**Mathematics: A Second Start 2nd Edition by S. Page, ISBN-13: 978-1898563044**

[PDF eBook eTextbook]

- Publisher: Woodhead Publishing; 2nd edition (September 1, 2002)
- Language: English
- 480 pages
- ISBN-10: 1898563047
- ISBN-13: 978-1898563044

Provides less mathematically minded students with a gentle introduction to basic mathematics and some more advanced topics. Covering algebra, trigonometry, calculus and statistics, it manages to combine clarity of presentation with liveliness of style and sympathy for students’ needs. It is straightforward, pragmatic and packed full of illustrative examples, exercises and self-test questions. The essentials of formal mathematics are lucidly explained, with terms such as ‘integral’ or ‘differential equation’ fully clarified.

**Table of Contents:**

Copyright Page

Table of Contents

Mathematics: A Second Start, 2nd edition

Preface to Second Edition

Introduction to the First Edition

Chapter 0. Using a Scientific Calculator

INTRODUCTION

GETTING TO KNOW YOUR CALCULATOR

CALCULATING WITH YOUR CALCULATOR

Chapter 1. The Set of Real Numbers

NUMBERS AND SYMBOLS

SETS AND SUBSETS

THE NATURAL NUMBERS

THE BASIC LAWS OF NATURAL NUMBERS

IRRATIONAL NUMBERS

SUMMARY

Chapter 2. Number Skills

WORKING WITH DIRECTED NUMBERS

WORKING WITH FRACTIONS

Chapter 3. Algebra: a Basic Toolkit

WHY LEARN ALGEBRA?

THE FOUR RULES

SIMPLE SUBSTITUTION

ADDITION AND SUBTRACTION OF ALGEBRAIC TERMS

MULTIPLICATION AND DIVISION OF **ALGEBRAIC** QUANTITIES

Chapter 4. Algebra: More Tools

THE THREE RULES OF INDICES

SURDS

Chapter 5. Products

THE BINOMIAL SERIES

Chapter 6. Factors

SPECIAL CASES

Chapter 7. Equations and Inequalities

MAINTAINING THE BALANCE

SUMMARY

INTERVALS AND INEQUALITIES

PROPERTIES OF INEQUALITIES

SOLUTION OF INEQUALITIES

MODULUS OR ABSOLUTE VALUE

Chapter 8. Manipulation of Formulae

INTRODUCTION

SUBSTITUTION

TRANSPOSITION

A SYSTEMATIC METHOD FOR TRANSPOSING

ELIMINATION

Chapter 9. Quadratic Equations

ZERO PRODUCTS

SOLUTION OF QUADRATIC EQUATIONS

Chapter 10. Simultaneous Equations

INTRODUCTION

SOLUTION BY ELIMINATION

SOLUTION BY SUBSTITUTION

SOLUTION IF ONE OF THE EQUATIONS IS NOT LINEAR

PROBLEMS LEADING TO SIMULTANEOUS EQUATIONS

Chapter 11. Indices and Logarithms

FURTHER INDICES

LOGARITHMS

Chapter 12. Functions and Graphs

FUNCTIONS

COMPOSITE FUNCTIONS

GRAPHS OF FUNCTIONS

Chapter 13. Linear Graphs and Their Use in Experimental Work

THE STRAIGHT LINE LAW

TO FIND LINEAR LAWS IN PRACTICAL CASES

Chapter 14. Calculus – the Mathematics of Change

LIMITS – THE BACKGROUND TO **CALCULUS**

THREE IMPORTANT ‘FRACTIONS’

THE BEGINNINGS OF RELATIVE GROWTH

Chapter 15. Applications of Differentiation

RATES OF CHANGE WITH RESPECT TO TIME

STATIONARY VALUES

HOW TO DIFFERENTIATE MORE DIFFICULT EXPRESSIONS

Chapter 16. Integration

INTEGRATION AS THE LIMIT OF A SUM

AREAS: DEFINITE INTEGRALS

SOLIDS OF REVOLUTION

Chapter 17. Introduction to Trigonometry

THE SINE, COSINE AND TANGENT OF AN ANGLE

USING A CALCULATOR

ANGLES OF ANY MAGNITUDE

EQUIVALENT ANGLES

TRIGONOMETRIC RATIOS FOR ANGLES OF ANY MAGNITUDE

TRIGONOMETRIC RATIOS WHEN OP LIES ON THE AXES

THE ASSOCIATED ACUTE ANGLE

USE OF CALCULATORS

GRAPHS OF THE TRIGONOMETRIC RATIOS

TO FIND ALL THE ANGLES WITH A GIVEN SIN, COS OR TAN

THE MINOR RATIOS

GRAPHS

USE OF CALCULATOR WITH THE MINOR RATIOS

THE THEOREM OF PYTHAGORAS

Chapter 18. Calculus of Trigonometry

RADIANS: A NEW WAY OF MEASURING ANGLES

THE ADDITION FORMULAE

SMALL ANGLES

DIFFERENTIATION OF TRIGONOMETRIC FUNCTIONS

Chapter 19. The Law of Natural Growth

COMPOUND INTEREST

DIFFERENTIATION AND INTEGRATION OF THE FUNCTION y = ex

DIFFERENTIATION OF y = ln x

GRAPHS OF ex, e-x, In x

THE EXPONENTIAL FUNCTION AND THE LAW OF NATURAL GROWTH

Chapter 20. Some Applications of Logarithms

USE OF LOGARITHMS TO LINEARISE GRAPHS

THE USE OF LOGARITHMIC GRAPH PAPER

DIFFERENTIATION OF LOGARITHMIC FUNCTIONS

Chapter 21. A First Look at Statistics

ON THE AVERAGE

THE MEAN

CODING

SAMPLING

FREQUENCY DISTRIBUTIONS

DISCRETE AND CONTINUOUS MEASUREMENTS, GROUPING

TALLY MARKS

GRAPHICAL REPRESENTATION OF FREQUENCY DISTRIBUTIONS

MEASURES OF SPREAD

VARIANCE AND STANDARD DEVIATION

Chapter 22. Probability

CHANCE, PROBABILITY AND POSSIBILITY

POSSIBILITY

EQUIPROBABLE EVENTS

THE LAWS OF PROBABILITY

SUMMARY OF PROBABILITY LAWS

PROBABILITY TREES

Chapter 23. Probability Distributions

TYPES OF PROBABILITY DISTRIBUTIONS

STANDARD DEVIATION AND THE NORMAL CURVE

THE STANDARD NORMAL DISTRIBUTION

GRAPH OF THE STANDARD NORMAL CURVE

SAMPLING FROM NORMAL POPULATIONS

CONFIDENCE INTERVALS AND SAMPLING

THE 95% CONFIDENCE INTERVAL

Appendix

Answers

Index

* Sheila Page *is a professor of mathematics at the University of Bradford, England. John Berry is professor of mathematics education at the University of Plymouth, England, and director of the Center for Teaching Mathematics.

* Howard Hampson* is head of the department of mathematics at Further Education College, Torquay.

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