$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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