Oxford International AQA Examinations: International A Level Further Mathematics with Mechanics

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Description

Contents

Reviews

Language

English

ISBN

9780198411369

Front Cover

Title Page

Contents

AS Pure

1 Loci, Graphs and Algebra

1.1 Loci

1.2 Rational functions

1.3 Conic sections

Summary

Review exercises

Practice examination questions

2 Complex Numbers

2.1 What is a complex number?

2.2 Calculating with complex numbers

2.3 Argand diagram

2.4 Loci in the complex plane

Summary

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3 Roots and Coefficients of a Quadratic Equation

3.1 Roots of a quadratic equation

3.2 Finding an equation with roots that area function of existing roots

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4 Series

4.1 Summation formulae

4.2 Method of differences

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5 Trigonometry

5.1 General solutions of trigonometric equations

5.2 Solving equations involving more complicated terms

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6 Calculus

6.1 Gradient of a tangent to a curve

6.2 Rates of change

6.3 Improper integrals

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7 Matrices and Transformations

7.1 Introduction to matrices

7.2 Transformations

7.3 Common transformations

7.4 Invariant points and lines

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8 Linear Graphs

8.1 Relationship between data

8.2 When the power of x is unknown, or when x is in the exponent

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9 Numerical Methods

9.1 Solutions of polynomial equations

9.2 Step-by-step solution of differential equations

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10 Bayes’ Theorem

10.1 Tree diagrams

10.2 Bayes’ Theorem

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11 Discrete Uniform and Geometric Distributions

11.1 Discrete uniform distribution

11.2 Geometric distribution

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12 Probability Generating Functions

12.1 Probability generating functions and their properties

12.2 Some standard distributions

12.3 Sums of independent random variables

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13 Linear Combinations of Discrete Random Variables

13.1 Linear combinations of discrete random variables

13.2 Independent discrete random variables

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14 Constant Velocity in Two Dimensions

14.1 Vectors in component form

14.2 Position, displacement, distance,velocity and speed

14.3 Resultant velocity

14.4 Relative velocity, closest approach and interception

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15 Dimensional Analysis

15.1 Dimensions and dimensional consistency

15.2 Finding a formula

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16 Collisions in One Dimension

16.1 Impulse and momentum

16.2 The principle of conservation of linear momentum

16.3 Elastic impact

16.4 Multiple collisions

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A2 Pure

17 Roots and Polynomials

17.1 Roots of higher-order equations

17.2 Complex roots of a polynomial equation

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18 Proof by Induction and Finite Series

18.1 Proof by induction

18.2 Finite series

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19 Series and Limits

19.1 Convergence

19.2 Maclaurin’s theorem

19.3 Finding the limits of a series

19.4 Improper integrals

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20 De Moivre’s Theorem

20.1 De Moivre’s theorem

20.2 Further applications of de Moivre’s theorem to complex numbers

20.3 Trigonometric identities

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21 Polar Coordinates

21.1 Position of a point

21.2 Sketching curves given in polar coordinates

21.3 Area of a sector of a curve

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22 The Calculus of Inverse Trigonometrical Functions

22.1 Inverse trigonometric functions

22.2 Differentiation and integration of inverse trigonometric functions

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23 Arc Length and Area of Surface of Revolution

23.1 Arc length

23.2 Area of a surface of revolution

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24 Hyperbolic Functions

24.1 Hyperbolic functions

24.2 Differentiation of hyperbolic functions

24.3 Inverse hyperbolic functions

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25 Differential Equations of First and Second Order

25.1 First-order linear equations

25.2 Second-order differential equations

25.3 Using a complementary function and particular integral to solve a first order equation

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26 Vectors and Three-Dimensional Coordinate Geometry

26.1 Vectors

26.2 Vector product

26.3 Applications of vectors to coordinate geometry

26.4 Equation of a line

26.5 Equation of a plane

26.6 Scalar triple product and its applications

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27 Solutions of Linear Equations

27.1 Simultaneous linear equations

27.2 Using determinants to find the number of solutions of three simultaneous equations

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28 Matrix Algebra

28.1 Inverse matrices

28.2 Transformations

28.3 Invariant points and lines

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A2 Mechanics

29 Vertical Circular Motion

29.1 Circular motion with non-uniformspeed

29.2 Leaving the circular path

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30 Collisions in Two Dimensions

30.1 Impulse and momentum in two dimensions

30.2 Elastic impact

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31 Projectiles Launched onto Inclined Planes

31.1 Inclined plane

31.2 Other problems

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32 Elastic Strings and Springs

32.1 Elastic strings and springs

31.2 Work and energy

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33 Application of Differential Equations

33.1 Variable forces

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34 Simple Harmonic Motion

34.1 Oscillation

34.2 Solving the SHM equation of motion

34.3 Simple pendulum

Summary

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Answers

Index

Back Cover

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