Essential Specialist Mathematics Third Edition Teacher CD-Rom

by Michael Evans , Josian Astruc , Sue Avery , Neil Cracknell , Peter Jones

• ISBN13: 9780521611169
• ISBN10: 0521611164
• Format: CD
• Copyright: 2006-08-01
• Publisher: Cambridge University Press

Summary

Essential Mathematics provides a single unified course of study which addresses all the key skills outcomes.

Table of Contents

Introduction

A toolbox

Circular functions

Solving right-angled triangles

The sine and cosine rules

Geometry prerequisites

Sequences and series

Circles

Ellipses and hyperbolae

Vectors

Introduction to vectors

Resolution of a vector into rectangular components

Scalar (or dot) product of vectors

Vector resolutes

Vector proofs

Circular functions

The tangent function

The reciprocal circular functions

Compound and double angle formulae

Inverses of circular functions

Solution of equations

Complex numbers

The set of complex numbers, C

The complex conjugate and division

The modulus-argument form of a complex number

Basic operations on complex numbers in the modulus-argument form

Factorisation of polynomials in C

Solution of polynomial equations

Using De Moivre's theorem to solve equations in the form zn=a where a = C

Relations and regions of the complex plane

Revision of chapters 2-4

Summary of chapters 2-4

Short answer questions

Multiple choice questions

Analysis questions

Differentiation and rational functions

A review

Derivatives of x=f(y)

Derivatives of inverse circular functions

Second derivatives

Related rates

Graphs of some rational functions

A summary of differentiation

Implicit differentiation

Antidifferentiation

Antidifferentiation

Antiderivatives involving inverse circular functions

Integration by substitution

Definite integrals by substitution

Use of trigonometric identities for integration

Partial fractions

Further techniques and miscellaneous exercises

Applications of integration

Areas of regions

Area of a region between two curves

Integration using a graphics calculator

Volumes of solids of revolution

Numerical methods of integration

Differential equations

An introduction to differential equations

Solution of differential equations of the form dy/dx=f(x) and d2y/dx2=f(x)

The solution of differential equations of the form dy/dx=f(y)

Application of differential equations

Differential equations with related rates

A numerical solution to a differential equation

Kinematics

Position velocity and acceleration

Constant acceleration

Velocity time graphs

Differential equations of the form v=f(x) and a=f(v)

Other expressions for acceleration

Revision of chapters 6-10

Summary of chapters 6-10

Short answer questions

Multiple choice questions

Analysis questions

Vector functions

Vector equations

Position vectors as a function of time

Vector calculus

Velocity and acceleration for motion along a curve

Distance travelled by a particle along a curve

Dynamics

Force

Newton's laws of motion

Resolution of forces and inclined planes

Connected particles

Variable forces

Equilibrium

Friction and equilibrium

Vector functions

Revision of chapters 12-13

Summary of chapters 12-13

Short answer questions

Multiple choice questions

Analysis questions

Graphics calculator appendix 1

Answers

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