Applied mathematics in chemical engineering:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York [u.a.]
McGraw-Hill
1957
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | McGraw-Hill series in chemical engineering.
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001495155&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XII, 413 S. zahlr. graph. Darst. 24 cm |
Internformat
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| 100 | 1 | |a Mickley, Harold S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Applied mathematics in chemical engineering |c Harold S. Mickley ; Thomas K. Sherwood ; Charles E. Reed |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b McGraw-Hill |c 1957 | |
| 300 | |a XII, 413 S. |b zahlr. graph. Darst. |c 24 cm | ||
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| 490 | 0 | |a McGraw-Hill series in chemical engineering. | |
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| 650 | 4 | |a Mathematische Physik | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0022 IV 2645-15 0102 CHE 020f 2001 A 25108 0732 12.52.13 |
|---|---|
| DE-BY-TUM_katkey | 374350 |
| DE-BY-TUM_location | Mag 01 LSB |
| DE-BY-TUM_media_number | TEMP2715428 040010438814 TEMP3141476 |
| _version_ | 1821940887626711040 |
| adam_text | CONTENTS
Preface vij
Chapter 1. Treatment of Engineering Data 1
1 1. Introduction
1 2. Graphical Representation 1
1 3. Elimination of Trial and Error 4
1 4. Misleading Methods of Correlation 6
1 5. Empirical Equations 8
1 6. Interpolation 15
1 7. Newton s Formula 16
1 8. Lagrange s Interpolation Formula 19
1 9. Extrapolation 21
1 10. Differentiation 21
1 11. Change of Variable 23
1 12. Graphical Differentiation 24
1 13. Numerical Differentiation 25
1 14. Maxima and Minima 28
1 15. Evaluation of Indeterminate Fractions 30
1 16. Integration 31
1 17. Graphical Integration 32
1 18. Graphical Construction of Integral Curves 33
1 19. Numerical Integration 35
Bibliography 42
Problems 42
Chapter 2. Interpretation of Engineering Data 46
2 1. Introduction 46
2 2. Explanation of Terms 47
2 3. Significant Figures 49
2 4. Significant Figures and the Operations of Arithmetic 50
2 5. Classification of Measurements 52
2 6. Propagation of Errors 53
2 7. Variance and Distribution of Random Errors 59
2 8. Properties of the Variance 63
2 9. Confidence Limits for Small Samples 66
2 10. Analysis of Variance 71
2 11. Design of Experiments 81
2 12. Least Squares 95
2 13. Other Applications 99
Bibliography 99
Problems 100
we
x contents
Chapter 3. Mathematical Formulation of the Physical Problem . . 105
3 1. Introduction 105
3 2. Formulation of the Differential Equation 105
3 3. Application of the Law of Conservation of Mass 106
3 4. Application of the Law of Conservation of Energy 110
3 5. Summary of Steps 112
3 6. Rate Equations 114
3 7. Rate Equations for Homogeneous Chemical Reactions . . . .117
3 8. Flow Systems 120
3 9. The General Problem 128
Problems 129
Chapter 4. Solution of Ordinary Differential Equations .... 134
4 1. Functional Relationships 134
4 2. Mathematical Origin of Differential Equations 134
4 3. Definition of Terms 135
4 4. Ordinary Differential Equations 136
4 5. Partial Differential Equations 136
4 6. Classification of Ordinary Differential Equations 136
4 7. Separable Equations 138
4 8. Equations Made Separable by Change of Variable 138
4 9. Homogeneous Equations 139
4 10. Equations of First Order and First Degree with Linear Coefficients . 139
4 11. Exact Equations 140
4 12. Linear Equation of the First Order 141
4 13. Bernoulli s Equation 141
4 14. Other Integrating Factors 141
4 15. Integration of Exact Equations 141
4 16. Equations of the First Order and Higher Degree 142
4 17. Clairaut s Equation 145
4 18. Singular Solutions 145
4 19. Equations with Missing Terms 146
4 20. General Properties of Linear Equations 148
4 21. Linear Equations with Constant Coefficients 150
4 22. Determination of the Complementary Function 151
4 23. Exponential Functions 152
4 24. Determination of the Particular Integral 152
4 25. The Euler Equation 155
4 26. Simultaneous Linear Differential Equations 156
Bibliography 158
Problems 159
Chapter 5. Series and Numerical Solutions of Ordinary Differential
Equations 163
5 1. Introduction 163
5 2. Series Solutions 163
5 3. Power Series 163
5 4. Taylor Series 165
5 5. Linear Second order Equations with Variable Coefficients . . . .165
5 6. The Method of Frobenius 166
5 7. Exceptional Cases: 8i — ss = 0 or Integer 169
CONTENTS Xi
5 8. Bessel s Equation , 170
5 9. Generalized Form of Bessel s Equation 174
5 10. Properties of Bessel Functions 174
5 11. Examples of Bessel function Solutions 179
5 12. Important Second order Equations 183
5 13. Numerical solution Methods 187
5 14. Modified Euler Method 187
5 15. Method of W. E. Milne 191
5 16. Method of Runge Kutta 193
5 17. Numerical Solution of Equations of Higher Order 195
5 18. Application of Runge Kutta Method to Higher order Equations . . 198
5 19. Use of Taylor s Series 198
Bibliography 200
Problems 200
Chapter 6. Formulation of Partial Differential Equations . . . 204
6 1. Introduction 204
6 2. Partial Derivatives 204
6 3. Differentiation of Composite Functions 207
6 4. Differentiation Formulas 209
6 5. Differentiation of Implicit Functions 215
6 6. Directional Derivatives 217
6 7. Maxima and Minima 219
6 8. Differentiation of Integrals 220
6 9. Exact Differentials 221
6 10. Formulation of Partial Differential Equations 223
6 11. Vectors 228
6 12. Scalar, or Dot, Product 230
6 13. Vector, or Cross, Product 230
6 14. Multiple Products 231
6 15. Differentiation of Vectors 232
6 16. The Position Vector R 233
6 17. Scalar and Vector Fields 233
6 18. Vector Differential Operator 235
6 19. Line Integrals 237
6 20. Surface Integrals 238
6 21. Coordinate Transformation 239
6 22. Mass Transfer in a Binary Gas Mixture ... 241
6 23. The Equations of Motion of a Perfect Fluid 245
Bibliography 248
Problems 249
Chapter 7. Solution of Partial Differential Equations 252
7 1. Nature of a Partial Differential Equation 252
7 2. Types of Partial Differential Equations 252
7 3. Boundary Conditions 253
7 4. Method of Solution of Partial Differential Equations 253
7 5. Separation of Variables 256
7 6. Orthogonal Functions 259
7 7. Expansion in a Series of Orthogonal Functions 261
7 8. Expansion in a Double Series of Orthogonal Functions 265
xii CONTENTS
7 9. Fourier Series 268
7 10. Representation over an Infinite Interval 271
7 11. Potential Flow around a Sphere 274
7 12. Conduction of Heat and Diffusion of Matter 277
Bibliography 278
Problems 278
Chapter 8. The Laplace Transform 281
8 1. Introduction 281
8 2. Illustration of the Transform Method 281
8 3. Properties of the Transformation 282
8 4. The Inverse Transform 284
8 5. Convolution 285
8 6. Solution of a Partial Differential Equation 285
8 7. Inversion by the Method of Residues 289
8 8. Applications to Chemical Engineering 298
8 9. Utility of the Transform Method 307
Bibliography 307
Problems 307
Chapter 9. Analysis of Stagewise Processes by the Calculus of Finite
Differences 320
9 1. Introduction 320
9 2. Solution of Linear Difference Equations 322
9 3. Illustrative Examples 324
9 4. Unsteady state Operation 328
9 5. Illustrative Examples 329
Bibliography 340
Problems 340
Chapter 10. The Numerical Solution of Partial Differential
Equations 343
10 1. Introduction 343
10 2. Example of a Numerical Solution 345
10 3. Mathematical Formulation of Finite difference Equations .... 350
10 4. Boundary Conditions for Initial value Problems 353
10 5. Convergence and Stability of Numerical Solutions of Initial value
Problems 357
10 6. Solution by Iteration 364
10 7. Equations with Variable Coefficients 365
10 8. Graphical Methods 367
10 9. Three or More Independent Variables 373
10 10. Illustrative Examples 376
10 11. Boundary value Problems 389
10 12. Treatment of Boundary Conditions 395
10 13. Other Applications 395
10 14. Convergence of the Relaxation Method 397
10 15. Conformal Mapping 397
Bibliography 399
Problems 401
Index 405
|
| any_adam_object | 1 |
| author | Mickley, Harold S. Sherwood, Thomas K. Reed, Charles E. |
| author_facet | Mickley, Harold S. Sherwood, Thomas K. Reed, Charles E. |
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| discipline | Mathematik |
| edition | 2. ed. |
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| illustrated | Illustrated |
| indexdate | 2024-12-20T07:48:43Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001495155 |
| oclc_num | 315697 |
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| owner_facet | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-29T DE-83 DE-210 |
| physical | XII, 413 S. zahlr. graph. Darst. 24 cm |
| psigel | TUB-nveb |
| publishDate | 1957 |
| publishDateSearch | 1957 |
| publishDateSort | 1957 |
| publisher | McGraw-Hill |
| record_format | marc |
| series2 | McGraw-Hill series in chemical engineering. |
| spellingShingle | Mickley, Harold S. Sherwood, Thomas K. Reed, Charles E. Applied mathematics in chemical engineering Analyse mathématique Physique mathématique Mathematische Physik Mathematical analysis Mathematical physics Mathematik (DE-588)4037944-9 gnd Technische Chemie (DE-588)4078178-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd Differentialgleichung (DE-588)4012249-9 gnd Chemische Verfahrenstechnik (DE-588)4069941-9 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4078178-1 (DE-588)4042805-9 (DE-588)4012249-9 (DE-588)4069941-9 |
| title | Applied mathematics in chemical engineering |
| title_auth | Applied mathematics in chemical engineering |
| title_exact_search | Applied mathematics in chemical engineering |
| title_full | Applied mathematics in chemical engineering Harold S. Mickley ; Thomas K. Sherwood ; Charles E. Reed |
| title_fullStr | Applied mathematics in chemical engineering Harold S. Mickley ; Thomas K. Sherwood ; Charles E. Reed |
| title_full_unstemmed | Applied mathematics in chemical engineering Harold S. Mickley ; Thomas K. Sherwood ; Charles E. Reed |
| title_short | Applied mathematics in chemical engineering |
| title_sort | applied mathematics in chemical engineering |
| topic | Analyse mathématique Physique mathématique Mathematische Physik Mathematical analysis Mathematical physics Mathematik (DE-588)4037944-9 gnd Technische Chemie (DE-588)4078178-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd Differentialgleichung (DE-588)4012249-9 gnd Chemische Verfahrenstechnik (DE-588)4069941-9 gnd |
| topic_facet | Analyse mathématique Physique mathématique Mathematische Physik Mathematical analysis Mathematical physics Mathematik Technische Chemie Numerische Mathematik Differentialgleichung Chemische Verfahrenstechnik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001495155&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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