Scientific computing with MATLAB:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press, Taylor & Francis Group
[2016]
|
| Edition: | Second edition |
| Series: | A Chapman & Hall Book
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 586 Seiten Diagramme |
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MARC
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| 245 | 1 | 0 | |a Scientific computing with MATLAB |c Dingyü Xue, Northeastern University, Shenyang, China ; YangQuan Chen, University of California, Merced, USA |
| 250 | |a Second edition | ||
| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press, Taylor & Francis Group |c [2016] | |
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Record in the Search Index
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| adam_text | Contents
Preface xiii
Preface of the First Edition xv
1 Computer Mathematics Languages — An Overview 1
1.1 Computer Solutions to Mathematics Problems ......................... 1
1.1.1 Why should we study computer mathematics language?............ 1
1.1.2 Analytical solutions versus numerical solutions............... 5
1.1.3 Mathematics software packages: an overview ................... 5
1.1.4 Limitations of conventional computer languages................ 6
1.2 Summary of Computer Mathematics Languages .......................... 8
1.2.1 A brief historic review of MATLAB ................................ 8
1.2.2 Three widely used computer mathematics languages............. 8
1.2.3 Introduction to free scientific open-source softwares............. 9
1.3 Outline of the Book .................................................... 9
1.3.1 The organization of the book...................................... 9
1.3.2 How to learn and use MATLAB ..................................... 11
1.3.3 The three-phase solution methodology............................. 11
Exercises................................................................... 13
Bibliography................................................................ 13
2 Fundamentals of MATLAB Programming and Scientific Visualization 15
2.1 Essentials in MATLAB Programming ...................................... 16
2.1.1 Variables and constants in MATLAB................................ 16
2.1.2 Data structures.................................................. 16
2.1.3 Basic statement structures of MATLAB............................. 18
2.1.4 Colon expressions and sub-matrices extraction.................... 19
2.2 Fundamental Mathematical Calculations ................................. 20
2.2.1 Algebraic operations of matrices................................. 20
2.2.2 Logic operations of matrices..................................... 22
2.2.3 Relationship operations of matrices.............................. 22
2.2.4 Simplifications and presentations of analytical results ......... 22
2.2.5 Basic number theory computations................................. 24
2.3 Flow Control Structures of MATLAB Language ......................... 25
2.3.1 Loop control structures.......................................... 26
2.3.2 Conditional control structures................................... 27
2.3.3 Switch structure................................................. 28
2.3.4 Trial structure.................................................. 2^
2.4 Writing and Debugging MATLAB Functions ................................ 30
v
VI
Contents
2.4.1 Basic structure of MATLAB functions...............................*
2.4.2 Programming of functions with variable numbers of arguments m
inputs and outputs................................................
2.4.3 Inline functions and anonymous functions..........................
2.4.4 Pseudo code and source code protection............................
2.5 Two-dimensional Graphics ................................................
2.5.1 Basic statements of two-dimensional plotting......................
2.5.2 Plotting with multiple horizontal or vertical axes................
2.5.3 Other two-dimensional plotting functions..........................
2.5.4 Plots of implicit functions.......................................
2.5.5 Graphics decorations..............................................
2.5.6 Data file access with MATLAB......................................
2.6 Three-dimensional Graphics ..............................................
2.6.1 Plotting of three-dimensional curves..............................
2.6.2 Plotting of three-dimensional surfaces............................
2.6.3 Viewpoint settings in 3D graphs...................................
2.6.4 Surface plots of parametric equations.............................
2.6.5 Spheres and cylinders.............................................
2.6.6 Drawing 2D and 3D contours........................................
2.6.7 Drawing 3D implicit functions ....................................
2.7 Four-dimensional Visualization...........................................
Exercises ....................................................................
Bibliography..................................................................
30
33
34
34
35
35
37
38
39
40 42 44
44
45
48
49
50
51
52
53 55 60
3 Calculus Problems
61
3.1 Analytical Solutions to Limit Problems ......................
3.1.1 Limits of univariate functions.........................
3.1.2 Limits of interval functions...........................
3.1.3 Limits of multivariate functions.......................
3.2 Analytical Solutions to Derivative Problems .................
3.2.1 Derivatives and high-order derivatives.................
3.2.2 Partial derivatives of multivariate functions..........
3.2.3 Jacobian matrix of multivariate functions..............
3.2.4 Hessian partial derivative matrix......................
3.2.5 Partial derivatives of implicit functions..............
3.2.6 Derivatives of parametric equations....................
3.2.7 Gradients, divergences and curls of fields.............
3.3 Analytical Solutions to Integral Problems....................
3.3.1 Indefinite integrals...................................
3.3.2 Computing definite, infinite and improper integrals .
3.3.3 Computing multiple integrals...........................
3.4 Series Expansions and Finite-term Series Approximations
3.4.1 Taylor series expansion .....................
3.4.2 Fourier series expansion...................
3.5 Infinite Series and Products ...
3.5.1 Series.........................* ‘ ’.................
3.5.2 Product of sequences...............
3.5.3 Convergence test of infinite series ....
61
62
64
66
67
67
69
71
72 72 74
74
75
76
77
79
80 80 83 86
87
88 89
Contents
vii
3.6 Path Integrals and Line Integrals.......................................... 91
3.6.1 Path integrals...................................................... 91
3.6.2 Line integrals................................................... 93
3.7 Surface Integrals.......................................................... 94
3.7.1 Scalar surface integrals......................................... 94
3.7.2 Vector surface integrals......................................... 96
3.8 Numerical Differentiation............................................... 97
3.8.1 Numerical differentiation algorithms............................. 97
3.8.2 Central-point difference algorithm with MATLAB implementation . 98
3.8.3 Gradient computations of functions with two variables.............. 100
3.9 Numerical Integration Problems ........................................... 101
3.9.1 Numerical integration from given data using trapezoidal method . . 102
3.9.2 Numerical integration of univariate functions...................... 103
3.9.3 Numerical infinite integrals....................................... 106
3.9.4 Evaluating integral functions...................................... 107
3.9.5 Numerical solutions to double integrals ........................... 108
3.9.6 Numerical solutions to triple integrals............................ Ill
3.9.7 Multiple integral evaluations...................................... 112
Exercises .................................................................... 113
Bibliography.................................................................. 119
4 Linear Algebra Problems 121
4.1 Inputting Special Matrices ............................................... 122
4.1.1 Numerical matrix input............................................. 122
4.1.2 Defining symbolic matrices......................................... 126
4.1.3 Sparse matrix input................................................ 127
4.2 Fundamental Matrix Operations............................................. 128
4.2.1 Basic concepts and properties of matrices.......................... 128
4.2.2 Matrix inversion................................................... 135
4.2.3 Generalized matrix inverse ........................................ 138
4.2.4 Matrix eigenvalue problems......................................... 140
4.3 Fundamental Matrix Transformations ....................................... 142
4.3.1 Similarity transformations and orthogonal matrices................. 142
4.3.2 Triangular and Cholesky factorizations............................. 144
4.3.3 Companion, diagonal and Jordan transformations .................... 149
4.3.4 Singular value decompositions...................................... 152
4.4 Solving Matrix Equations.................................................. 155
4.4.1 Solutions to linear algebraic equations............................ 155
4.4.2 Solutions to Lyapunov equations.................................... 158
4.4.3 Solutions to Sylvester equations................................... 161
4.4.4 Solutions of Diophantine equations................................. 163
4.4.5 Solutions to Riccati equations..................................... 165
4.5 Nonlinear Functions and Matrix Function Evaluations....................... 166
4.5.1 Element-by-element computations ................................... 166
4.5.2 Computations of matrix exponentials................................ 166
4.5.3 Trigonometric functions of matrices ............................... 168
4.5.4 General matrix functions .......................................... 171
4.5.5 Power of a matrix ................................................. 173
Contents
vm
Exercises.........................................
Bibliography .....................................
5 Integral Transforms and Complex-valued Functions
175
180
183
5.1 Laplace Transforms and Their Inverses ..................................
5.1.1 Definitions and properties........................................
5.1.2 Computer solution to Laplace transform problems...................
5.1.3 Numerical solutions of Laplace transforms.........................
5.2 Fourier Transforms and Their Inverses...................................
5.2.1 Definitions and properties........................................
5.2.2 Solving Fourier transform problems................................
5.2.3 Fourier sinusoidal and cosine transforms..........................
5.2.4 Discrete Fourier sine, cosine transforms..........................
5.2.5 Fast Fourier transforms...........................................
5.3 Other Integral Transforms ..............................................
5.3.1 Mellin transform..................................................
5.3.2 Hankel transform solutions........................................
5.4 z Transforms and Their Inverses.........................................
5.4.1 Definitions and properties of z transforms and inverses...........
5.4.2 Computations of 2 transform.......................................
5.4.3 Bilateral z transforms............................................
5.4.4 Numerical inverse z transform of rational functions...............
5.5 Essentials of Complex-valued Functions..................................
5.5.1 Complex matrices and their manipulations .........................
5.5.2 Mapping of complex-valued functions ..............................
5.5.3 Riemann surfaces..................................................
5.6 Solving Complex-valued Function Problems................................
5.6.1 Concept and computation of poles and residues.....................
5.6.2 Partial fraction expansion for rational functions.................
5.6.3 Inverse Laplace transform using PFEs..............................
5.6.4 Laurent series expansions.........................................
5.6.5 Computing closed-path integrals...................................
5.7 Solutions of Difference Equations ......................................
5.7.1 Analytical solutions of linear difference equations................
5.7.2 Numerical solutions of linear time varying difference equations . . .
5.7.3 Solutions of linear time-invariant difference equations ..........
5.7.4 Numerical solutions of nonlinear difference equations.............
Exercises....................................................................
Bibliography ..............................................................
184
184
185 187 190
190
191
193
194
195 197
197
198 200 200 201 202 203
203
204 204 206 207 207 210
214
215 219 221 221 222
224
225
226 230
6 Nonlinear Equations and Numerical Optimization Problems
231
6.1 Nonlinear Algebraic Equations .......................................... 232
6.1.1 Graphical method for solving nonlinear equations.................. 232
6.1.2 Quasi-analytic solutions to polynomial-type equations............. 234
6.1.3 Numerical solutions to general nonlinear equations................ 238
6.2 Nonlinear Equations with Multiple Solutions.............................. 240
6.2.1 Numerical solutions................................................ 241
6.2.2 Finding high-precision solutions.................... 9
Contents
IX
6.2.3 Solutions of under determined equations.............................. 247
6.3 Unconstrained Optimization Problems......................................... 248
6.3.1 Analytical solutions and graphical solution methods.................. 249
6.3.2 Solution of unconstrained optimization using MATLAB.................. 250
6.3.3 Global minimum and local minima...................................... 252
6.3.4 Solving optimization problems with gradient information ............. 255
6.4 Constrained Optimization Problems........................................... 257
6.4.1 Constraints and feasibility regions.................................. 257
6.4.2 Solving linear programming problems ................................. 258
6.4.3 Solving quadratic programming problems............................... 263
6.4.4 Solving general nonlinear programming problems....................... 264
6.5 Mixed Integer Programming Problems........................................ 268
6.5.1 Enumerate method in integer programming problems .................... 268
6.5.2 Solutions of linear integer programming problems..................... 270
6.5.3 Solutions of nonlinear integer programming problems.................. 271
6.5.4 Solving binary programming problems.................................. 273
6.5.5 Assignment problems.................................................. 275
6.6 Linear Matrix Inequalities ................................................ 276
6.6.1 A general introduction to LMIs....................................... 276
6.6.2 Lyapunov inequalities................................................ 277
6.6.3 Classification of LMI problems....................................... 279
6.6.4 LMI problem solutions with MATLAB.................................... 279
6.6.5 Optimization of LMI problems by YALMIP Toolbox....................... 281
6.7 Solutions of Multi-objective Programming Problems........................... 283
6.7.1 Multi-objective optimization model................................... 283
6.7.2 Least squares solutions of unconstrained multi-objective programming problems............................................................ 283
6.7.3 Converting multi-objective problems into single-objective ones . . . 284
6.7.4 Pareto front of multi-objective programming problems................. 287
6.7.5 Solutions of minimax problems........................................ 289
6.7.6 Solutions of multi-objective goal attainment problems................ 290
6.8 Dynamic Programming and Shortest Path Planning......................... 291
6.8.1 Matrix representation of graphs...................................... 292
6.8.2 Optimal path planning of oriented graphs............................. 292
6.8.3 Optimal path planning of undigraphs ................................. 296
6.8.4 Optimal path planning for graphs described by coordinates............ 296
Exercises...................................................................... 297
Bibliography.................................................................... 303
7 Differential Equation Problems 305
7.1 Analytical Solution Methods for Some Ordinary Differential Equations . . 306
7.1.1 Linear time-invariant ordinary differential equations................ 306
7.1.2 Analytical solution with MATLAB...................................... 307
7.1.3 Analytical solutions of linear state space equations................. 310
7.1.4 Analytical solutions to special nonlinear differential equations .... 311
7.2 Numerical Solutions to Ordinary Differential Equations...................... 312
7.2.1 Overview of numerical solution algorithms............................ 312
7.2.2 Fixed-step Runge-Kutta algorithm and its MATLAB implementation 314
X
Contents
7.2.3 Numerical solution to first-order vector ODEs.........................
7.3 Transforms to Standard Differential Equations...............................
7.3.1 Manipulating a single high-order ODE..................................
7.3.2 Manipulating multiple high-order ODEs.................................
7.3.3 Validation of numerical solutions to ODEs.............................
7.3.4 Transformation of differential matrix equations.......................
7.4 Solutions to Special Ordinary Differential Equations........................
7.4.1 Solutions of stiff ordinary differential equations....................
7.4.2 Solutions of implicit differential equations..........................
7.4.3 Solutions to differential algebraic equations.........................
7.4.4 Solutions of switching differential equations.........................
7.4.5 Solutions to linear stochastic differential equations..................
7.5 Solutions to Delay Differential Equations...................................
7.5.1 Solutions of typical delay differential equations.....................
7.5.2 Solutions of differential equations with variable delays..............
7.5.3 Solutions of neutral-type delay differential equations................
7.6 Solving Boundary Value Problems.............................................
7-6.1 Shooting algorithm for linear equations................................
7.6.2 Boundary value problems of nonlinear equations........................
7.6.3 Solutions to general boundary value problems..........................
7.7 Introduction to Partial Differential Equations..............................
7.7.1 Solving a set of one-dimensional partial differential equations . , . .
7.7.2 Mathematical description to two-dimensional PDEs .....................
7-7.3 The GUI for the PDE Toolbox — an introduction..........................
7.8 Solving ODEs with Block Diagrams in Simulink ...............................
7.8.1 A brief introduction to Simulink......................................
7.8.2 Simulink — relevant blocks............................................
7.8.3 Using Simulink for modeling and simulation of ODEs ...................
Exercises................................................................
Bibliography................................................
315
320
320
321
325
326 32K 320 332 335
337
338 342 342 344
347
348 348 350 352 355 355
357
358 365 365 365 367 373 379
8 Data Interpolation and Functional Approximation Problems 381
8.1 Interpolation and Data Fitting.............................
8.1.1 One-dimensional data interpolation...................
8.1.2 Definite integral evaluation from given samples......
8.1.3 Two-dimensional grid data interpolation..............
8.1.4 Two-dimensional scattered data interpolation.........
8.1.5 Optimization problems based on scattered sample data
8.1.6 High-dimensional data interpolations.................
8.2 Spline Interpolation and Numerical Calculus ...............
8.2.1 Spline interpolation in MATLAB.......................
8.2.2 Numerical differentiation and integration with splines .
8.3 Fitting Mathematical Models from Data .....................
8.3.1 Polynomial fitting...................................
8.3.2 Curve fitting by linear combination of basis functions .
8.3.3 Least squares curve fitting..........................
8.3.4 Least squares fitting of multivariate functions......
8.4 Rational Function Approximations..........................
382
382
385
387
389
392
393
394
395 398 401 401 403 405
407
408
Contents
xi
8.4.1 Approximation by continued fraction expansions..................... 408
8.4.2 Pade rational approximations....................................... 412
8.4.3 Special approximation polynomials.................................. 414
8.5 Special Functions and Their Plots .................................. 416
8.5.1 Gamma functions.................................................... 416
8.5.2 Beta functions .................................................... 418
8.5.3 Legendre functions................................................. 419
8.5.4 Bessel functions................................................... 420
8.5.5 Mittag-Leffler functions........................................... 421
8.6 Signal Analysis and Digital Signal Processing............................. 425
8.6.1 Correlation analysis............................................... 425
8.6.2 Power spectral analysis............................................ 427
8.6.3 Filtering techniques and filter design............................. 429
Exercises...................................................................... 433
Bibliography................................................................... 436
9 Probability and Mathematical Statistics Problems 437
9.1 Probability Distributions and Pseudorandom Numbers ....................... 438
9.1.1 Introduction to probability density functions and cumulative distribution functions........................................................... 438
9.1.2 Probability density functions and cumulative distribution functions
of commonly used distributions..................................... 439
9.1.3 Random numbers and pseudorandom numbers............................ 447
9.2 Solving Probability Problems.............................................. 448
9.2.1 Histogram and pie representation of discrete numbers .............. 448
9.2.2 Probability computation of continuous functions.................... 450
9.2.3 Monte Carlo solutions to mathematical problems..................... 451
9.2.4 Simulation of random walk processes................................ 453
9.3 Fundamental Statistical Analysis.......................................... 454
9.3.1 Mean and variance of stochastic variables.......................... 454
9.3.2 Moments of stochastic variables.................................... 456
9.3.3 Covariance analysis of multivariate stochastic variables........... 457
9.3.4 Joint PDFs and CDFs of multivariate normal distributions........... 458
9.3.5 Outliers, quartiles and box plots.................................. 459
9.4 Statistical Estimations .................................................. 462
9.4.1 Parametric estimation and interval estimation...................... 462
9.4.2 Multivariate linear regression and interval estimation............. 463
9.4.3 Nonlinear least squares parametric and interval estimations........ 466
9.4.4 Maximum likelihood estimations..................................... 468
9.5 Statistical Hypothesis Tests.............................................. 469
9.5.1 Concept and procedures for statistic hypothesis test............... 469
9.5.2 Hypothesis tests for distributions................................. 471
9.6 Analysis of Variance...................................................... 474
9.6.1 One-way ANOVA ..................................................... 474
9.6.2 Two-way ANOVA ..................................................... 476
9.6.3 n-way ANOVA........................................................ 478
9.7 Principal Component Analysis ............................................. 478
Exercises...................................................................... 480
Contents
xii
Bibliography........*..............................
10 Topics on Nontraditional Mathematical Branches
4*3
485
10.1 Fuzzy Logic and Fuzzy Inference............................................
10.1.1 MATLAB solutions to classical set problems .........................
10.1.2 Fuzzy sets and membership functions ................................
10.1.3 Fuzzy rules and fuzzy inference.....................................
10.2 Rough Set Theory and Its Applications......................................
10.2.1 Introduction to rough set theory....................................
10.2.2 Data processing problem solutions using rough sets..................
10.3 Neural Network and Applications in Data Fitting Problems...................
10.3.1 Fundamentals of neural networks.....................................
10.3.2 Feedforward neural network..........................................
10.3.3 Radial basis neural networks and applications.......................
10.3.4 Graphical user interface for neural networks........................
10.4 Evolutionary Computing and Global Optimization Problem Solutions . . .
10.4.1 Basic idea of genetic algorithms....................................
10.4.2 Solutions to optimization problems with genetic algorithms..........
10.4.3 Solving constrained problems........................................
10.4.4 Solving optimization problems with Global Optimization Toolbox
10.4.5 Towards accurate global minimum solutions...........................
10.5 Wavelet Transform and Its Applications in Data Processing..................
10.5.1 Wavelet transform and waveforms of wavelet bases....................
10.5.2 Wavelet transform in signal processing problems.....................
10.5.3 Graphical user interface in wavelets ...............................
10.6 Fractional-order Calculus..................................................
10.6.1 Definitions of fractional-order calculus............................
10.6.2 Properties and relationship of various fractional-order differentiation
definitions.........................................................
10.6.3 Evaluating fractional-order differentiation.........................
10.6.4 Solving fractional-order differential equations.....................
10.6.5 Block diagram based solutions of nonlinear fractional-order ordinary
differential equations..............................
10.6.6 Object-oriented modeling and analysis of linear fractional-order
systems....................................
Exercises..............................
Bibliography ......................
485
485
488
404
4M
406
409
502
503
504 511 514
516
517
518 522 522
528
529
530 534 538
538
539
540
541 547
553
557
564
567
MATLAB Functions Index
569
Index
577
|
| any_adam_object | 1 |
| author | Xue, Dingyu Chen, Yangquan 1966- |
| author_GND | (DE-588)1098160967 (DE-588)121213277 |
| author_facet | Xue, Dingyu Chen, Yangquan 1966- |
| author_role | aut aut |
| author_sort | Xue, Dingyu |
| author_variant | d x dx y c yc |
| building | Verbundindex |
| bvnumber | BV043500197 |
| classification_rvk | ST 601 |
| ctrlnum | (OCoLC)953391073 (DE-599)BVBBV043500197 |
| dewey-full | 502.8553 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 502 - Miscellany |
| dewey-raw | 502.8553 |
| dewey-search | 502.8553 |
| dewey-sort | 3502.8553 |
| dewey-tens | 500 - Natural sciences and mathematics |
| discipline | Allgemeine Naturwissenschaft Informatik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV043500197 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:27:22Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028916609 |
| oclc_num | 953391073 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-83 |
| owner_facet | DE-473 DE-BY-UBG DE-83 |
| physical | XVII, 586 Seiten Diagramme |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | CRC Press, Taylor & Francis Group |
| record_format | marc |
| series2 | A Chapman & Hall Book |
| spelling | Xue, Dingyu Verfasser (DE-588)1098160967 aut Scientific computing with MATLAB Dingyü Xue, Northeastern University, Shenyang, China ; YangQuan Chen, University of California, Merced, USA Second edition Boca Raton ; London ; New York CRC Press, Taylor & Francis Group [2016] © 2016 XVII, 586 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier A Chapman & Hall Book Science / Data processing Datenverarbeitung Naturwissenschaft Wissenschaftliches Rechnen (DE-588)4338507-2 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf MATLAB (DE-588)4329066-8 s Wissenschaftliches Rechnen (DE-588)4338507-2 s DE-604 Chen, Yangquan 1966- Verfasser (DE-588)121213277 aut Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028916609&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Xue, Dingyu Chen, Yangquan 1966- Scientific computing with MATLAB Science / Data processing Datenverarbeitung Naturwissenschaft Wissenschaftliches Rechnen (DE-588)4338507-2 gnd MATLAB (DE-588)4329066-8 gnd |
| subject_GND | (DE-588)4338507-2 (DE-588)4329066-8 |
| title | Scientific computing with MATLAB |
| title_auth | Scientific computing with MATLAB |
| title_exact_search | Scientific computing with MATLAB |
| title_full | Scientific computing with MATLAB Dingyü Xue, Northeastern University, Shenyang, China ; YangQuan Chen, University of California, Merced, USA |
| title_fullStr | Scientific computing with MATLAB Dingyü Xue, Northeastern University, Shenyang, China ; YangQuan Chen, University of California, Merced, USA |
| title_full_unstemmed | Scientific computing with MATLAB Dingyü Xue, Northeastern University, Shenyang, China ; YangQuan Chen, University of California, Merced, USA |
| title_short | Scientific computing with MATLAB |
| title_sort | scientific computing with matlab |
| topic | Science / Data processing Datenverarbeitung Naturwissenschaft Wissenschaftliches Rechnen (DE-588)4338507-2 gnd MATLAB (DE-588)4329066-8 gnd |
| topic_facet | Science / Data processing Datenverarbeitung Naturwissenschaft Wissenschaftliches Rechnen MATLAB |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028916609&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT xuedingyu scientificcomputingwithmatlab AT chenyangquan scientificcomputingwithmatlab |