Introducing Pure Mathematics
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Description
Contents
Reviews
Language
English
ISBN
9781382018173
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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