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Summary
Summary
This is a comprehensive pre-degree maths text for vocational courses and foundation modules at degree level. John Bird's approach, based on numerous worked examples supported by problems, is ideal for students of a wide range of abilities, and can be worked through at the student's own pace. Theory is kept to a minimum, placing a firm emphasis on problem-solving skills, and making this a thoroughly practical introduction to the core mathematics needed for engineering studies and practice. The book presents a logical topic progression, rather than following the structure of a particular syllabus. However, coverage has been carefully matched to the two mathematics units within the new BTEC National specifications and AVCE specifications. New sections on Boolean algebra and logic circuits have been added to ensure full syllabus match. multiple choice questions, and 15 assessment papers. Throughout the book assessment papers are provided that are ideal for use as tests or homework. These are the only problems where answers are not provided in the book.
Table of Contents
| Number and Algebra |
| Revision of fractions, decimals and percentages |
| Indices, standard form and engineering notation |
| Computer numbering systems |
| Calculations and evaluation of formulae |
| Algebra |
| Further algebra |
| Partial fractions |
| Simple equations |
| Simultaneous equations |
| Transposition of formulae |
| Quadratic equations |
| Inequalities |
| Logarithms |
| Exponential functions |
| Number sequences |
| Binomial theorem |
| Solving equations by iterative methods |
| Mensuration: |
| Areas of plane figures |
| The circle and its properties |
| Volumes and surface areas of common solids |
| Irregular areas and volumes and mean values of waveforms |
| Trigonometry: |
| Introduction to trigonometry |
| Trigonometric waveforms |
| Cartesian and polar co-ordinates |
| Triangles and some practical applications |
| Trigonometric identities and equations |
| Compound angles |
| Graphs: |
| Straight line graphs Reduction of non-linear laws to linear form |
| Graphs with logarithmic scales |
| Graphical solution of equations |
| Functions and their curves |
| Vectors: |
| Vectors |
| Combination of waveforms |
| Complex numbers: |
| Complex numbers |
| De Moivres theorem |
| Statistics: |
| Presentation of statistical data |
| Measures of central tendency and dispersion |
| Probability |
| The binomial and Poisson distributions |
| The normal distribution |
| Differential calculus: |
| Introduction to differentiation |
| Methods of differentiation |
| Some applications of differentiation |
| Differentiation of parametric equations |
| Differentiation of implicit functions |
| Logarithmic differentiation |
| Integral calculus: |
| Standard integration |
| Integration using algebraic substitutions |
| Integration using trigonometric substitutions |
| Integration using partial fractions |
| The t = tan substitution |
| Integration by parts |
| Numerical integration |
| Areas under and between curves |
| Mean and root mean square values |
| Volumes of solids of revolution |
| Centroids of simple shapes |
| Second moments of area |
| Further number and algebra: |
| Boolean algebra and logic circuits |
| The theory of matrices and determinants |
| The solution of simultaneous equations by matrices and determinants |
| Differential equations: |
| Introduction to differential equations |
| Index |
