Mathematics for physical chemistry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier
2013
|
| Edition: | 4. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XI, 247 S. graph. Darst. |
| ISBN: | 9780124158092 |
Staff View
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| 245 | 1 | 0 | |a Mathematics for physical chemistry |c Robert G. Mortimer |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier |c 2013 | |
| 300 | |a XI, 247 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804150296677449728 |
|---|---|
| adam_text | Titel: Mathematics for physical chemistry
Autor: Mortimer, Robert G
Jahr: 2013
Contents
Preface xi 3.2 Coordinate Systems in Two Dimensions 26
3.3 Coordinate Systems in Three Dimensions 27
3.3.1 Cartesian Coordinates 27
3.3.2 Spherical Polar Coordinates 27
3.3.3 Cylindrical Polar Coordinates 28
1 Problem Solving and Numerical 3.4 Imaginary and Complex Numbers 29
Mathematics 3.4.1 Mathematical Operations with Complex
Numbers 29
1.1 Problem Solving 1 3.4.2 The Argand Diagram 29
1.2 Numbers and Measurements 1 3.4.3 The Complex Conjugate 31
1.3 Numerical Mathematical Operations 2 3.4.4 The Magnitude of a Complex Quantity 31
1.3.1 Binary Arithmetic Operations 2 3 4 5 Roofc. of a Comp,ex Number 32
1.3.2 Additional Numerical Operations 2 3 5 prob|em So|ving an(J Symbo|ic Mathematics 32
1.4 Units of Measurement 3
1.5 The Factor-Label Method 5
1.6 Measurements, Accuracy, and Significant
Djpjts 5 4.1 Vectors in Two Dimensions 35
1.6.1 Scientific Notation 6 4.1.1 The Sum and Difference of Two Vectors 35
1.6.2 Roundine 6 4.1.2 The Product of a Vector and a Scalar 36
4 Vectors and Vector Algebra
1.6.3 Significant Digits in a Calculated
Quantity
4.1.3 Unit Vectors 36
4.1.4 The Scalar Product of Two Vectors 37
4.1.5 The Magnitude of a Vector 38
2 Mathematical Functions 4.2 Vectors in Three Dimensions 38
4.2.1 Unit Vectors in Three Dimensions 38
2.1 Mathematical Functions in Physical 4.2.2 The Magnitude of a Vector 38
Chemistry 11 42.3 The Sum and Difference of Two
2.1.1 Functions in Thermodynamics 11 Vectors 39
2.1.2 Functions in Quantum Mechanics 12 4.2.4 The Product of a Scalar and a Vector 39
2.1.3 Function Notation 12 4.2.5 The Scalar Product of Two Vectors 39
2.1.4 Continuity 12 4.2.6 The Vector Product of Two Vectors 39
2.1.5 Graphs of Functions 12 4.3 physical Examples of Vector Products 40
2.2 Important Families of Functions 15 4.3.1 Magnetic Force 40
2.2.1 Linear Functions 15 4.3.2 Electrostatic Force 41
2.2.2 Quadratic Functions 16 4.3.3 Angular Momentum 41
2.2.3 Cubic Functions 16
2.2.4 Logarithms 16 5 Problem Solving and the Solution of
2.2.5 Exponentials 17 Algebraic Equations
2.2.6 Trigonometrie Functions 18
2.2.7 Inverse Trigonometrie Functions 21 51 Algebraic Methods for Solving One Equation
2.2.8 Hyperbolic Trigonometrie Functions 22
2.2.9 Significant Digits in Logarithms,
with One Unknown 43
5.1.1 Polynomial Equations 43
Exponential^, Ind Trigonometrie SA 2 Approximate Solutions to Equations 44
Functions 22 5.2 Numerical Solution of Algebraic Equations 47
2.3 Generating Approximate Graphs 22 521 Graphical Solution of Algebraic
Equations 47
5.2.2 Trial and Error 48
5.2.3 The Method of Bisection 48
5.2.4 Solving Equations Numerically with
3.1 The Algebra of Real Scalar Variables 25 Excel 48
vii
Problem Solving and Symbolic
Mathematics: Algebra
CvüT)
Contents
5.3 A Brief Introduction to Mathematica 49 7.5 Techniques of Integration 80
5.3.1 Numerical Calculations with 7.5.1 The Method of Substitution 80
Mathematica 49 7.5.2 Integration by Parts 80
5.3.2 Symbolic Algebra with Mathematica 51 7.5.3 The Method of Partial Fractions 81
5.3.3 Solving Equations with Mathematica 52 7.5.4 Integration with Mathematica 83
5.3.4 Graphing with Mathematica 53 7.6 Numerical Integration 83
5.4 Simultaneous Equations: Two Equations with 7.6.1 The Bar-Graph Approximation 83
Two Unknowns 53 7.6.2 The Trapezoidal Approximation 83
5.4.1 The Method of Substitution 53 7.6.3 Simpson s Rule 84
5.4.2 The Method of Elimination 54 7.6.4 Numerical Integration with
5.4.3 Consistency and Independence in Mathematica 85
Simultaneous Equations 54
5.4.4 Homogeneous Linear Equations 54 8 Differential Calculus with Several
5.4.5 Using Mathematica to Solve Independent Variables
Simultaneous Equations 55
8.1 Functions of Several Independent Variables 89
6 Differential Calculus 8.2 Changes in a Function of Several Variables,
Partial Derivatives 91
6.1 The Tangent Line and the Derivative of a 8.2.1 Differentials 91
Function 59 8.3 Change of Variables 92
6.1.1 The Derivative 60 8.4 Useful Partial Derivative Identities 93
6.1.2 Derivatives of Specific Functions 61 8.4.1 The Variable-Change Identity 93
6.2 Differentials 61 8.4.2 The Reciprocal Identity 94
6.3 Some Useful Derivative Identities 63 8.4.3 The Euler Reciprocity Relation 94
6.3.1 The Derivative of a Constant 63 8.4.4 The Maxwell Relations 94
6.3.2 The Derivative of a Function Times a 8.4.5 The Cycle Rule 95
Constant 63 8.4.6 The Chain Rule 95
6.3.3 The Derivative of a Product of Two 8.5 Thermodynamic Variables Related to Partial
Functions 63 Derivatives 95
6.3.4 The Derivative of the Sum of Two 8.6 Exact and Inexact Differentials 96
Functions 63 8.6.1 Integrating Factors 97
6.3.5 The Derivative of the Difference of 8.7 Maximum and Minimum Values of Functions
Two Functions 63 of Several Variables 98
6.3.6 The Derivative of the Quotient of Two 8.7.1 Constrained Maximum/Minimum
Functions 63 Problems 99
6.3.7 The Derivative of a Function of a 8.7.2 Lagrange s Method of Undetermined
Function (The Chain Rule) 63 Multipliers 99
6.4 Newton s Method 64 8.8 Vector Derivative Operators 101
6.5 Higher-Order Derivatives 65 8.8.1 Vector Derivatives in Cartesian
6.5.1 The Curvature of a Function 66 Coordinates 101
6.6 Maximum-Minimum Problems 66 8.8.2 Vector Derivatives in Other Coordinate
6.7 Limiting Values of Functions 67 Systems 103
6.8 L Höpital s Rule 68
9 Integral Calculus with Several
7 Integral Calculus Independent Variables
7.1 The Antiderivative of a Function 73 9.1 Line Integrals 107
7.1.1 Position, Velocity, and Acceleration 73 9.1.1 Line Integrals of Exact Differentials 108
7.2 The Process of Integration 74 9.1.2 Line Integrals of Inexact Differentials 109
7.2.1 The Definite Integral as an Area 76 9.1.3 Line Integrals with Three Integration
7.2.2 Facts about Integrals 76 Variables 109
7.2.3 Derivatives of Definite Integrals 78 9.1.4 Line Integrals in Thermodynamics 110
7.3Tablesof Indefinite Integrals 78 9.2 Multiple Integrals 1H
7.4 Improper Integrals 79 9.2.1 Double Integrals 111
Contents f ix j
9.2.2 The Double Integral Representing 12.4 Differential Equations with Separable
a Volume 112 Variables 149
9.2.3 Triple Integrals 113 12.5 Exact Differential Equations 149
9.2.4 Changing Variables in Multiple Integrals 113 12.6 Solution of Inexact Differential Equations
Using Integrating Factors 150
10 Mathematical Series 12.7 Partial Differential Equations 151
12.7.1 Waves in a String 151
12.7.2 Solution by Separation of Variables 151
10.1.1 Some Convergent Constant Series 120 UJJ The Schrödinger Equation 154
10.1.2 The Geometrie Series 120 12 8 Solution of Differential Equations Using
10.1.3 The Harmonie Series 121 Laplace Transforms 154
10.1.4 Tests for Convergence 121 12_9 Numerica, Solution of Differential
10.1 Constant Series 119
10.2 Power Series 122
Equations 155
10.2.1 Maclaurin Series 122 12.9.1 Euler s Method 155
10.2.2 Taylor Series 123
10.2.3 The Convergence of Power Series 124 U93 So|ution of Differential Equations
10.2.4 Power Series in Physical with Mathematica
12.9.2 The Runge-Kutta Method 156
156
Chemistry 125
10.3 Mathematical Operations on Series 126 13 Operators, Matrices, and Croup
10.4 Power Series with More Than One Theorv
Independent Variable 126
13.1 Mathematical Operators 161
11 Functional Series and Integral 13-1-1 Eigenfunctions and Eigenvalues 162
Transforms 13.1.2 Operator Algebra 162
13.1.3 Operators in Quantum
11.1 Fourier Series 129 Mechanics 164
11.1.1 Finding the Coefficients of a 13.2 Symmetry Operators 165
Fourier Series-Orthogonality 129 13.3 The Operation of Symmetry Operators
11.1.2 Fourier Series with Complex on Functions 167
Exponential Basis Functions 132 13.4 Matrix Algebra 169
11.2 Other Functional Series with Orthogonal 13.4.1 The Equality of Two Matrices 169
Basis Sets 132 13.4.2 The Sum of Two Matrices 169
11.2.1 Hilbert Space 132 13.4.3 The Product of a Scalar and a
11.2.2 Determining the Expansion Matrix 169
Coefficients 133 13.4.4 The Product of Two Matrices 169
11.3 Integral Transforms 134 13.4.5 The Identity Matrix 170
11.3.1 Fourier Transforms (Fourier 13.4.6 The Inverse of a Matrix 1 71
Integrals) 134 13.4.7 Matrix Terminology 172
11.3.2 Laplace Transforms 136 13.5 Determinants 172
13.6 Matrix Algebra with Mathematica 174
12 Differential Equations 13.7 An Elementary Introduction to Group
Theory 175
12.1 Differential Equations and Newton s 13 8 Symmetry Operators and Matrix
Representations 177
Laws of Motion 139
12.2 Homogeneous Linear Differential
Equations with Constant Coefficients 141 14 jhe So|utjon 0f Simultaneous
12.2.1 The Harmonie Oscillator 141 Algebraic Equations with More
12.2.2 The Damped Harmonie ^ Twq ünknowns
Oscillator-A Nonconservative
System 144 14.1 Cramer s Rule 183
12.3 Inhomogeneous Linear Differential 14.2 Linear Dependence and Inconsistency 185
Equations: The Forced Harmonie 14.3 Solution by Matrix Inversion 185
Oscillator 147 14.4 Gauss-Jordan Elimination 186
12.3.1 Variation of Parameters Method 147 14.5 Linear Homogeneous Equations 186
ra
Contents
14.6 Matrix Eigenvalues and 16.2 Curve Fitting 209
Eigenvectors 187 16.2.1 The Method of Least Squares
14.7 The Use of Mathematica to Solve (Regression) 210
Simultaneous Equations 189 16.2.2 Linear Least Squares
14.8 The Use of Mathematica to Find Matrix (Linear Regression) 211
Eigenvalues and Eigenvectors 189 16.2.3 The Correlation Coefficient and the
Covariance 213
15 Probability, Statistics, and 16.2.4 Error Propagation in Linear
Experimental Errors Least Squares 214
16.2.5 Carrying Out Least-Squares
15.1 Experimental Errors in Measured pjts wjtf1 £xce 216
Quantities 191
16.2.6 Some Warnings About Least-
15.1.1 Systematic and Random Squares Procedures 217
Errors 191
16.2.7 Weighting Factors in Linear
15.2 Probability Theory 192 Least Squares 217
15.2.1 Properties of a Population 192 16.2.8 Linear Least Squares with Fixed
15.2.2 The Uniform Probability S|ope or |ntercept 219
Distribution 196 16.3 Data Reduction with a Derivative 219
15.2.3 The Gaussian Distribution 196
15.2.4 Probability Distributions in Appendices
Quantum Mechanics 198
15.2.5 Probability Distributions in Gas Appendix A Values of Physical Constants 223
Kinetic Theory 199 Appendix B Some Mathematical Formulas
15.2.6 Time Averages 201 and Identities 224
15.3 Statistics and the Properties ofa Appendix C Infinite Series 224
Samnle 201 Appendix DA Short Table of Derivatives 226
15.4 Numerical Estimation of Random Appendix E A Short Table of Indefinite
Integrals 226
Appendix F A Short Table of Definite Integrals 228
16 Data Reduction and the Propagation APPendix G r*™ tegrals with Exponentials
r r r ° in the Integrands: The Error
°f ErrorS Function 230
16.1 The Combination of Errors 207 Appendix H Answers to Selected Numerical
16.1.1 The Combination of Random and Exercises and Problems 231
Systematic Errors 207
* r * -, r n *¦ n ^ Additional Reading 2.5/
16.1.2 Error Propagation in Data ö
Reduction with a Formula 208 Index 241
Errors 202
|
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| id | DE-604.BV040978694 |
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| indexdate | 2024-07-10T00:36:40Z |
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| isbn | 9780124158092 |
| language | English |
| lccn | 2012047249 |
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| physical | XI, 247 S. graph. Darst. |
| publishDate | 2013 |
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| publishDateSort | 2013 |
| publisher | Elsevier |
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| spelling | Mortimer, Robert G. Verfasser aut Mathematics for physical chemistry Robert G. Mortimer 4. ed. Amsterdam [u.a.] Elsevier 2013 XI, 247 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematik Chemistry, Physical and theoretical Mathematics Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Physikalische Chemie (DE-588)4045959-7 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Physikalische Chemie (DE-588)4045959-7 s Mathematik (DE-588)4037944-9 s DE-604 Mathematische Methode (DE-588)4155620-3 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025956739&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mortimer, Robert G. Mathematics for physical chemistry Mathematik Chemistry, Physical and theoretical Mathematics Mathematische Methode (DE-588)4155620-3 gnd Physikalische Chemie (DE-588)4045959-7 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4155620-3 (DE-588)4045959-7 (DE-588)4037944-9 |
| title | Mathematics for physical chemistry |
| title_auth | Mathematics for physical chemistry |
| title_exact_search | Mathematics for physical chemistry |
| title_full | Mathematics for physical chemistry Robert G. Mortimer |
| title_fullStr | Mathematics for physical chemistry Robert G. Mortimer |
| title_full_unstemmed | Mathematics for physical chemistry Robert G. Mortimer |
| title_short | Mathematics for physical chemistry |
| title_sort | mathematics for physical chemistry |
| topic | Mathematik Chemistry, Physical and theoretical Mathematics Mathematische Methode (DE-588)4155620-3 gnd Physikalische Chemie (DE-588)4045959-7 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathematik Chemistry, Physical and theoretical Mathematics Mathematische Methode Physikalische Chemie |
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