Exam (elaborations)

Exam (elaborations) TEST BANK FOR The Chemistry Maths Book 2nd Edition

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TEST BANK FOR The Chemistry Maths Book 2nd Edition

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Maastricht University (UM)

Exam (elaborations) TEST BANK FOR The Chemistry Maths Book 2nd Edition Numbers, variables, and units 1 1.1 Concepts 1 1.2 Real numbers 3 1.3 Factorization, factors, and factorials 7 1.4 Decimal representation of numbers 9 1.5 Variables 13 1.6 The algebra of real numbers 14 1.7 Complex numb...

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Uploaded on February 13, 2022
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Maastricht University (UM)
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,The Chemistry Maths Book

Second Edition

Erich Steiner
University of Exeter

without mathematics the sciences cannot be understood, nor
made clear, nor taught, nor learned.
(Roger Bacon, 1214–1292)

1

,Contents

1 Numbers, variables, and units 1
1.1 Concepts 1
1.2 Real numbers 3
1.3 Factorization, factors, and factorials 7
1.4 Decimal representation of numbers 9
1.5 Variables 13
1.6 The algebra of real numbers 14
1.7 Complex numbers 19
1.8 Units 19
1.9 Exercises 29

2 Algebraic functions 31
2.1 Concepts 31
2.2 Graphical representation of functions 32
2.3 Factorization and simpliﬁcation of expressions 34
2.4 Inverse functions 37
2.5 Polynomials 40
2.6 Rational functions 50
2.7 Partial fractions 52
2.8 Solution of simultaneous equations 55
2.9 Exercises 58

3 Transcendental functions 62
3.1 Concepts 62
3.2 Trigonometric functions 63
3.3 Inverse trigonometric functions 72
3.4 Trigonometric relations 73
3.5 Polar coordinates 77
3.6 The exponential function 80
3.7 The logarithmic function 83
3.8 Values of exponential and logarithmic functions 86
3.9 Hyperbolic functions 87
3.10 Exercises 89

4 Differentiation 93
4.1 Concepts 93
4.2 The process of differentiation 94
4.3 Continuity 97
4.4 Limits 98
4.5 Differentiation from ﬁrst principles 100
4.6 Differentiation by rule 102
4.7 Implicit functions 110

, viii Contents

4.8 Logarithmic differentiation 111
4.9 Successive differentiation 113
4.10 Stationary points 114
4.11 Linear and angular motion 118
4.12 The differential 119
4.13 Exercises 122

5 Integration 126
5.1 Concepts 126
5.2 The indeﬁnite integral 127
5.3 The deﬁnite integral 132
5.4 The integral calculus 142
5.5 Uses of the integral calculus 147
5.6 Static properties of matter 148
5.7 Dynamics 152
5.8 Pressure–volume work 157
5.9 Exercises 160

6 Methods of integration 163
6.1 Concepts 163
6.2 The use of trigonometric relations 163
6.3 The method of substitution 165
6.4 Integration by parts 173
6.5 Reduction formulas 176
6.6 Rational integrands. The method of partial fractions 179
6.7 Parametric differentiation of integrals 184
6.8 Exercises 187

7 Sequences and series 191
7.1 Concepts 191
7.2 Sequences 191
7.3 Finite series 196
7.4 Inﬁnite series 203
7.5 Tests of convergence 204
7.6 MacLaurin and Taylor series 208
7.7 Approximate values and limits 214
7.8 Operations with power series 219
7.9 Exercises 221

8 Complex numbers 225
8.1 Concepts 225
8.2 Algebra of complex numbers 226
8.3 Graphical representation 228
8.4 Complex functions 235
8.5 Euler’s formula 236
8.6 Periodicity 240

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