Computational science and engineering:
Encompasses the full range of computational science and engineering from modelling to solution, both analytical and numerical. It develops a framework for the equations and numerical methods of applied mathematics. Gilbert Strang has taught this material to thousands of engineers and scientists (and...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Wellesley, Ma.
Wellesley-Cambridge Press
2007
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Encompasses the full range of computational science and engineering from modelling to solution, both analytical and numerical. It develops a framework for the equations and numerical methods of applied mathematics. Gilbert Strang has taught this material to thousands of engineers and scientists (and many more on MIT's OpenCourseWare 18.085-6) ... The book is solution-based and not formula-based: it integrates analysis and algorithms and MATLAB codes to explain each topic as effectively as possible. The topics include applied linear algebra and fast solvers, differential equations with finite differences and finite elements, Fourier analysis and optimization. This book also serves as a reference for the whole community of computational scientists and engineers. Supporting resources, including MATLAB codes, problem solutions and video lectures from Gilbert Strang's 18.085 courses at MIT, are provided at math.mit.edu/cse"--Publisher's website |
| Beschreibung: | Literaturverz. S. 698 - 703 Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XI, 735 S. graph. Darst. |
| ISBN: | 9780961408817 0961408812 |
Internformat
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| 500 | |a Literaturverz. S. 698 - 703 | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 520 | 3 | |a Encompasses the full range of computational science and engineering from modelling to solution, both analytical and numerical. It develops a framework for the equations and numerical methods of applied mathematics. Gilbert Strang has taught this material to thousands of engineers and scientists (and many more on MIT's OpenCourseWare 18.085-6) ... The book is solution-based and not formula-based: it integrates analysis and algorithms and MATLAB codes to explain each topic as effectively as possible. The topics include applied linear algebra and fast solvers, differential equations with finite differences and finite elements, Fourier analysis and optimization. This book also serves as a reference for the whole community of computational scientists and engineers. Supporting resources, including MATLAB codes, problem solutions and video lectures from Gilbert Strang's 18.085 courses at MIT, are provided at math.mit.edu/cse"--Publisher's website | |
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Datensatz im Suchindex
| _version_ | 1804137675196727296 |
|---|---|
| adam_text | TABLE
OF
CONTENTS
L
Applied
Linear Algebra
1
1.1
Four Special Matrices
1
1.2
Differences, Derivatives, Boundary Conditions
13
1.3
Elimination Leads to
К
=
LD
Ľ1
26
1.4
Inverses and Delta Functions
36
1.5
Eigenvalues and Eigenvectors
46
1.6
Positive Definite Matrices
66
1.7
Numerical Linear Algebra:
LU,
QR,
SVD
78
1.8
Best Basis from the
SVD
92
I A Framework for Applied Mathematics
98
2.1
Equilibrium and the Stiffness Matrix
98
2.2
Oscillation by Newton s Law 111
2.3
Least Squares for Rectangular Matrices
128
2.4
Graph Models and Kirchhoff s Laws
142
2.5
Networks and Transfer Functions
156
2.6
Nonlinear Problems
171
2.7
Structures in Equilibrium
185
2.8
Covariances and Recursive Least Squares
200
* 2.9
Graph Cuts and Gene Clustering
217
і
Boundary Value Problems
229
3.1
Differential Equations and Finite Elements
229
3.2
Cubic Splines and Fourth-Order Equations
245
3.3
Gradient and Divergence
255
3.4
Laplace s Equation
269
3.5
Finite Differences and Fast
Poisson
Solvers
283
3.6
The Finite Element Method
293
3.7
Elasticity and Solid Mechanics
310
I Fourier Series and Integrals
317
4.1
Fourier Series for Periodic Functions
317
4.2
Chebyshev. Legendre. and Bessel
334
4.3
Discrete Fourier Transform and the FFT
346
4.4
Convolution and Signal Processing
356
4.5
Fourier Integrals
367
4.6
Deconvolution and Integral Equations
381
4.7
Wavelets and Signal Processing
388
ІІЇ
iv
Table
of Contents
5
Analytic Functions
403
5.1
Taylor Series and Complex Integration
403
5.2
Famous Functions and Great Theorems
419
5.3
The Laplace Transform and ^-Transform
426
5.4
Spectral Methods of Exponential Accuracy
440
6
Initial Value Problems
456
6.1
Introduction
456
6.2
Finite Difference Methods
461
6.3
Accuracy and Stability for
щ
=
cux
472
6.4
Wave Equations and Staggered Leapfrog
485
6.5
Diffusion, Convection, and Finance
500
6.6
Nonlinear Flow and Conservation Laws
517
6.7
Fluid Flow and Navier-Stokes
533
6.8
Level Sets and Fast Marching
547
7
Solving Large Systems
551
7.1
Elimination with Reordering
551
7.2
Iterative Methods
563
7.3
Multigrid Methods
571
7.4
Krylov Subspaces and Conjugate Gradients
586
8
Optimization and Minimum Principles
598
8.1
Two Fundamental Examples
598
8.2
Regularized Least Squares
613
8.3
Calculus of Variations
627
8.4
Errors in Projections and Eigenvalues
646
8.5
The Saddle Point Stokes Problem
652
8.6
Linear Programming and Duality
661
8.7
Adjoint Methods in Design
678
Linear Algebra in a Nutshell
685
Sampling and Aliasing
691
Computational Science and Engineering
694
Bibliography
698
Index
704
|
| adam_txt |
TABLE
OF
CONTENTS
L
Applied
Linear Algebra
1
1.1
Four Special Matrices
1
1.2
Differences, Derivatives, Boundary Conditions
13
1.3
Elimination Leads to
К
=
LD
Ľ1
26
1.4
Inverses and Delta Functions
36
1.5
Eigenvalues and Eigenvectors
46
1.6
Positive Definite Matrices
66
1.7
Numerical Linear Algebra:
LU,
QR,
SVD
78
1.8
Best Basis from the
SVD
92
I A Framework for Applied Mathematics
98
2.1
Equilibrium and the Stiffness Matrix
98
2.2
Oscillation by Newton's Law 111
2.3
Least Squares for Rectangular Matrices
128
2.4
Graph Models and Kirchhoff's Laws
142
2.5
Networks and Transfer Functions
156
2.6
Nonlinear Problems
171
2.7
Structures in Equilibrium
185
2.8
Covariances and Recursive Least Squares
200
* 2.9
Graph Cuts and Gene Clustering
217
і
Boundary Value Problems
229
3.1
Differential Equations and Finite Elements
229
3.2
Cubic Splines and Fourth-Order Equations
245
3.3
Gradient and Divergence
255
3.4
Laplace's Equation
269
3.5
Finite Differences and Fast
Poisson
Solvers
283
3.6
The Finite Element Method
293
3.7
Elasticity and Solid Mechanics
310
I Fourier Series and Integrals
317
4.1
Fourier Series for Periodic Functions
317
4.2
Chebyshev. Legendre. and Bessel
334
4.3
Discrete Fourier Transform and the FFT
346
4.4
Convolution and Signal Processing
356
4.5
Fourier Integrals
367
4.6
Deconvolution and Integral Equations
381
4.7
Wavelets and Signal Processing
388
ІІЇ
iv
Table
of Contents
5
Analytic Functions
403
5.1
Taylor Series and Complex Integration
403
5.2
Famous Functions and Great Theorems
419
5.3
The Laplace Transform and ^-Transform
426
5.4
Spectral Methods of Exponential Accuracy
440
6
Initial Value Problems
456
6.1
Introduction
456
6.2
Finite Difference Methods
461
6.3
Accuracy and Stability for
щ
=
cux
472
6.4
Wave Equations and Staggered Leapfrog
485
6.5
Diffusion, Convection, and Finance
500
6.6
Nonlinear Flow and Conservation Laws
517
6.7
Fluid Flow and Navier-Stokes
533
6.8
Level Sets and Fast Marching
547
7
Solving Large Systems
551
7.1
Elimination with Reordering
551
7.2
Iterative Methods
563
7.3
Multigrid Methods
571
7.4
Krylov Subspaces and Conjugate Gradients
586
8
Optimization and Minimum Principles
598
8.1
Two Fundamental Examples
598
8.2
Regularized Least Squares
613
8.3
Calculus of Variations
627
8.4
Errors in Projections and Eigenvalues
646
8.5
The Saddle Point Stokes Problem
652
8.6
Linear Programming and Duality
661
8.7
Adjoint Methods in Design
678
Linear Algebra in a Nutshell
685
Sampling and Aliasing
691
Computational Science and Engineering
694
Bibliography
698
Index
704 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
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| illustrated | Illustrated |
| index_date | 2024-07-02T20:57:42Z |
| indexdate | 2024-07-09T21:16:04Z |
| institution | BVB |
| isbn | 9780961408817 0961408812 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016515258 |
| oclc_num | 176240837 |
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| physical | XI, 735 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Wellesley-Cambridge Press |
| record_format | marc |
| spelling | Strang, Gilbert 1934- Verfasser (DE-588)141888474 aut Computational science and engineering Gilbert Strang Wellesley, Ma. Wellesley-Cambridge Press 2007 XI, 735 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 698 - 703 Hier auch später erschienene, unveränderte Nachdrucke Encompasses the full range of computational science and engineering from modelling to solution, both analytical and numerical. It develops a framework for the equations and numerical methods of applied mathematics. Gilbert Strang has taught this material to thousands of engineers and scientists (and many more on MIT's OpenCourseWare 18.085-6) ... The book is solution-based and not formula-based: it integrates analysis and algorithms and MATLAB codes to explain each topic as effectively as possible. The topics include applied linear algebra and fast solvers, differential equations with finite differences and finite elements, Fourier analysis and optimization. This book also serves as a reference for the whole community of computational scientists and engineers. Supporting resources, including MATLAB codes, problem solutions and video lectures from Gilbert Strang's 18.085 courses at MIT, are provided at math.mit.edu/cse"--Publisher's website Mathematik Naturwissenschaft Engineering mathematics Numerical analysis Science Mathematics Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Angewandte Mathematik (DE-588)4142443-8 gnd rswk-swf Wissenschaftliches Rechnen (DE-588)4338507-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Numerische Mathematik (DE-588)4042805-9 s Angewandte Mathematik (DE-588)4142443-8 s DE-604 Wissenschaftliches Rechnen (DE-588)4338507-2 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016515258&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Strang, Gilbert 1934- Computational science and engineering Mathematik Naturwissenschaft Engineering mathematics Numerical analysis Science Mathematics Numerische Mathematik (DE-588)4042805-9 gnd Angewandte Mathematik (DE-588)4142443-8 gnd Wissenschaftliches Rechnen (DE-588)4338507-2 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4142443-8 (DE-588)4338507-2 (DE-588)4123623-3 |
| title | Computational science and engineering |
| title_auth | Computational science and engineering |
| title_exact_search | Computational science and engineering |
| title_exact_search_txtP | Computational science and engineering |
| title_full | Computational science and engineering Gilbert Strang |
| title_fullStr | Computational science and engineering Gilbert Strang |
| title_full_unstemmed | Computational science and engineering Gilbert Strang |
| title_short | Computational science and engineering |
| title_sort | computational science and engineering |
| topic | Mathematik Naturwissenschaft Engineering mathematics Numerical analysis Science Mathematics Numerische Mathematik (DE-588)4042805-9 gnd Angewandte Mathematik (DE-588)4142443-8 gnd Wissenschaftliches Rechnen (DE-588)4338507-2 gnd |
| topic_facet | Mathematik Naturwissenschaft Engineering mathematics Numerical analysis Science Mathematics Numerische Mathematik Angewandte Mathematik Wissenschaftliches Rechnen Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016515258&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT stranggilbert computationalscienceandengineering |