An Introduction To Applied Calculus For Social And Life Sciences

Front cover......Page 1
Title page......Page 2
Imprint page......Page 3
Contents......Page 4
About the authors......Page 8
1.1 Number systems......Page 10
1.2 Exponents and surds......Page 13
1.3 Logarithms......Page 17
2.1 Polynomials and rational expressions......Page 22
2.2 Solving equations......Page 26
2.3 Simultaneous equations......Page 30
3.1 Intervals......Page 35
3.2 Absolute values......Page 38
3.3 Quadratic inequalities......Page 41
4.1 Algebra of functions......Page 46
4.2 Composition of functions......Page 50
4.3 Quadratic functions......Page 51
4.6 Exponential functions......Page 54
4.7 Exponential growth and decay......Page 60
4.8 Trigonometric functions......Page 65
4.9 Solving trigonometric equations......Page 77
4.10 Piece-wise functions......Page 81
4.11 Graphing of basic functions......Page 84
4.12 Intersection of graphs......Page 91
4.13 Functional models......Page 95
5.1 The limit of a function......Page 103
5.2 Limits of various types of functions......Page 107
5.3 Limits involving infinity......Page 109
5.4 One-sided limits and continuity......Page 111
5.5 Continuity......Page 113
5.6 Continuity of polynomials and rational functions......Page 116
5.7 The Intermediate Value Theorem......Page 118
6.1 The derivative......Page 123
6.2 Differentiability and continuity......Page 127
6.3 Differentiation techniques......Page 129
6.4 Product and quotient rules......Page 131
6.5 Composition of functions......Page 133
6.6 The power rule......Page 135
6.7 Higher order derivatives......Page 136
6.8 Evaluating limits using L’Hôpital’s rule......Page 137
6.9 Implicit differentiation......Page 138
6.10 Related rates......Page 141
7.1 Derivatives of logarithmic functions......Page 149
7.2 Derivatives of exponential functions......Page 151
7.3 Logarithmic differentiation......Page 152
7.4 Derivatives of trigonometric functions......Page 154
7.5 Learning curves......Page 157
7.6 Logistic curves......Page 159
8.1 Increasing and decreasing functions......Page 164
8.2 Relative extrema......Page 168
8.3 Vertical and horizontal asymptotes......Page 179
8.4 Curve sketching......Page 181
8.5 Graphs involving exponential functions......Page 186
8.6 Graphs with oblique asymptotes......Page 188
8.7 Newton’s Method......Page 191
8.8 Optimisation......Page 194
8.9 Applied optimisation......Page 195
9.1 Anti-differentiation......Page 204
9.2 Rules for integration......Page 206
9.3 Integration by substitution......Page 208
9.4 Definite integral......Page 215
9.5 Integrating rational functions......Page 223
9.6 Area between curves......Page 224
9.7 The average value of a function......Page 228
9.8 Integration by parts......Page 229
9.9 Integration of trigonometric functions......Page 234
10.1 Mathematical modelling......Page 241
10.3 Differential equations......Page 242