalities

Further simultaneous equations

2 Geometry

Pythagoras’ theorem

Trigonometric ratios

Three-dimensional appications

Sine and cosine rules

Plane shapes

Radian measure

Volume

3 Functions

Transformation of the graph of a fuction

Mappings

Modulus function

Even and odd functions

Periodic functions

Composite functions

Inverse fuctions

4 Polynomials

Addition and subraction of polynomials

Multipication of polynomials

Dividing polynomials

Factorising polynomials

5 Coordinate geometry

Distance between two points

Mid-point of a straight line

Gradient of a straight line

Parallel and perpendicular lines

General equation of a straight

Distance of a point from a line

Intersection of two straight lines

Angle between two straight lines

6 Differentiation I

Gradients of curves

Differentiation from first principles

Sum or difference of two functions

Second derivative

Tangents and normals to a curve

Maximum, minimum and point of inflexion

Second derivative and stationary points

Increasing and decreasing functions

Practical applications of maxima and minima

7 Integration I

Area under a curve

Area between a curve and the y-axis

Area between two curves

Volume of revolution about the x-axis

Volumes of revolution about other axes

8 The circle

Tangents to a circle

Intersection of two circles

9 Sequences and series

Convergent and divergent

Oscillating sequences

Periodic sequences

Series and sigma notation

Convergent and divergent series

Arithmetic progressions

Infinite geometric progresions

Mixed example

10 Binomial expansions

Binomial theorem for a positive integral index

Expansion of (a+x)n

Approximations

Binomial theorem when n is not a positive integer

11 Algebraic fractions

Partial fractions

Application of partial fractions to series expansion

12 Differentiation II

Function of a function

Inverse function of a function (integration of f’(x)[f(x)]n)

Product rule

Quotient rule

Applications

13 Differentiation III

Implicit functions

Parametric equations

Rates of change

14 Trigonometry I

Trigonometric functions

Trigonometric equations

Standard trigonometric identities

Further trigonometric equations

Proving trigonometric identities

15 Trigonometry II

Compound angles

Double angles

Half-angle and other formulae

Factor formulae

Radians

16 Calculus with trigonometry

Differentiation of Sin x and Cos x

Differentiation of sin nx and cos nx

Differentiation of sinnx and cosnx

Differentiation of tan x, cosec x, sec x and cot x

17 Indices and logarithms

Indices

Surds

Logarithms

18 Calculus with exponentials and logarithms

Exponential functions

Natural logarithms

Definite integrals involving logarithms

Applications

19 Integration II

Change of variable

Standard forms

Using partial fractions

Integration by parts

Integral of tan x, cosec x, sec x and cot x

Further results

Differential equations

Application to exponential laws of growth and decay

20 Numerical methods

Numerical solution of equations

Graphical methods

Iterative methods

Trapezium rule

Simpsons rule

21 Vectors

Addition and subracton of vectors

Position vectors

Scalar product

Vector equation of a line

22 Proof

Impication between mathematical statements

Disproving statements

Proof by contradiction

Answer

Index

Back Cover

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