Gespeichert in:
| Titel: | Advanced engineering mathematics |
|---|---|
| Von: |
Erwin Kreyszig
|
| Person: |
Kreyszig, Erwin
1922-2008 Verfasser aut |
| Hauptverfasser: | |
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York [u.a.]
Wiley
1993
|
| Ausgabe: | 7. ed. |
| Notation: | SK 110 SK 950 |
| Schlagwörter: | |
| Medienzugang: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005401149&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | Getr. Zählung graph. Darst. |
| ISBN: | 0471599891 0471553808 |
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Contents
Part A. ORDINARY DIFFERENTIAL EQUATIONS 1
CHAPTER 1 First Order Differential Equations 2
1.1 Basic Concepts and Ideas, 2
1.2 Separable Differential Equations, 10
1.3 Modeling: Separable Equations, 13
1.4 Reduction to Separable Form. Optional, 20
1.5 Exact Differential Equations, 23
1.6 Integrating Factors, 27
1.7 Linear Differential Equations, 30
1.8 Modeling: Electric Circuits, 37
1.9 Orthogonal Trajectories of Curves. Optional, 43
1.10 Approximate Solutions: Direction Fields, Iteration, 48
1.11 Existence and Uniqueness of Solutions, 53
Chapter Review Questions and Problems, 58
Chapter Summary, 60
CHAPTER 2 Second Order Linear Differential Equations 62
2.1 Homogeneous Linear Equations, 62
2.2 Homogeneous Equations with Constant Coefficients, 69
2.3 Case of Complex Roots. Complex Exponential Function, 73
2.4 Differential Operators. Optional, 77
2.5 Modeling: Free Oscillations (Mass Spring System), 80
2.6 Euler Cauchy Equation, 90
2.7 Existence and Uniqueness Theory. Wronskian, 93
2.8 Nonhomogeneous Equations, 99
2.9 Solution by Undetermined Coefficients, 102
2.10 Solution by Variation of Parameters, 106
2.11 Modeling: Forced Oscillations. Resonance, 109
2.12 Modeling of Electric Circuits, 116
2.13 Complex Method for Particular Solutions. Optional, 121
Chapter Review Questions and Problems, 124
Chapter Summary, 126
CHAPTER 3 Higher Order Linear Differential Equations 128
3.1 Homogeneous Linear Equations, 128
3.2 Homogeneous Equations with Constant Coefficients, 136
3.3 Nonhomogeneous Equations, 141
3.4 Method of Undetermined Coefficients, 143
3.5 Method of Variation of Parameters, 146
Chapter Review Questions and Problems, 150
Chapter Summary, 151
xi
xii Contents
CHAPTER 4 Systems of Differential Equations.
Phase Plane, Stability 152
4.0 Introduction: Vectors, Matrices, 152
4.1 Introductory Examples, 158
4.2 Basic Concepts and Theory, 163
4.3 Homogeneous Linear Systems with Constant Coefficients, 166
4.4 Phase Plane, Critical Points, Stability, 176
4.5 Phase Plane Methods for Nonlinear Systems, 180
4.6 Nonhomogeneous Linear Systems, 186
Chapter Review Questions and Problems, 193
Chapter Summary, 195
CHAPTER 5 Series Solutions of Differential Equations.
Special Functions 197
5.1 Power Series Method, 197
5.2 Theory of the Power Series Method, 201
5.3 Legendre's Equation. Legendre Polynomials Pn(x), 209
5.4 Frobenius Method, 215
5.5 Bessel's Equation. Bessel Functions /„(.*:), 225
5.6 Further Properties of Jv{x), 232
5.7 Bessel Functions of the Second Kind, 236
5.8 Sturm Liouville Problems. Orthogonality, 241
5.9 Eigenfunction Expansions, 249
Chapter Review Questions and Problems, 258
Chapter Summary, 259
CHAPTER 6 Laplace Transforms 261
6.1 Laplace Transform. Inverse Transform. Linearity, 262
6.2 Transforms of Derivatives and Integrals, 268
6.3 s Shifting, f Shifting, Unit Step Function, 275
6.4 Further Applications. Dirac's Delta Function, 284
6.5 Differentiation and Integration of Transforms, 289
6.6 Convolution. Integral Equations, 293
6.7 Partial Fractions. Systems of Differential Equations, 299
6.8 Periodic Functions. Further Applications, 309
6.9 Laplace Transform: General Formulas, 317
6.10 Table of Laplace Transforms, 318
Chapter Review Questions and Problems, 320
Chapter Summary, 323
Part B. LINEAR ALGEBRA, VECTOR CALCULUS 325
CHAPTER 7 Linear Algebra: Matrices, Vectors, Determinants 326
7.1 Basic Concepts, 327
7.2 Matrix Addition, Scalar Multiplication, 330
7.3 Matrix Multiplication, 334
7.4 Linear Systems of Equations. Gauss Elimination, 344
7.5 Linear Independence. Vector Space. Rank of a Matrix, 354
7.6 Linear Systems: General Properties of Solutions, 361
Contents xiii
7.7 Inverse of a Matrix, 365
7.8 Determinants, 370
7.9 Rank in Terms of Determinants. Cramer's Rule, 380
7.10 Eigenvalues, Eigenvectors, 386
7.11 Some Applications of Eigenvalue Problems, 392
7.12 Symmetric, Skew Symmetric, and Orthogonal Matrices, 397
7.13 Hermitian, Skew Hermitian, and Unitary Matrices, 401
7.14 Properties of Eigenvectors. Diagonalization, 408
7.15 Vector Spaces, Inner Product Spaces, Linear Transformations.
Optional, 414
Chapter Review Questions and Problems, 422
Chapter Summary, 426
CHAPTER 8 Vector Differential Calculus. Grad, Div, Curl 428
8.1 Vector Algebra in 2 Space and 3 Space, 429
8.2 Inner Product (Dot Product), 436
8.3 Vector Product (Cross Product), 442
8.4 Vector and Scalar Functions and Fields. Derivatives, 451
8.5 Curves. Tangents. Arc Length, 457
8.6 Velocity and Acceleration, 464
8.7 Curvature and Torsion of a Curve. Optional, 469
8.8 Review from Calculus in Several Variables. Optional, All
8.9 Gradient of a Scalar Field. Directional Derivative, 475
8.10 Divergence of a Vector Field, 482
8.11 Curl of a Vector Field, 486
8.12 Grad, Div, Curl in Curvilinear Coordinates. Optional, 488
Chapter Review Questions and Problems, 494
Chapter Summary, 497
CHAPTER 9 Vector Integral Calculus. Integral Theorems 500
9.1 Line Integrals, 500
9.2 Line Integrals Independent of Path, 507
9.3 From Calculus: Double Integrals. Optional, 515
9.4 Green's Theorem in the Plane, 522
9.5 Surfaces for Surface Integrals, 529
9.6 Surface Integrals, 534
9.7 Triple Integrals. Divergence Theorem of Gauss, 544
9.8 Further Applications of the Divergence Theorem, 550
9.9 Stokes's Theorem, 556
Chapter Review Questions and Problems, 562
Chapter Summary, 563
Part C. FOURIER ANALYSIS AND
PARTIAL DIFFERENTIAL EQUATIONS 565
CHAPTER 10 Fourier Series, Integrals, and Transforms 566
10.1 Periodic Functions. Trigonometric Series, 566
10.2 Fourier Series, 569
10.3 Functions of Any Period p = 2L, 577
xiv Contents
10.4 Even and Odd Functions, 580
10.5 Half Range Expansions, 585
10.6 Complex Fourier Series. Optional, 588
10.7 Forced Oscillations, 591
10.8 Approximation by Trigonometric Polynomials, 595
10.9 Fourier Integrals, 598
10.10 Fourier Cosine and Sine Transforms, 606
10.11 Fourier Transform, 611
10.12 Tables of Transforms, 619
Chapter Review Questions and Problems, 622
Chapter Summary, 624
CHAPTER 11 Partial Differential Equations 626
11.1 Basic Concepts, 627
11.2 Modeling: Vibrating String, Wave Equation, 629
11.3 Separation of Variables. Use of Fourier Series, 631
11.4 D'Alembert's Solution of the Wave Equation, 639
11.5 Heat Equation: Solution by Fourier Series, 645
11.6 Heat Equation: Solution by Fourier Integrals, 657
11.7 Modeling: Membrane, Two Dimensional Wave Equation, 662
11.8 Rectangular Membrane, Use of Double Fourier Series, 664
11.9 Laplacian in Polar Coordinates, 672
11.10 Circular Membrane. Use of Fourier Bessel Series, 675
11.11 Laplace's Equation. Potential, 682
11.12 Laplacian in Spherical Coordinates. Legendre's Equation, 686
11.13 Solution by Laplace Transforms, 692
11.14 Solution by Fourier Transforms, 696
Chapter Review Questions and Problems, 700
Chapter Summary, 702
Part D. COMPLEX ANALYSIS 705
CHAPTER 12 Complex Numbers. Complex Analytic Functions 706
12.1 Complex Numbers. Complex Plane, 706
12.2 Polar Form of Complex Numbers. Powers and Roots, 711
12.3 Curves and Regions in the Complex Plane, 718
12.4 Limit. Derivative. Analytic Function, 721
12.5 Cauchy Riemann Equations, 726
12.6 Exponential Function, 731
12.7 Trigonometric Functions, Hyperbolic Functions, 735
12.8 Logarithm. General Power, 739
12.9 Mapping by Special Functions. Optional, 743
Chapter Review Questions and Problems, 747
Chapter Summary, 749
CHAPTER 13 Complex Integration 751
13.1 Line Integral in the Complex Plane, 751
13.2 Two Integration Methods. Examples, 755
13.3 Cauchy's Integral Theorem, 761
Contents xv
13.4 Existence of Indefinite Integral, 768
13.5 Cauchy's Integral Formula, 770
13.6 Derivatives of Analytic Functions, 774
Chapter Review Questions and Problems, 778
Chapter Summary, 780
CHAPTER 14 Power Series, Taylor Series, Laurent Series 781
14.1 Sequences, Series, Convergence Tests, 781
14.2 Power Series, 791
14.3 Functions Given by Power Series, 796
14.4 Taylor Series, 802
14.5 Power Series: Practical Methods, 808
14.6 Uniform Convergence, 812
14.7 Laurent Series, 821
14.8 Singularities and Zeros. Infinity, 828
Chapter Review Questions and Problems, 834
Chapter Summary, 835
CHAPTER 15 Residue Integration Method 837
15.1 Residues, 837
15.2 Residue Theorem, 842
15.3 Evaluation of Real Integrals, 845
15.4 Further Types of Real Integrals, 849
Chapter Review Questions and Problems, 856
Chapter Summary, 857
CHAPTER 16 Conformal Mapping 859
16.1 Conformal Mapping, 859
16.2 Linear Fractional Transformations, 863
16.3 Special Linear Fractional Transformations, 868
16.4 Mapping by Other Functions, 873
16.5 Riemann Surfaces, 878
Chapter Review Questions and Problems, 883
Chapter Summary, 884
CHAPTER 17 Complex Analysis Applied to Potential Theory 885
17.1 Electrostatic Fields, 886
17.2 Use of Conformal Mapping, 890
17.3 Heat Problems, 894
17.4 Fluid Flow, 898
17.5 Poisson's Integral Formula, 905
17.6 General Properties of Harmonic Functions, 910
Chapter Review Questions and Problems, 914
Chapter Summary, 915
PartE. NUMERICAL METHODS 916
CHAPTER 18 Numerical Methods in General 918
18.1 Introduction, 919
18.2 Solution of Equations by Iteration, 925
xvi Contents
18.3 Interpolation, 936
18.4 Splines, 949
18.5 Numerical Integration and Differentiation, 957
Chapter Review Questions and Problems, 968
Chapter Summary, 970
CHAPTER 19 Numerical Methods in Linear Algebra 972
19.1 Linear Systems: Gauss Elimination, 972
19.2 Linear Systems: LU Factorization, Matrix Inversion, 981
19.3 Linear Systems: Solution by Iteration, 986
19.4 Linear Systems: Ill Conditioning, Norms, 993
19.5 Method of Least Squares, 1000
19.6 Matrix Eigenvalue Problems: Introduction, 1004
19.7 Inclusion of Matrix Eigenvalues, 1006
19.8 Eigenvalues by Iteration (Power Method), 1012
19.9 Deflation of a Matrix, 1016
19.10 Householder Tridiagonalization and QR Factorization, 1019
Chapter Review Questions and Problems, 1029
Chapter Summary, 1031
CHAPTER 20 Numerical Methods for Differential Equations 1034
20.1 Methods for First Order Differential Equations, 1034
20.2 Multistep Methods, 1044
20.3 Methods for Second Order Differential Equations, 1048
20.4 Numerical Methods for Elliptic Partial Differential Equations, 1055
20.5 Neumann and Mixed Problems. Irregular Boundary, 1065
20.6 Methods for Parabolic Equations, 1070
20.7 Methods for Hyperbolic Equations, 1075
Chapter Review Questions and Problems, 1078
Chapter Summary, 1081
PartF. OPTIMIZATION, GRAPHS 1083
CHAPTER 21 Unconstrained Optimization, Linear Programming 1084
21.1 Basic Concepts. Unconstrained Optimization, 1084
21.2 Linear Programming, 1088
21.3 Simplex Method, 1092
21.4 Simplex Method: Degeneracy, Difficulties in Starting, 1097
Chapter Review Questions and Problems, 1102
Chapter Summary, 1104
CHAPTER 22 Graphs and Combinatorial Optimization 1105
22.1 Graphs and Digraphs, 1105
22.2 Shortest Path Problems. Complexity, 1110
22.3 Bellman's Optimality Principle. Dijkstra's Algorithm, 1116
22.4 Shortest Spanning Trees. Kruskal's Greedy Algorithm, 1120
22.5 Prim's Algorithm for Shortest Spanning Trees, 1125
22.6 Networks. Flow Augmenting Paths, 1128
22.7 Ford Fulkerson Algorithm for Maximum Flow, 1134
Contents xvii
22.8 Assignment Problems. Bipartite Matching, 1138
Chapter Review Questions and Problems, 1145
Chapter Summary, 1147
PartG. PROBABILITY AND STATISTICS 1148
CHAPTER 23 Probability Theory 1149
23.1 Experiments, Outcomes, Events, 1149
23.2 Probability, 1153
23.3 Permutations and Combinations, 1160
23.4 Random Variables, Probability Distributions, 1165
23.5 Mean and Variance of a Distribution, 1173
23.6 Binomial, Poisson, and Hypergeometric Distributions, 1178
23.7 Normal Distribution, 1184
23.8 Distributions of Several Random Variables, 1191
Chapter Review Questions and Problems, 1200
Chapter Summary, 1203
CHAPTER 24 Mathematical Statistics 1205
24.1 Nature and Purpose of Statistics, 1205
24.2 Random Sampling. Random Numbers, 1207
24.3 Processing of Samples, 1209
24.4 Sample Mean, Sample Variance, 1216
24.5 Estimation of Parameters, 1219
24.6 Confidence Intervals, 1222
24.7 Testing of Hypotheses, Decisions, 1232
24.8 Quality Control, 1244
24.9 Acceptance Sampling, 1249
24.10 Goodness of Fit. *2 Test, 1255
24.11 Nonparametric Tests, 1258
24.12 Pairs of Measurements. Fitting Straight Lines, 1261
Chapter Review Questions and Problems, 1267
Chapter Summary, 1270
APPENDIX 1 References Al
APPENDIX 2 Answers to Odd Numbered Problems A6
APPENDIX 3 Auxiliary Material A66
A3.1 Formulas for Special Functions, A66
A3.2 Partial Derivatives, A72
A3.3 Sequences and Series, A74
APPENDIX 4 Additional Proofs A77
APPENDIX 5 Tables A97
INDEX II |
| any_adam_object | 1 |
| author | Kreyszig, Erwin 1922-2008 |
| author_GND | (DE-588)117714518 |
| author_facet | Kreyszig, Erwin 1922-2008 |
| author_role | aut |
| author_sort | Kreyszig, Erwin 1922-2008 |
| author_variant | e k ek |
| building | Verbundindex |
| bvnumber | BV008184003 |
| callnumber-first | Q - Science |
| callnumber-label | QA401 |
| callnumber-raw | QA401 |
| callnumber-search | QA401 |
| callnumber-sort | QA 3401 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 110 SK 950 |
| classification_tum | MAT 023f MAT 001f |
| ctrlnum | (OCoLC)831320397 (DE-599)BVBBV008184003 |
| dewey-full | 510/.2462 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510/.2462 |
| dewey-search | 510/.2462 |
| dewey-sort | 3510 42462 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 7. ed. |
| format | Book |
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| genre | 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content |
| genre_facet | Aufgabensammlung |
| id | DE-604.BV008184003 |
| illustrated | Illustrated |
| indexdate | 2025-02-11T15:01:36Z |
| institution | BVB |
| isbn | 0471599891 0471553808 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005401149 |
| oclc_num | 831320397 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-92 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-573 DE-20 DE-858 DE-11 DE-188 DE-862 DE-BY-FWS |
| owner_facet | DE-91G DE-BY-TUM DE-92 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-573 DE-20 DE-858 DE-11 DE-188 DE-862 DE-BY-FWS |
| physical | Getr. Zählung graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Wiley |
| record_format | marc |
| spellingShingle | Kreyszig, Erwin 1922-2008 Advanced engineering mathematics Analyse (wiskunde) gtt Mathématiques de l'ingénieur Physique mathématique Wiskunde gtt Mathematik Mathematische Physik Engineering mathematics Mathematical physics Maple V (DE-588)4276266-2 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Maple V 4.0 (DE-588)4407788-9 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4276266-2 (DE-588)4137304-2 (DE-588)4407788-9 (DE-588)4037944-9 (DE-588)4143389-0 |
| title | Advanced engineering mathematics |
| title_auth | Advanced engineering mathematics |
| title_exact_search | Advanced engineering mathematics |
| title_full | Advanced engineering mathematics Erwin Kreyszig |
| title_fullStr | Advanced engineering mathematics Erwin Kreyszig |
| title_full_unstemmed | Advanced engineering mathematics Erwin Kreyszig |
| title_short | Advanced engineering mathematics |
| title_sort | advanced engineering mathematics |
| topic | Analyse (wiskunde) gtt Mathématiques de l'ingénieur Physique mathématique Wiskunde gtt Mathematik Mathematische Physik Engineering mathematics Mathematical physics Maple V (DE-588)4276266-2 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Maple V 4.0 (DE-588)4407788-9 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Analyse (wiskunde) Mathématiques de l'ingénieur Physique mathématique Wiskunde Mathematik Mathematische Physik Engineering mathematics Mathematical physics Maple V Ingenieurwissenschaften Maple V 4.0 Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005401149&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kreyszigerwin advancedengineeringmathematics |
Inhaltsverzeichnis
UB Lesesaal Mathematik
Signatur notieren und vor Ort nutzen oder für zwei Wochen ausleihen| Signatur: | 80 SK 950 K92 A2(7) |
|---|---|
| Exemplar 1 | entleihbar Vorhanden |
UB Lesesaal Physik
Signatur notieren und vor Ort nutzen oder für zwei Wochen ausleihen| Signatur: | 84 SK 950 K92 A2(7) |
|---|---|
| Exemplar 1 | entleihbar Vorhanden |
An OTH ausleihen
Ausleihen an der OTH sind mit eigenem Ausweis möglich.