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Exploring Numerical Methods: An Introduction to Scientific Computing using MATLAB: . [Kietas viršelis]

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  • Formatas: Hardback, 473 pages, aukštis x plotis: 242x196 mm, weight: 992 g
  • Išleidimo metai: 14-Jan-2003
  • Leidėjas: Jones and Bartlett Publishers, Inc
  • ISBN-10: 0763714992
  • ISBN-13: 9780763714994
Kitos knygos pagal šią temą:
Exploring Numerical Methods: An Introduction to Scientific Computing using MATLAB: .Didesnis paveikslėlis
  • Formatas: Hardback, 473 pages, aukštis x plotis: 242x196 mm, weight: 992 g
  • Išleidimo metai: 14-Jan-2003
  • Leidėjas: Jones and Bartlett Publishers, Inc
  • ISBN-10: 0763714992
  • ISBN-13: 9780763714994
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780763714994.html
Raktažodžiai:
Exploring Numerical Methods is designed to provide beginning engineering and science students, as well as upper-level mathematics students, with an introduction to numerical analysis that emphasizes insight and hands-on experience. To serve the needs of both the younger and the more experienced audience, each chapter begins with an intuitive presentation of motivation and simple algorithms. Topics are developed progressively within each chapter and the advanced material, which reveals underlying theory and discusses complicated methods, is clearly marked. The text takes a focused approach to introducing the more important numerical algorithms and exposes students to partial differential equations by using simple prototypes. This text provides a strong experiential basis for future study.
Numerical Analysis and Scientific Computing
1(10)
Computing with Numbers
11(20)
Number Representation
11(2)
Floating-Point Representation
13(4)
Rounding Errors: A Practical View
17(8)
Theories of Rounding Error*
25(6)
The Solution of Systems of Linear Equations
31(26)
The Gauss Elimination Method
32(7)
Computing the Inverse of a Matrix
39(3)
Least Squares Solutions
42(4)
Testing the Accuracy of a Solution
46(2)
Error Analysis for Matrix Problems*
48(9)
Polynomials and Polynomial Approximations
57(36)
Some Important Properties of Polynomials
57(4)
Polynomial Approximation by Interpolation
61(8)
Polynomial Approximation by Least Squares
69(2)
Least Squares Approximation and Orthogonol Polynomials*
71(8)
Legendre Polynomials
72(1)
Chebyshev Polynomials of the First Kind
72(1)
Chebyshev Polynomials of the Second Kind
73(1)
Laguerre Polynomials
73(1)
Hermite Polynomials
74(5)
Fourier Approximations*
79(5)
Best Approximations in the Maximum Norm*
84(9)
Piecewise Polynomials and Data Fitting
93(32)
Piecewise Polynomial Functions
95(4)
Bases for Piecewise Polynomials
99(6)
Approximation of Functions by Piecewise Polynomials
105(10)
Data Fitting*
115(10)
Numerical Differentiation and Integration
125(46)
Finite Differences and Numerical Evaluation of Derivatives
126(5)
Numerical Integration by Interpolation
131(7)
The Rectangular and Midpoint Rules
132(1)
The Trapezoidal Rule
132(1)
The Simpson Method
133(1)
The Three-Eights Rule
133(5)
Error Analysis for Interpolatory Quadratures
138(5)
Adaptive Quadrature
143(5)
Gaussian Quadrature*
148(8)
Dealing with Difficult Integrands*
156(9)
Multi-Dimensional Integration*
165(6)
The Solution of Nonlinear Equations
171(38)
Some Simple Root-Finding Methods
172(7)
Convergence Rates of Root-Finding Methods
179(3)
Difficulties with Root-Finding
182(3)
The Solution of Simultaneous Equations by Newton's Method
185(4)
The Method of Successive Substitution*
189(6)
Minimization Methods*
195(5)
Roots of Polynomials*
200(5)
Selecting a Root-Finding Method*
205(4)
Advanced Matrix Algorithms
209(28)
The LU and Cholesky Factorizations
209(8)
The QR Decomposition and Least Squares Solutions
217(6)
The Singular Value Decomposition*
223(6)
Sparse Matrices*
229(8)
Eigenvalue Problems
237(30)
Some Useful Results
239(6)
The Power Method
245(4)
The Jacobi and Householder Methods for Symmetric Matrices*
249(7)
Eigenvalues of Nonsymmetric Matrices*
256(2)
Finding Eigenvectors by Inverse Iteration*
258(3)
Error Estimates for Symmetric Matrices*
261(6)
Initial Value Problems for Ordinary Differential Equations
267(46)
Existence and Uniqueness of the Solution
269(4)
Some Simple Numerical Methods
273(4)
Multistep and Predictor-Corrector Methods
277(5)
Runge-Kutta Methods
282(4)
Systems and Equations of Higher Order
286(3)
Convergence of Approximations*
289(8)
Stability*
297(8)
Stiff Equations*
305(4)
Error Estimation and Step Size Selection*
309(4)
Boundary and Eigenvalue Problems for Ordinary Differential Equations
313(30)
Shooting Methods
315(6)
Finite Difference Methods*
321(8)
The Collocation, Least Squares, and Galerkin's Methods*
329(7)
Eigenvalue Problems for Differential Equations*
336(7)
Initial Value Problems for Partial Differential Equations*
343(22)
Finite Difference Methods for the Heat Equation
345(11)
Finite Difference Methods for the Wave Equation
356(3)
Semi-Discretization and the Method of Lines
359(2)
Distinction between Parabolic and Hyperbolic Equations
361(4)
Boundary Value Problems for Partial Differential Equations*
365(18)
Finite Difference Methods
366(4)
Error Analysis for the Finite Difference Method
370(2)
Solving Finite Difference Systems
372(4)
The Finite Element Method
376(3)
Multidimensional Equations
379(4)
Ill-Conditioned and Ill-Posed Problems*
383(30)
The Numerical Rank of a Matrix
384(3)
Computing Generalized Solutions
387(2)
Inverse and Ill-Posed Problems
389(4)
Regularization
393(3)
The Tikhonov Method
396(6)
Choosing the Regularization Parameters
402(5)
The Numerical Solution of Integral Equations of the First Kind
407(4)
Conclusions
411(2)
Numerical Computing in MATLAB
413(14)
MATLAB Arithmetic and Standard Functions
413(3)
Solving Linear Systems
416(1)
Polynomials and Polynomial Approximations
417(1)
Interpolation and Data Fitting
418(1)
Numerical Integration
419(2)
Root-Finding
421(1)
Matrix Functions in MATLAB
422(2)
Software for Eigensolutions
424(1)
Software for ODE Initial Value Problems
425(2)
NASOFT User Manual and Example Scripts
427(22)
Piecewise Polynomial Approximations
427(3)
hat
427(1)
quad_q
428(1)
quad_r
428(1)
spl_b3
429(1)
spl_b31
429(1)
spl_b32
430(1)
Data Fitting
430(2)
lsq_lin
431(1)
lsq_quad
431(1)
lsq_cspl
432(1)
Numerical Integration
432(4)
gauss
432(1)
quad_cg
433(1)
quad_dbl
434(1)
quad_sim
435(1)
Solving Problems of Nonlinear Equations
436(3)
muller
436(2)
newton
438(1)
Eigenvalue Problems
439(2)
eigpower
439(1)
jacobi
440(1)
hholder
440(1)
Solution of Ordinary Differential Equations---Initial Value Problems
441(2)
oderk4
441(1)
odepc
442(1)
Linear Two-Point Boundary Value Problems
443(2)
bvp_fd
443(1)
bvp_coll
444(1)
Partial Differential Equations
445(2)
heat
445(1)
wave
446(1)
Ill-Conditioned Linear Systems
447(1)
tik_reg
447(1)
Example Scripts
448(1)
NASOFT
448(1)
Explorations
449(16)
Floating-Point Representation, Rounding, and Accuracy of Elementary Functions
449(2)
Solving Linear Systems
451(1)
Approximation by Polynomials
452(1)
Interpolation and Data Fitting with Piecewise Polynomials
453(2)
Approximating Derivatives and Integrals
455(2)
Solving Nonlinear Equations
457(1)
Matrix Methods
458(1)
Computing Eigensystems of Matrices
458(1)
ODE Initial Value Problems
459(2)
ODE Boundary and Eigenvalue Problems
461(1)
The Heat and Wave Equations
462(1)
PDE Boundary Value Problems
462(1)
Ill-Posed Problems and Regularization
463(2)
References 465(2)
Subject Index 467(2)
Index 469
Peter Linz, Professor Emeritus, University of California, Davis Peter Linz is Professor Emeritus in the Department of Computer Science at the University of California, Davis.'Linz received his Ph.D. from the University of Wisconsin.'Professor Linz's research emphasizes the development of a theory of numerical analysis that can be used in the construction of reliable numerical methods used in the design of problem-solving environments for scientific computing.'Linz has released the seventh edition of An Introduction to Formal Languages and Automata, as well as Exploring Numerical Methods: An Introduction to Scientific Computing.' Richard L.C. Wang, Ph.DDoctor Wang received his Ph.D. in Mathematics from the University of California at Davis in 1985. Since then, Dr. Wang has worked as an algorithm developer and numerical analyst for several companies including Lockheed Missiles and Spaces, KLA and others in the silicon valley. Dr. Wang is currently working for Peoplesoft, Inc. as an algorithm specialist.