《管理数学 英文版》

1 Elementary algebra1

Introduction1

1.1 Algebraic expressions and equations1

1.2 The addition and subtraction of algebraic forms3

1.3 Products of positive and negative real numbers6

1.4 Expansion of bracketed terms7

1.5 Fractions10

1.6 Exponents13

1.7 Negative exponents18

1.8 Cancelling out terms19

1.9 The order and hierarchy of operations20

1.10 Factorization22

1.11 Degree of an expression27

1.12 Perfect squares28

1.13 Applications29

Additional examples32

2 Solving equations35

Introduction35

2.1 Drawing graphs36

2.2 Straight-line or linear functions36

2.3 Quadratic functions38

2.4 Cubic fUnctions41

2.5 Algebraic solution of equations43

2.6 Equations involving fractions44

2.7 QUadratic equations45

2.8 Formula for solving quadratic equations46

2.9 Solution of cubic equations48

2.10 APPlications50

Additional examples54

3 Simultaneous equations and inequalities57

Introduction57

3.1 Simple equations with one variable58

3.2 Pairs of equations58

3.3 Using a set of equations as a model61

3.4 Sets of three or more equations64

3.5 Independent and dependent equations69

3.6 Linear and non-linear equations70

3.7 Inequalities73

3.8 Simultaneous inequalities79

3.9 Applications of inequalities81

Additional examples86

4.1 Arithmetic progression(AP)89

4 Series89

Introduction89

4.2 The sigma notation for summation93

4.3 Sum of terms of an AP96

4.4 Geometric progression(GP)100

4.5 Sum of terms of a GP101

4.6 Notation for interest calculations103

4.7 Compound interest104

Additional examples107

5 Logarithms and exponentials109

Introduction109

5.1 Logarithms and exponents109

5.2 How logarithms work112

9.2 Rules for integration115

5.3 Rules for combining logarithms118

5.4 The exponential function and continuous compounding119

5.5 Nominal interest rates and effective interest rates123

5.6 Negative growth124

5.7 Application129

Additional examples132

6 Matrices134

Introduction134

6.1 Matrix notation135

6.2 Equality, addition and subtraction of matrices138

6.3 Multiplication of matrices140

6.4 Transposing matrices148

6.5 Matrix formulation of simultaneous equations151

6.6 The identity matrix and the inverse154

6.7 Determinants157

6.8 The inverse of a 2×2 matrix159

6.9 Summary161

Additional examples162

7 Differentiation164

Introduchon164

7.1 The slope of a straight line166

7.2 Finding the equation of a straight line168

7.3 A numerical method for finding the slope of a curve169

7.4 The general method of differentiation174

7.5 Rules for derivatives175

7.6 The derivative of the reciprocal of a function178

Additional examples181

8.1 The second and higher derivatives183

Introduction183

8 More about differentiation183

8.2 Alternative notation for the derivative186

8.3 Maxima and minima187

8.4 Points of inflexion192

8.5 The function of a function rule194

8.6 The product rule199

8.7 Mixing the function of a function and product rules203

8.8 Differentiating expressions containing fractions204

8.9 Continuous functions206

8.10 Partial derivatives208

Additional examples209

9 Integration212

Introduction212

9.1 Integration as the reverse of differentiation213

9.3 The definite integral217

9.4 The integral as the area between the curve and the x-axis219

9.5 A general remark on integration and differentiation223

Additional examples224

10 The application of mathematics228

10.1 Mathematical style228

10.2 Tackling mathematical examination questions229

10.3 Formulating real-life problems230

10.4 Solving real-life problems230

Appendix The Greek alphabet232

Solutions to ad■ examples233

Index263