Exercises in computational mathematics with MATLAB:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2014
|
| Series: | Problem books in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 372 S. graph. Darst. |
| ISBN: | 9783662435106 9783662524008 |
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MARC
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| 100 | 1 | |a Lyche, Tom |e Verfasser |0 (DE-588)106006202X |4 aut | |
| 245 | 1 | 0 | |a Exercises in computational mathematics with MATLAB |c Tom Lyche ; Jean-Louis Merrien |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2014 | |
| 300 | |a XII, 372 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Problem books in mathematics | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 An Introduction to MATLAB Commands................................. 1
1.1 Elementary Commands.............................................. 1
1.2 Matrices, Vectors, Arrays........................................ 2
1.3 M-Files........................................................ 4
1.4 Mathematics and MATLAB........................................... 5
1.5 Examples of Elementary Graphs.................................... 6
1.6 Solutions for Sect. 1.4.......................................... 8
2 Matrices and Linear Systems........................................ 9
2.1 Some Matrix Computations........................................ 10
2.2 Block Multiplication........................................... 12
2.3 Diagonally Dominant Matrices.................................... 13
2.4 LU-Factorization of Diagonally Dominant Tridiagonal Systems .... 15
2.5 Symmetric Positive Definite Systems and Cholesky
Factorization................................................... 16
2.6 Solutions ...................................................... 16
2.6.1 Some Matrix Computations................................. 16
2.6.2 Block Multiplication..................................... 19
2.6.3 Diagonally Dominant Matrices............................. 21
2.6.4 LU-Factorization of Diagonally Dominant Tridiagonal
Systems.................................................. 21
2.6.5 Symmetric Positive Definite Systems and Cholesky
Factorization............................................ 22
3 Matrices, Eigenvalues and Eigenvectors ............................ 25
3.1 Elementary Computations......................................... 26
3.2 The Power and Inverse Power Methods............................. 28
3.3 The QR Method................................................... 30
3.4 Application to the Buckling of a Beam........................... 31
3.5 Solutions ...................................................... 33
3.5.1 Elementary Computations.................................. 33
3.5.2 The Power and Inverse Power Methods...................... 36
IX
x Contents
3.5.3 The QR Method............................................. 38
3.5.4 Application to the Buckling of a Beam..................... 40
4 Matrices, Norms and Conditioning...................................... 43
4.1 Elementary Examples.............................................. 44
4.2 Conditioning and Error........................................... 45
4.3 Conditioning, Eigenvalues and Determinant........................ 47
4.4 Solutions ....................................................... 54
4.4.1 Elementary Examples ...................................... 54
4.4.2 Conditioning and Error.................................... 55
4.4.3 Conditioning, Eigenvalues and Determinant................. 57
5 Iterative Methods..................................................... 65
5.1 Fixed-Point Methods.............................................. 66
5.2 Iterative Methods for Linear Systems............................. 69
5.2.1 The Methods of Jacobi and Gauss Seidel ................... 69
5.2.2 Gradient Methods.......................................... 72
5.3 Subdivision Schemes ............................................. 76
5.4 A Nonlinear Pendulum............................................. 78
5.5 Solutions ....................................................... 83
5.5.1 Fixed Point Methods....................................... 83
5.5.2 Iterative Methods for Linear Systems ..................... 86
5.5.3 Subdivision Schemes....................................... 94
5.5.4 A Nonlinear Pendulum ..................................... 97
6 Polynomial Interpolation..............................................103
6.1 Some Special Cases ..............................................105
6.2 Lagrange Interpolation...........................................106
6.2.1 The Lagrange Basis........................................107
6.2.2 The Newton Form ..........................................107
6.2.3 The Error Term............................................108
6.2.4 The Runge Phenomenon.................................... 110
6.3 Stable Lagrange Interpolation....................................Ill
6.3.1 The Univariate Case.......................................Ill
6.3.2 Application to Interpolating Surfaces.....................114
6.4 Approximation of Derivatives, Part I ............................115
6.5 Solutions .......................................................118
6.5.1 Some Special Cases........................................118
6.5.2 Lagrange Interpolation....................................121
6.5.3 Stable Lagrange Interpolation.............................125
6.5.4 Approximation of Derivatives, Part I......................128
7 Bezier Curves and Bernstein Polynomials...............................131
7.1 Bezier Curves and the de Casteljau Algorithm ....................132
7.2 Bernstein Polynomials............................................136
7.3 Shape Preservation...............................................140
Contents
xi
7.4 Smooth Joining of Bezier Curves..................................141
7.5 Solutions .......................................................142
7.5.1 Bezier Curves and the de Casteljau Algorithm..............142
7.5.2 Bernstein Basis Polynomials...............................144
7.5.3 Shape Preservation........................................147
7.5.4 Smooth Joining of Bezier Curves...........................149
8 Piecewise Polynomials, Interpolation and Applications...............153
8.1 Quadratic and Cubic Hermite Interpolation........................154
8.2 Cubic Spline Interpolation.......................................156
8.3 Approximation of the Derivatives.................................163
8.4 Approximation of the Length of a Curve...........................166
8.5 Solutions .......................................................167
8.5.1 Quadratic and Cubic Hermite Interpolation.................167
8.5.2 Cubic Spline Interpolation................................170
8.5.3 Approximation of the Derivatives..........................173
8.5.4 Approximation of the Length of a Curve....................174
9 Approximation of Integrals..........................................177
9.1 Basic Quadrature Rules .........................................179
9.1.1 Quadrature Rules and Degree of Precision..................179
9.1.2 Weighted Quadrature Rules.................................1S1
9.2 Monte Carlo Method...............................................184
9.3 Trapezoidal Rule............................................... 186
9.4 Extrapolation....................................................192
9.5 A Global Quadrature..............................................195
9.6 Solutions .......................................................199
9.6.1 Basic Quadrature Rules....................................199
9.6.2 Monte Carlo Method........................................206
9.6.3 Trapezoidal Rule .........................................208
9.6.4 Extrapolation.............................................212
9.6.5 A Global Quadrature.......................................216
10 Linear Least Squares Methods .......................................221
10.1 Orthogonal Projections and Orthogonal Sums.......................222
10.2 Curve Fitting by Least Squares...................................225
10.3 Periodic Signal .................................................229
10.4 Savitsky-Golay Filter............................................232
10.5 Ordinary Differential Equation and Least Squares ................236
10.6 Solutions .......................................................238
10.6.1 Orthogonal Projections and Orthogonal Sums................238
10.6.2 Curve Fitting by Least Squares............................241
10.6.3 Periodic Signal...........................................244
10.6.4 Savitsky-Golay Filter.....................................245
10.6.5 Ordinary Differential Equation and Least Square...........247
Contents
xii
11 Continuous and Discrete Approximations..............................249
11.1 Polynomial Approximation with || • ||oo..........................249
11.2 Fourier Series Solution of the Heat Equation.....................258
11.3 Discrete Signal and Haar Wavelets................................261
11.4 Solutions .......................................................266
11.4.1 Polynomial Approximation with || • ¡|oo.................266
11.4.2 Fourier Series Solution of the Heat Equation...........274
11.4.3 Discrete Signal and Haar Wavelets......................276
12 Ordinary Differential Equations, One Step Methods...................281
12.1 Linear Differential System and Euler’s Methods...................285
12.2 Other Examples of One Step Methods...............................288
12.3 Predictor-Corrector..............................................293
12.4 Application of ODE Solvers to the Shooting Method................294
12.5 Solutions .......................................................301
12.5.1 Linear Differential System and Euler’s Methods..........301
12.5.2 Other Examples of One Step Methods.......................305
12.5.3 Predictor-Corrector .....................................313
12.5.4 Application of ODE Solvers to the Shooting Method .....314
13 Finite Differences for Differential and Partial Differential
Equations.............................................................321
13.1 Definitions of Finite Differences................................321
13.2 Applications of Finite Differences in Dimension 1................323
13.3 Finite Differences in Dimension 2................................332
13.4 The Heat Equation and Approximations.............................337
13.5 Solutions .......................................................342
13.5.1 Definitions of Finite Differences.........................342
13.5.2 Applications of Finite Differences in Dimension 1.........344
13.5.3 Finite Differences in Dimension 2.........................352
13.5.4 The Heat Equation and Approximations......................357
References.................................................................363
Index of Names.............................................................365
Subject Index..............................................................367
MATLAB Index
371
|
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| illustrated | Illustrated |
| indexdate | 2024-07-10T01:12:54Z |
| institution | BVB |
| isbn | 9783662435106 9783662524008 |
| language | English |
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| physical | XII, 372 S. graph. Darst. |
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| publisher | Springer |
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| series2 | Problem books in mathematics |
| spelling | Lyche, Tom Verfasser (DE-588)106006202X aut Exercises in computational mathematics with MATLAB Tom Lyche ; Jean-Louis Merrien Berlin [u.a.] Springer 2014 XII, 372 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Problem books in mathematics MATLAB (DE-588)4329066-8 gnd rswk-swf MATLAB (DE-588)4329066-8 s DE-604 Merrien, Jean-Louis Verfasser aut Erscheint auch als Online-Ausgabe 978-3-662-43511-3 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027548735&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lyche, Tom Merrien, Jean-Louis Exercises in computational mathematics with MATLAB MATLAB (DE-588)4329066-8 gnd |
| subject_GND | (DE-588)4329066-8 |
| title | Exercises in computational mathematics with MATLAB |
| title_auth | Exercises in computational mathematics with MATLAB |
| title_exact_search | Exercises in computational mathematics with MATLAB |
| title_full | Exercises in computational mathematics with MATLAB Tom Lyche ; Jean-Louis Merrien |
| title_fullStr | Exercises in computational mathematics with MATLAB Tom Lyche ; Jean-Louis Merrien |
| title_full_unstemmed | Exercises in computational mathematics with MATLAB Tom Lyche ; Jean-Louis Merrien |
| title_short | Exercises in computational mathematics with MATLAB |
| title_sort | exercises in computational mathematics with matlab |
| topic | MATLAB (DE-588)4329066-8 gnd |
| topic_facet | MATLAB |
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