Understanding Pure Mathematics
$56.25

Understanding Pure Mathematics

By Thorning, Sadler
US$ 56.25
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Book Description

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.

Table of Contents
  • Front Cover
  • IFC
  • Title Page
  • Preface
  • Contents
  • Introductory work
    • The number line
    • Inequalities
    • Basic algebraic manipulation
    • Surds
    • Quadratics
    • 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
    • Quadratics
    • 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
    • The gradient of a curve
    • Differentiation of axn
    • Maximum, minimum and points of inflexion
    • Small changes
    • More about points of inflexion
  • 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
  • Answers
  • Index
  • IBC
  • Back Cover
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