\$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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