Mathematics for chemistry:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow
Longman Scientific & Technical
1995
|
| Edition: | 1. publ. |
| Series: | Essential maths for students
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 286 S. graph. Darst. |
| ISBN: | 0582219701 |
Staff View
MARC
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| 100 | 1 | |a Doggett, Graham |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematics for chemistry |c Graham Doggett and Brian T. Sutcliffe |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow |b Longman Scientific & Technical |c 1995 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction x
Mathematics in the context of chemistry x
Organization of the text xii
Acknowledgements xiv
1 Numbers, symbols and rules 1
1.1 Numbers 2
Kinds of numbers 2
Relations involving numbers 3
Operations on numbers 4
Addition or subtraction 4
Multiplication 4
Division 5
Exponential notation 5
Laws of exponents 5
Rational exponents 6
Real number exponents 7
Scientific notation 8
1.2 Symbols and more rules 10
1.3 Simple polynomial equations 15
1.4 A first look at complex numbers 17
2 Functions of a single variable 1 g
2.1 The idea of function 19
Simple algebraic functions 19
The inverse function 21
More on the domain 22
Functions as prescriptions 25
2.2 Exponential functions 27
2.3 The logarithm function 29
2.4 Trigonometrical functions 32
Inverse trigonometrical functions 33
Trigonometrical relations and identities 33
2.5 Hyperbolic functions 34
Inverse hyperbolic functions 35
3 Limits, small steps and smoothness 37
3.1 Some examples of limiting processes 37
vi Contents
3.2 Defining the limiting process 38
Functions of an integer variable 38
Functions of a real variable 40
Testing for continuity 40
3.3 Some examples in the use of limits 41
4 Rates of change and differentiation 45
4.1 Defining rate of change 46
Average rate of change 46
Instantaneous rate of change 46
4.2 Differentiation of some standard functions 47
Differentiation of xn 48
Differentiation of sin x and cos x 48
An important limit 49
Differentiating the exponential and logarithm functions 50
4.3 Functions with discontinuities 51
4.4 Basic rules for differentiation 51
Sums, products and quotients of functions 51
The chain rule 53
4.5 Higher order derivatives 54
4.6 Maxima and minima 57
4.7 The differentiation of functions of two or more variables:
a preview 61
The partial derivative 62
I 5 Differentials small and not so small changes 64
5.1 The tangent approximation 66
5.2 Some further uses of the tangent approximation 68
The Newton Raphson method 68
Reformulating the tangent approximation 70
5.3 The differential of a function of two variables: a preview 72
5.4 Some discussion of the idea of a differential 73
6 Integration undoing the effects of differentiation 76
6.1 The antiderivative function and the / operator 77
Further properties of the / operator 80
6.2 Methods for evaluating integrals 80
Rearrangement of the integrand 81
6.3 The substitution method 81
A useful result 85
6.4 Integrals involving rational polynomial functions 86
Use of partial fractions 86
6.5 Integration by parts 89
6.6 The definite integral 91
6.7 Improper integrals 95
6.8 Numerical determination of definite integrals 99
7 Power series: a new look at functions 101
7.1 The Maclaurin series 102
Testing for convergence 102
Contents vii
7.2 The Taylor series 104
7.3 Manipulating power series 108
Limits revisited 114
8 Complex numbers revisited 116
8.1 More manipulations with complex numbers 116
8.2 Cartesian and polar representations of complex numbers 118
8.3 Euler s theorem 119
8.4 Powers of complex numbers: the de Moivre theorem 121
Extension of the de Moivre result to negative and rational
powers 121
8.5 Roots of complex numbers 123
Logarithms revisited 124
9 The solution of simple differential equations the nuts and
bolts of kinetics 126
9.1 First order differential equations 127
9.2 Separation of variables for first order differential equations 128
A surface chemistry example 132
9.3 First order linear differential equations 133
The solution of a first order linear differential equation 134
Sequential first order reactions revisited 136
9.4 Second order differential equations 136
Simple harmonic motion 136
Inhomogeneous second order differential equations 139
9.5 Power series solution of differential equations 141
A simple example 142
10 Functions of two or more variables differentiation revisited 145
10.1 The representation of functions of two or more variables 145
Coordinate systems for properties depending upon two
variables 146
10.2 Differentiation of functions of two or more variables 148
The partial derivative 148
Higher order partial derivatives 150
Differentiating under the integral sign a useful procedure 151
Maxima, minima and saddle points 152
10.3 The differential, dz 153
10.4 Application of differentials to error calculations 154
Formulae with a single measured property 154
Formulae with two or more measured properties 154
10.5 The chain rule and the effects of changing variables 155
10.6 Exact differentials 157
Finding the function, given its differential 157
10.7 Thermodynamic applications 158
11 Multiple integrals integrating functions of several variables 160
11.1 Double integrals in terms of Cartesian coordinates 160
11.2 Integration over ncn rectangular regions 163
viii Contents
Integration over a triangular region 163
Integration over a sector 164
Integration over an annular region 166
11.3 A special integral 167
11.4 Integrals involving functions with more than two variables 169
12 Statistics 171
12.1 Statistics in a chemical context 171
12.2 The theory of linear regression 172
12.3 Validating linear regression 175
The distribution of the measured values 176
12.4 The normal distribution 178
Properties of continuous distributions 180
12.5 Sampling from a distribution of measured values 181
Properties of the normal distribution 182
Measures of statistical confidence 182
12.6 Confidence limits on regression calculations 185
13 Matrices a useful tool and a form of mathematical shorthand 188
13.1 Rules for matrix combination 190
13.2 Special forms of matrices and operations on matrices 192
The null matrix 193
The unit matrix 193
Symmetric matrices 193
The transpose of a matrix 194
The trace of a matrix 195
The complex conjugate of a matrix 195
The adjoint of a matrix 196
Hermitian matrices 196
Orthogonal matrices 196
Unitary matrices 196
13.3 Isomorphisms involving matrices 197
Some properties of groups 198
Group representations 201
The symmetry properties of ozone a chemical example 201
Isomorphisms between groups 205
14 Determinants — functions revisited and a new notation 206
14.1 The determinant of a square matrix 206
14.2 Properties of determinants 208
14.3 Determinants with functions as elements 210
14.4 Notation 213
14.5 Cofactors of determinants 214
Expanding a determinant in terms of cofactors 215
14.6 Matrices revisited 216
The inverse matrix 216
Solution of simultaneous equations 217
15 Vectors a formalism for directional properties 219
Contents ix
15.1 Conventions 220
15.2 Addition of vectors 221
15.3 Base vectors 222
15.4 Vector multiplication 223
The scalar product 223
The vector product 226
The vector product in chemistry 228
15.5 Geometry in two and three dimensions 228
The straight line 229
The plane 230
Determinants revisited 230
15.6 Differentiation revisited 232
15.7 Integration revisited 234
16 The eigenvalue problem an important link between theory
and experiment 236
16.1 Examples of eigenvalue problems 236
16.2 Defining an eigenvalue problem 237
16.3 Solving the eigenvalue problem 238
16.4 The case of repeated eigenvalues 240
The principal axis transformation 242
17 Curve fitting vectors revisited 245
17.1 Base vectors revisited 246
Dealing with n dimensions 247
17.2 Projecting a vector onto a subspace 247
17.3 Curve fitting 248
The straight line 248
The general straight line 250
Fitting a second degree polynomial 250
17.4 Conclusion 251
References 252
Appendix 1 255
SI prefixes and symbols for nth powers of 10
Appendix 2 256
Some trigonometry
Appendix 3 262
Derivatives of selected functions
Answers to problems 263
Index 280
|
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| discipline | Chemie Mathematik |
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| id | DE-604.BV014032360 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:56:25Z |
| institution | BVB |
| isbn | 0582219701 |
| language | English |
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| series2 | Essential maths for students |
| spelling | Doggett, Graham Verfasser aut Mathematics for chemistry Graham Doggett and Brian T. Sutcliffe 1. publ. Harlow Longman Scientific & Technical 1995 XIII, 286 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Essential maths for students Wiskunde gtt Mathematik Mathematics Mathematik (DE-588)4037944-9 gnd rswk-swf Chemie (DE-588)4009816-3 gnd rswk-swf Chemie (DE-588)4009816-3 s Mathematik (DE-588)4037944-9 s DE-604 Sutcliffe, Brian T. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009607726&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Doggett, Graham Sutcliffe, Brian T. Mathematics for chemistry Wiskunde gtt Mathematik Mathematics Mathematik (DE-588)4037944-9 gnd Chemie (DE-588)4009816-3 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4009816-3 |
| title | Mathematics for chemistry |
| title_auth | Mathematics for chemistry |
| title_exact_search | Mathematics for chemistry |
| title_full | Mathematics for chemistry Graham Doggett and Brian T. Sutcliffe |
| title_fullStr | Mathematics for chemistry Graham Doggett and Brian T. Sutcliffe |
| title_full_unstemmed | Mathematics for chemistry Graham Doggett and Brian T. Sutcliffe |
| title_short | Mathematics for chemistry |
| title_sort | mathematics for chemistry |
| topic | Wiskunde gtt Mathematik Mathematics Mathematik (DE-588)4037944-9 gnd Chemie (DE-588)4009816-3 gnd |
| topic_facet | Wiskunde Mathematik Mathematics Chemie |
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