A first course in applied mathematics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken
Wiley
2012
|
| Schlagworte: | |
| Online-Zugang: | 13 80 Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XVI, 439 S. Ill., graph. Darst. |
| ISBN: | 9781118229620 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | Titel: A first course in applied mathematics
Autor: Rebaza, Jorge C
Jahr: 2012
CONTENTS
Preface
Basics of Linear Algebra 1
1.1 Notation and Terminology 1
1.2 Vector and Matrix Norms 4
1.3 Dot Product and Orthogonality 8
1.4 Special Matrices 9
1.4.1 Diagonal and triangular matrices 9
1.4.2 Hessenberg matrices 10
1.4.3 Nonsingular and inverse matrices 11
1.4.4 Symmetric and positive definite matrices 12
1.4.5 Matrix exponential 14
1.4.6 Permutation matrices 15
1.4.7 Orthogonal matrices 17
1.5 Vector Spaces 21
1.6 Linear Independence and Basis 24
1.7 Orthogonalization and Direct Sums 31
1.8 Column Space, Row Space, and Null Space 34
1.8.1 Linear transformations 40
1.9 Orthogonal Projections 43
1.10 Eigenvalues and Eigenvectors 47
vii
1.11 Similarity 56
1.12 Bezier Curves and Postscript Fonts 59
1.12.1 Properties of Bezier curves 61
1.12.2 Composite Bezier curves 66
1.13 Final Remarks and Further Reading 68
Exercises 69
Ranking Web Pages 79
2.1 The Power Method 80
2.2 Stochastic, Irreducible, and Primitive Matrices 84
2.3 Google s PageRank Algorithm 92
2.3.1 The personalization vector 99
2.3.2 Speed of convergence and sparsity 100
2.3.3 Power method and reordering 105
2.4 Alternatives to the Power Method 106
2.4.1 Linear system formulation 107
2.4.2 Iterative aggregation/disaggregation (IAD) 111
2.4.3 IAD and linear systems 117
2.5 Final Remarks and Further Reading 120
Exercises 121
Matrix Factorizations 131
3.1 LU Factorization 132
3.1.1 The complex case 137
3.1.2 Solving several systems 137
3.1.3 The PA = LU factorization 139
3.2 QR Factorization 142
3.2.1 QR and Gram-Schmidt 143
3.2.2 The complex case 147
3.2.3 QR and similarity 148
3.2.4 The QR algorithm 149
3.2.5 QR and LU 151
3.3 Singular Value Decomposition (SVD) 155
3.3.1 The complex case 160
3.3.2 Low-rank approximations 161
3.3.3 SVD and spectral norm 164
3.4 Schur Factorization 166
3.4.1 The complex case 171
3.4.2 Schur factorization and invariant subspaces 172
3.4.3 Exchanging eigenblocks 177
3.4.4 Block diagonalization 180
3.5 Information Retrieval 186
3.5.1 Query matching 187
3.5.2 Low-rank query matching 190
3.5.3 Term-term comparison 192
3.6 Partition of Simple Substitution Cryptograms 194
3.6.1 Rank-1 approximation 197
3.6.2 Rank-2 approximation 199
3.7 Final Remarks and Further Reading 203
Exercises 205
Least Squares 215
4.1 Projections and Normal Equations 215
4.2 Least Squares and QR Factorization 224
4.3 Lagrange Multipliers 228
4.4 Final Remarks and Further Reading 231
Exercises 231
Image Compression 235
5.1 Compressing with Discrete Cosine Transform 236
5.1.1 1 -D discrete cosine transform 236
5.1.2 2-D discrete cosine transform 242
5.1.3 Image compression and the human visual system 245
5.1.4 Basis functions and images 247
5.1.5 Low-pass filtering 250
5.1.6 Quantization 254
5.1.7 Compression of color images 257
5.2 Huffman Coding 260
5.2.1 Huffman coding and JPEG 262
5.3 Compression with SVD 267
5.3.1 Compressing grayscale images 268
5.3.2 Compressing color images 268
5.4 Final Remarks and Further Reading 269
Exercises 271
Ordinary Differential Equations 277
6.1 One-Dimensional Differential Equations 278
6.1.1 Existence and uniqueness 278
6.1.2 A simple population model 284
6.1.3 Emigration 285
6.1.4 Time-varying emigration 285
6.1.5 Competition 286
6.1.6 Spring systems 287
6.1.7 Undamped equations 293
6.1.8 Damped equations 299
6.1.9 RLC circuits 303
6.2 Linear Systems of Differential Equations 307
6.3 Solutions via Eigenvalues and Eigenvectors 307
6.3.1 Chains of generalized eigenvectors 311
6.4 Fundamental Matrix Solution 312
6.4.1 Nonhomogeneous systems 314
6.5 Final Remarks and Further Reading 316
Exercises 316
325
326
327
335
337
340
342
348
352
360
365
374
376
376
379
380
382
385
385
8 Mathematical Models 395
8.1 Optimization of a Waste Management System 396
8.1.1 Background 396
8.1.2 Description of the system 397
8.1.3 Development of the mathematical model 398
8.1.4 Building the objective function 399
8.1.5 Building the constraints 400
8.1.6 Numerical experiments 400
8.2 Grouping Problem in Networks 404
Dyn; imical Systems
7.1 Linear Dynamical Systems
7.1.1 Dynamics in two dimensions
7.1.2 Trace-determinant analysis
7.1.3 Stable, unstable, and center subspaces
7.2 Nonlinear Dynamical Systems
7.2.1 Linearization around an equilibrium point
7.2.2 Linearization around a periodic orbit
7.2.3 Connecting orbits
7.2.4 Chaos
7.2.5 Bifurcations
7.3 Predator-prey Models with Harvesting
7.3.1 Boundedness of solutions
7.3.2 EquiUbrium point analysis
7.3.3 Bifurcations
7.3.4 Connecting orbits
7.3.5 Other models
7.4 Final Remarks and Further Reading
Exercises
405
406
407
409
8.3 American Cutaneous Leishmaniasis 410
410
413
414
416
418
8.4 Variable Population Interactions 420
420
421
425
References 431
Index 435
8.2.1 Background
8.2.2 The A^-median approach
8.2.3 The probabilistic approach
8.2.4 Numerical experiments
American Cutaneous Leishmaniasis
8.3.1 Background
8.3.2 Development of the mathematical model
8.3.3 Equilibria and periodic orbits
8.3.4 Stability properties
8.3.5 Numerical computations
Variable Population Interactions
8.4.1 Model formulation
8.4.2 Local stability of equilibria
8.4.3 Bifurcations
|
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| discipline | Mathematik |
| format | Book |
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| institution | BVB |
| isbn | 9781118229620 |
| language | English |
| lccn | 2011043340 |
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| subject_GND | (DE-588)4114528-8 (DE-588)4148259-1 |
| title | A first course in applied mathematics |
| title_auth | A first course in applied mathematics |
| title_exact_search | A first course in applied mathematics |
| title_full | A first course in applied mathematics Jorge Rebaza |
| title_fullStr | A first course in applied mathematics Jorge Rebaza |
| title_full_unstemmed | A first course in applied mathematics Jorge Rebaza |
| title_short | A first course in applied mathematics |
| title_sort | a first course in applied mathematics |
| topic | Mathematisches Modell (DE-588)4114528-8 gnd Computersimulation (DE-588)4148259-1 gnd |
| topic_facet | Mathematisches Modell Computersimulation |
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