Muutke küpsiste eelistusi

E-raamat: Numerical Methods: Fundamentals and Applications

  • Formaat: PDF+DRM
  • Ilmumisaeg: 09-May-2019
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108686600
Teised raamatud teemal:
  • Formaat - PDF+DRM
  • Hind: 86,44 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Numerical Methods: Fundamentals and ApplicationsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 09-May-2019
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108686600
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

Written in a lucid manner, this textbook gives an in-depth discussion of basic and advanced concepts of numerical methods. C programming codes are included in the textbook for better understanding of concepts. Pedagogical features including solved examples and unsolved exercises are interspersed throughout the book for better understanding.

Written in an easy-to-understand manner, this comprehensive textbook brings together both basic and advanced concepts of numerical methods in a single volume. Important topics including error analysis, nonlinear equations, systems of linear equations, interpolation and interpolation for Equal intervals and bivariate interpolation are discussed comprehensively. The textbook is written to cater to the needs of undergraduate students of mathematics, computer science, mechanical engineering, civil engineering and information technology for a course on numerical methods/numerical analysis. The text simplifies the understanding of the concepts through exercises and practical examples. Pedagogical features including solved examples and unsolved exercises are interspersed throughout the book for better understanding.

Muu info

Offers a comprehensive textbook for a course in numerical methods, numerical analysis and numerical techniques for undergraduate engineering students.
Preface xvii
Acknowledgments xxix
Chapter 1 Number Systems
1(12)
1.1 Introduction
1(1)
Table 1.1 Binary, Octal, Decimal and Hexadecimal Numbers
2(1)
1.2 Representation of Integers
2(6)
1.2.1 Conversion from Any Number System to the Decimal Number System
3(1)
1.2.2 Conversion between Binary, Octal and Hexadecimal Number Systems
4(1)
1.2.3 Conversion from Decimal Number System to Any Other Number System
4(2)
1.2.4 Conversion from One Number System to Any Other Number System
6(2)
1.3 Representation of Fractions
8(3)
Exercise 1
11(2)
Chapter 2 Error Analysis
13(34)
2.1 Absolute, Relative and Percentage Errors
13(3)
2.2 Errors in Modeling of Real World Problems
16(1)
2.2.1 Modeling Error
16(1)
2.2.2 Error in Original Data (Inherent Error)
16(1)
2.2.3 Blunder
16(1)
2.3 Errors in Implementation of Numerical Methods
17(24)
2.3.1 Round-off Error
17(5)
2.3.2 Overflow and Underflow
22(1)
2.3.3 Floating Point Arithmetic and Error Propagation
23(1)
2.3.3.1 Propagated Error in Arithmetic Operations
24(3)
2.3.3.2 Error Propagation in Function of Single Variable
27(1)
2.3.3.3 Error Propagation in Function of More than One Variable
28(2)
2.3.4 Truncation Error
30(3)
2.3.5 Machine eps (Epsilon)
33(1)
2.3.6 Epilogue
34(1)
2.3.7 Loss of Significance: Condition and Stability
34(7)
2.4 Some Interesting Facts about Error
41(6)
Exercise 2
42(5)
Chapter 3 Nonlinear Equations
47(77)
3.1 Introduction
47(1)
3.1.1 Polynomial Equations
48(1)
3.1.2 Transcendental Equations
48(1)
3.2 Methods for Solutions of the Equation ƒ(x) = 0
48(6)
3.2.1 Direct Analytical Methods
49(1)
3.2.2 Graphical Methods
49(2)
3.2.3 Trial and Error Methods
51(1)
3.2.4 Iterative Methods
52(2)
3.3 Bisection (or) Bolzano (or) Interval-Halving Method
54(5)
3.4 Fixed-Point Method (or) Direct-Iteration Method (or) Method of Successive-Approximations (or) Iterative Method (or) One-Point-Iteration Method
59(6)
3.5 Newton--Raphson (NR) Method
65(3)
3.6 Regula Falsi Method (or) Method of False Position
68(3)
3.7 Secant Method
71(3)
3.8 Convergence Criteria
74(12)
3.8.1 Convergence of Bisection Method
75(1)
3.8.2 Convergence of Fixed-Point Method
76(5)
3.8.3 Convergence of Newton--Raphson Method
81(4)
3.8.4 Convergence of Regula Falsi Method
85(1)
3.8.5 Convergence of Secant Method
85(1)
3.9 Order of Convergence
86(15)
3.9.1 Order of Convergence for Bisection Method
87(1)
3.9.2 Order of Convergence for Fixed-Point Method
88(2)
3.9.3 Order of Convergence for Newton--Raphson Method
90(7)
3.9.4 Order of Convergence for Secant Method
97(2)
3.9.5 Order of Convergence for Regula Falsi Method
99(2)
3.10 Muller Method
101(5)
3.11 Chebyshev Method
106(4)
3.12 Aitken Δ2 Process: Acceleration of Convergence of Fixed-Point Method
110(7)
Table 3.3 Formulation of Methods
115(1)
Table 3.4 Properties and Convergence of Methods
116(1)
3.13 Summary and Observations
117(1)
Exercise 3
118(6)
Chapter 4 Nonlinear Systems and Polynomial Equations
124(49)
4.1 Fixed-Point Method
125(6)
4.2 Seidel Iteration Method
131(4)
4.3 Newton--Raphson (NR) Method
135(9)
4.4 Complex Roots
144(3)
4.5 Polynomial Equations
147(5)
4.5.1 Descartes Rule of Signs
147(1)
4.5.2 Strum Sequence
148(4)
4.6 Birge--Vieta (or) Horner Method
152(4)
4.7 Lin--Bairstow Method
156(5)
4.8 Graeffe Root Squaring Method
161(12)
Table 4.2 Methods for Solutions of the Systems of Nonlinear Equations
169(1)
Table 4.3 Methods for the Solutions of the Polynomial Equations
170(1)
Exercise 4
171(2)
Chapter 5 Systems of Linear Equations
173(95)
5.1 Introduction
173(3)
5.2 Cramer Rule
176(2)
5.3 Matrix Inversion Method
178(4)
5.4 LU Decomposition (or) Factorization (or) Triangularization Method
182(10)
5.4.1 Doolittle Method
183(1)
5.4.2 Crout Method
183(7)
5.4.3 Cholesky Method
190(2)
5.5 Gauss Elimination Method
192(11)
5.5.1 Operational Counts for Gauss Elimination Method
197(2)
5.5.2 Thomas Algorithm (Tridiagonal Matrix Algorithm)
199(4)
5.6 Gauss--Jordan Method
203(3)
5.7 Comparison of Direct Methods
206(1)
5.8 Pivoting Strategies for Gauss Elimination Method
207(10)
5.9 Iterative Methods
217(1)
5.10 Jacobi Method (or) Method of Simultaneous Displacement
218(4)
5.11 Gauss--Seidel Method (or) Method of Successive Displacement (or) Liebmann Method
222(5)
5.12 Relaxation Method
227(10)
5.13 Convergence Criteria for Iterative Methods
237(8)
5.14 Matrix Forms and Convergence of Iterative Methods
245(11)
Table 5.2 Formulae for Iterative Methods
255(1)
5.15 Discussion
256(2)
5.16 Applications
258(10)
Exercise 5
261(7)
Chapter 6 Eigenvalues and Eigenvectors
268(31)
6.1 Introduction
268(2)
6.2 Eigenvalues and Eigenvectors
270(7)
6.2.1 Real Eigenvalues
271(2)
6.2.2 Complex Eigenvalues
273(1)
6.2.3 Matrix with Real and Distinct Eigenvalues
274(1)
6.2.4 Matrix with Real and Repeated Eigenvalues
275(1)
6.2.4.1 Linearly Independent Eigenvectors
275(1)
6.2.4.2 Linearly Dependent Eigenvectors
276(1)
6.3 Bounds on Eigenvalues
277(4)
6.3.1 Gerschgorin Theorem
277(2)
6.3.2 Brauer Theorem
279(2)
6.4 Rayleigh Power Method
281(10)
6.4.1 Inverse Power Method
285(3)
6.4.2 Shifted Power Method
288(3)
6.5 Rutishauser (or) LU Decomposition Method
291(8)
Exercise 6
295(4)
Chapter 7 Eigenvalues and Eigenvectors of Real Symmetric Matrices
299(32)
7.1 Introduction
299(8)
7.1.1 Similarity Transformations
304(2)
7.1.2 Orthogonal Transformations
306(1)
7.2 Jacobi Method
307(4)
7.3 Strum Sequence for Real Symmetric Tridiagonal Matrix
311(1)
7.4 Givens Method
312(7)
7.5 Householder Method
319(12)
Exercise 7
326(5)
Chapter 8 Interpolation
331(33)
8.1 Introduction
331(2)
8.2 Polynomial Forms
333(7)
8.2.1 Power Form
333(1)
8.2.2 Shifted Power Form
333(1)
8.2.3 Newton Form
334(1)
8.2.4 Nested Newton Form
334(1)
8.2.5 Recursive Algorithm for the Nested Newton Form
335(1)
8.2.6 Change of Center in Newton Form
336(4)
8.3 Lagrange Method
340(3)
8.4 Newton Divided Difference (NDD) Method
343(7)
8.4.1 Proof for Higher Order Divided Differences
346(1)
8.4.2 Advantages of NDD Interpolation over Lagrange Interpolation
347(1)
8.4.3 Properties of Divided Differences
348(2)
8.5 Error in Interpolating Polynomial
350(3)
8.6 Discussion
353(1)
8.7 Hermite Interpolation
354(3)
8.8 Piecewise Interpolation
357(2)
8.9 Weierstrass Approximation Theorem
359(5)
Exercise 8
359(5)
Chapter 9 Finite Operators
364(25)
9.1 Introduction
364(1)
9.2 Finite Difference Operators
365(2)
9.2.1 Forward Difference Operator (Δ)
365(1)
9.2.2 Backward Difference Operator (V)
366(1)
9.2.3 Central Difference Operator (δ)
366(1)
9.3 Average, Shift and Differential Operators
367(2)
9.3.1 Mean or Average Operator (μ)
367(1)
9.3.2 Shift Operator (E)
367(1)
9.3.3 Differential Operator (D)
368(1)
Table 9.1 Finite Differences and Other Operators
368(1)
9.4 Properties and Interrelations of Finite Operators
369(5)
9.4.1 Linearity and Commutative Properties
369(1)
9.4.2 Interrelations of Finite Operators
370(3)
Table 9.2 Relations between the Operators
373(1)
9.5 Operators on Some Functions
374(3)
9.6 Newton Divided Differences and Other Finite Differences
377(2)
9.7 Finite Difference Tables and Error Propagation
379(7)
Table 9.3 Forward Differences
380(1)
Table 9.4 Backward Differences
380(1)
Table 9.5 Central Differences
381(5)
Exercise 9
386(3)
Chapter 10 Interpolation for Equal Intervals and Bivariate Interpolation
389(56)
10.1 Gregory--Newton Forward Difference Formula
390(5)
10.1.1 Error in Newton Forward Difference Formula
393(2)
10.2 Gregory--Newton Backward Difference Formula
395(3)
10.2.1 Error in Newton Backward Difference Formula
397(1)
10.3 Central Difference Formulas
398(1)
10.4 Gauss Forward Central Difference Formula
399(3)
10.5 Gauss Backward Central Difference Formula
402(2)
10.6 Stirling Formula
404(2)
10.7 Bessel Formula
406(2)
10.8 Everett Formula
408(2)
10.9 Steffensen Formula
410(21)
Table 10.1 Finite Differences Formulas
412(19)
10.10 Bivariate Interpolation
431(14)
10.10.1 Lagrange Bivariate Interpolation
431(4)
10.10.2 Newton Bivariate Interpolation for Equi-spaced Points
435(7)
Exercise 10
442(3)
Chapter 11 Splines, Curve Fitting, and Other Approximating Curves
445(50)
11.1 Introduction
445(1)
11.2 Spline Interpolation
446(10)
11.2.1 Cubic Spline Interpolation
448(3)
11.2.2 Cubic Spline for Equi-spaced Points
451(5)
11.3 Bezier Curve
456(6)
11.4 B-Spline Curve
462(5)
11.5 Least Squares Curve
467(11)
11.5.1 Linear Curve (or) Straight Line Fitting
468(2)
11.5.2 Nonlinear Curve Fitting by Linearization of Data
470(1)
Table 11.1 Linearization of Nonlinear Curves
471(3)
11.5.3 Quadratic Curve Fitting
474(4)
11.6 Chebyshev Polynomials Approximation
478(6)
11.7 Approximation by Rational Function of Polynomials (Pade Approximation)
484(11)
Table 11.2 Summary and Comparison
488(1)
Exercise 11
489(6)
Chapter 12 Numerical Differentiation
495(14)
12.1 Introduction
495(2)
12.2 Numerical Differentiation Formulas
497(12)
Table 12.1 Summary Table for Numerical Differentiation Formulas
498(9)
Exercise 12
507(2)
Chapter 13 Numerical Integration
509(67)
13.1 Newton-Cotes Quadrature Formulas (Using Lagrange Method)
510(7)
13.1.1 Trapezoidal Rule (n = 1)
512(1)
13.1.2 Simpson 1/3 Rule (n = 2)
513(1)
13.1.3 Simpson 3/8 Rule (n = 3)
514(1)
13.1.4 Boole Rule (n = 4)
514(1)
13.1.5 Weddle Rule (n = 6)
515(2)
13.2 Composite Newton--Cotes Quadrature Rules
517(11)
13.2.1 Composite Trapezoidal Rule
517(1)
13.2.2 Composite Simpson 1/3 Rule
518(1)
13.2.3 Composite Simpson 3/8 Rule
519(1)
13.2.4 Composite Boole Rule
519(9)
13.3 Errors in Newton--Cotes Quadrature Formulas
528(7)
13.3.1 Error in Trapezoidal Rule (n = 1)
529(1)
13.3.2 Error in Simpson 1/3 Rule (n = 2)
529(1)
13.3.3 Error in Simpson 3/8 Rule (n = 3)
530(1)
13.3.4 Error in Boole Rule (n = 4)
531(1)
13.3.5 Error in Weddle Rule (n = 6)
531(3)
Table 13.1 Newton--Cotes Quadrature Formulas
534(1)
13.4 Gauss Quadrature Formulas
535(18)
13.4.1 Gauss--Legendre Formula
535(11)
13.4.2 Gauss--Chebyshev Formula
546(3)
13.4.3 Gauss--Laguerre Formula
549(2)
13.4.4 Gauss--Hermite Formula
551(2)
13.5 Euler--Maclaurin Formula
553(5)
13.6 Richardson Extrapolation
558(2)
13.7 Romberg Integration
560(7)
Table 13.2 Numerical Techniques for Integration
565(2)
13.8 Double Integrals
567(9)
13.8.1 Trapezoidal Rule
567(2)
13.8.2 Simpson 1/3 Rule
569(2)
Exercise 13
571(5)
Chapter 14 First Order Ordinary Differential Equations: Initial Value Problems
576(66)
14.1 Some Important Classifications and Terms
577(5)
14.1.1 Ordinary and Partial Differential Equations
577(1)
14.1.2 Order and Degree of Differential Equations
578(1)
14.1.3 Homogeneous and Non-homogeneous Differential Equations
578(1)
14.1.4 Constant and Variable Coefficient Differential Equations
579(1)
14.1.5 Linear and Nonlinear Differential Equations
579(1)
14.1.6 General, Particular and Singular Solutions
580(1)
14.1.7 Initial Value Problem (IVP) and Boundary Value Problem (BVP)
580(1)
14.1.8 Existence and Uniqueness of Solutions
581(1)
14.1.9 Comparison of Analytical and Numerical Methods
582(1)
14.2 Picard Method of Successive Approximations
582(3)
14.3 Taylor Series Method
585(4)
14.4 Euler Method
589(3)
14.5 Modified (or) Improved Euler Method (or) Heun Method
592(5)
14.6 Runge-Kutta (RK) Methods
597(11)
14.7 Milne Method (Milne Simpson Method)
608(8)
14.8 Adams Method (Adams--Bashforth Predictor and Adams--Moulton Corrector Formulas)
616(7)
14.9 Errors in Numerical Methods
623(1)
14.10 Order and Stability of Numerical Methods
624(2)
14.11 Stability Analysis of IVP y' = Ay, y(0) = y0
626(2)
14.12 Backward Euler Method
628(14)
Table 14.1 Numerical Schemes for IVP
634(2)
Exercise 14
636(6)
Chapter 15 Systems of First Order ODEs and Higher Order ODEs: Initial and Boundary Value Problems
642(37)
15.1 Picard Method
644(3)
15.2 Taylor Series Method
647(1)
15.3 Euler Method
648(4)
15.4 Runge-Kutta Fourth Order Method
652(6)
Table 15.1 Formulations for Solutions of IVPs
658(1)
15.5 Boundary Value Problem: Shooting Method
658(3)
15.6 Finite Difference Approximations for Derivatives
661(3)
15.6.1 First Order Derivatives
662(1)
15.6.2 Second Order Derivatives
663(1)
15.7 Boundary Value Problem: Finite Difference Method
664(4)
15.8 Finite Difference Approximations for Unequal Intervals
668(3)
15.9 Discussion
671(8)
Exercise 15
672(7)
Chapter 16 Partial Differential Equations: Finite Difference Methods
679(100)
16.1 Classification of Second-Order Quasi-Linear PDEs
680(2)
16.2 Initial and Boundary Conditions
682(1)
16.3 Finite Difference Approximations for Partial Derivatives
683(5)
16.4 Parabolic Equation (1-dimensional Heat Conduction Equation)
688(13)
16.4.1 Bender--Schmidt Explicit Scheme
689(1)
16.4.2 Crank--Nicolson (CN) Scheme
690(1)
16.4.3 General Implicit Scheme
691(1)
16.4.4 Richardson Scheme
692(1)
16.4.5 Du-Fort and Frankel Scheme
692(9)
16.5 Consistency, Convergence and Stability of Explicit and Crank--Nicolson Schemes
701(9)
16.5.1 Consistency
702(1)
16.5.2 Consistency of Explicit Scheme
703(1)
16.5.3 Convergence and Order
704(1)
16.5.4 Stability
705(1)
16.5.5 Matrix Method for Stability of Explicit Scheme
705(2)
16.5.6 Matrix Method for Stability of CN Scheme
707(1)
16.5.7 Neumann Method for Stability of Explicit Scheme
708(1)
16.5.8 Neumann Method for Stability of CN Scheme
709(1)
Table 16.1 Summary Table of Finite Difference Methods for 1-Dimensional Heat Conduction Equation
710(1)
16.6 2-Dimensional Heat Conduction Equation
711(6)
16.6.1 Explicit Scheme
711(1)
16.6.2 Crank--Nicolson (CN) Scheme
712(2)
16.6.3 Alternating Direction Implicit (ADI) Scheme
714(3)
Table 16.2 Summary Table of Finite Difference Methods for 2-Dimensional Heat Conduction Equation
717(8)
16.7 Elliptic Equations (Laplace and Poisson Equations)
725(25)
16.7.1 Laplace Equation
726(14)
16.7.2 Poisson Equation
740(10)
16.8 Hyperbolic Equation (Wave Equation)
750(9)
16.8.1 Explicit Scheme
751(1)
16.8.2 Implicit Scheme
751(8)
16.9 Creating Own Scheme for a Problem
759(2)
Exercise 16.1 Parabolic Equation (Heat Conduction (or) Diffusion Equation)
761(9)
Exercise 16.2 Elliptic Equation (Laplace and Poisson Equations)
770(3)
Exercise 16.3 Hyperbolic Equation (Wave Equation)
773(12)
Appendix A Comparison of Analytical and Numerical Techniques 779(2)
Appendix B Numerical Techniques and Computer 781(2)
Appendix C Taylor Series 783(3)
Taylor Series for the Functions of More than One Variable
785(1)
Lagrange Mean Value (LMV) Theorem
785(1)
Rolle Theorem
785(3)
Appendix D Linear and Nonlinear 786(2)
Appendix E Graphs of Standard Functions 788(2)
Algebraic Functions
788(1)
Transcendental Functions
789(1)
Appendix F Greek Letters 790(1)
Index 791
Rajesh Kumar Gupta is an associate professor in the department of mathematics and statistics at the Central University of Punjab, India. His current research includes nonlinear partial differential equations, Lie group theory, fractional order partial differential equations, exact solutions and symmetries for nonlinear systems. He has taught courses including numerical methods with C programming, engineering mathematics, partial differential equations, complex analysis and abstract algebra at undergraduate and graduate levels. He has more than ten years of teaching experience and has published more than fifty research papers.
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97811086866002e.html
Märksõnad: