文件名称：Introductory Mathematics for the Life Sciences
文件大小：3.12MB
文件格式：PDF
更新时间：2012-06-15 15:14:43
Mathematic
1 Numbers 1 1.1 Introduction 1 1.2 Real numbers 1 1.3 Modulus 3 1.4 Functions with multiple operations 4 1.5 Commutative and associative laws of addition and multiplication 5 Summary 7 End of unit questions 8 2 Fractions, Percentages and Ratios 9 2.1 Introduction 9 2.2 Fractions—rational and irrational numbers 9 2.3 Factorisation and equivalent fractions 11 2.4 Addition and subtraction of fractions 14 2.5 Multiplication of fractions 15 2.6 Division of fractions 15 2.7 Percentages 16 2.8 Ratios 19 Summary 21 End of unit questions 22 3 Basic Algebra and Measurement 25 3.1 Introduction 25 3.2 Measurement 25 3.3 Algebraic notation 28 3.3.1 Addition 29 3.3.2 Subtraction 29 3.3.3 Multiplication 30 3.3.4 Division 30 3.3.5 Brackets 30 3.4 Substitution 31 3.5 Factorising simple formulae 32 3.6 Algebraic fractions 33 6 CONTENTS 3.6.1 Multiplication and division of algebraic fractions 34 3.6.2 Addition and subtraction of algebraic fractions 34 3.7 Transposing formulae 35 3.8 Inequalities 38 3.8.1 Intervals 39 3.9 Applications in biological science 40 3.9.1 Equilibrium constants—an example of algebraic fraction 41 Summary 42 End of unit questions 43 4 Powers and Scientific Notation 47 4.1 Introduction 47 4.2 Powers 47 4.3 Multiplication and division using powers 51 4.4 Powers of powers 53 4.5 Fractional indices 53 4.6 Indices and biology 54 Summary 56 End of unit questions 57 5 Concentration and Accuracy 59 5.1 Introduction 59 5.2 Concentration, volume and amount 59 5.2.1 Percentage weight/volume 60 5.2.2 Percentage volume/volume 60 5.2.3 Percentage weight/weight 61 5.2.4 Moles and molarity 63 5.3 Accuracy: significant figures and decimal places 66 5.3.1 Significant figures 66 5.3.2 Decimal places 68 5.3.3 Accuracy 69 Summary 71 End of unit questions 71 6 Tables, Charts and Graphs 73 6.1 Introduction 73 6.2 Raw data and frequency tables 73 6.2.1 Table preparation 74 6.2.2 Frequency tables 78 6.3 Charts, diagrams and plots 81 6.3.1 Pictograms 81 6.3.2 Pie charts 82 CONTENTS 7 6.3.3 Bar charts 83 6.3.4 Dot plots 85 6.3.5 Histograms 88 6.3.6 Scatter graphs 89 6.4 Plots linking three variables 96 6.4.1 Three-dimensional plots 96 6.4.2 Triangular charts 97 6.4.3 Nomograms 100 Summary 103 End of unit questions 103 7 Linear Functions 107 7.1 Introduction 107 7.2 Functions 107 7.2.1 Inverse functions 109 7.2.2 Monotone functions 111 7.3 Special linear equations 113 7.4 General linear equations 115 7.4.1 Determining the equation of a straight line 117 7.5 Solving linear equations 119 7.6 Biological applications 120 7.6.1 The Beer-Lambert law—an example of a special linear equation 120 7.6.2 The Lineweaver—Burk plot 122 Summary 126 End of unit questions 126 8 Power Functions 129 8.1 Introduction 129 8.2 Power functions 129 8.3 Polynomials 131 8.4 Solving quadratic equations 132 8.4.1 Solving by factorisation 132 8.4.2 Solving by using a formula 134 8.5 Applications in life sciences 135 8.5.1 Quadratics as a tool to calculate pH 136 8.5.2 Quadratic equations and rates 137 Summary 137 End of unit questions 138 9 Exponential Functions 141 9.1 Introduction 141 9.2 Sequences 141 9.2.1 Geometric sequences 142 9.2.2 Arithmetic mean 143 8 CONTENTS 9.3 Exponential functions 144 9.4 Solving exponential equations 147 9.5 Applications in biology 148 9.5.1 Exponential growth 148 9.5.2 Exponential decay 151 9.5.3 Geometric series 153 Summary 155 End of unit questions 155 10 Logarithmic Functions 157 10.1 Introduction 157 10.2 Defining logarithms 157 10.2.1 Logarithms to the base ten (log ) 159 10 10.2.2 Logarithms to the base two (log ) 160 2 10.2.3 Natural logarithms (log ) 160 e 10.3 Rules for manipulating logarithmic expressions 161 10.3.1 Law for the addition of logarithms 161 10.3.2 Law for the subtraction of logarithms 162 10.3.3 Law for logarithms of power terms 163 10.4 Using logarithms to transform data 164 10.4.1 Logarithmic transformation of exponential functions 165 10.4.2 Logarithmic transformation of power functions 166 10.5 Semi-logarithmic plots 166 10.5.1 Exponential functions 167 10.6 Double-logarithmic plots 170 10.6.1 The Hill plot and allosteric enzymes 171 10.7 Logarithms and biology 173 Summary 176 End of unit questions 177 11 Introduction to Statistics 179 11.1 Introduction 179 11.2 Sampling 179 11.3 Normal distribution 181 11.4 Means, medians and modes 183 11.4.1 The arithmetic mean 184 11.4.2 The median and quartiles 188 11.4.3 The mode 190 11.4.4 Representing the data with a box plot 190 11.4.5 Mean, median or mode? 191 11.5 Measuring variability 193 11.5.1 Variance 193 11.5.2 Standard deviation 196 CONTENTS 9 11.6 Sampling distribution of the mean 198 11.6.1 Standard error of the mean 199 11.7 Confidence levels and the t-distribution 200 Summary 202 End of unit questions 203 Appendix: Solutions to Problems 205 Worked examples 205 End of unit questions 214 Index 227