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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