\$62.48

# Introducing Pure Mathematics

By Garry Wiseman, Robert Smedley, Ian Cook, Graham Upton, Thorning, Sadler
US\$ 62.48
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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.

• Front Cover
• Title Page
• Contents
• Preface
• 1 Algebra
• Linear equations
• Linear inequalities
• Simutaneous linear equations
• Completing the square
• Discriminant of a quadratic equation
• Sketching the graph of a quadratic function
• Maxima and minima
• Further simultaneous equations
• 2 Geometry
• Pythagoras’ theorem
• Trigonometric ratios
• Three-dimensional appications
• Sine and cosine rules
• Plane shapes
• 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
• 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
• 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
• Index
• Back Cover
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