Introducing Pure Mathematics
$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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