$58.49

# Introducing Pure Mathematics

By Garry Wiseman, Robert Smedley, Ian Cook, Graham Upton, Thorning, Sadler

US$ 58.49

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Book Description

This text is clearly set out with an excellent combination of clear examples and explanations, and plenty of practice material - ideal for supporting students who are working alone. Each chapter concludes with a selection of exam-style questions, giving students lots of practice for the real thing.

Table of Contents

- 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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