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Numerical Methods in Engineering and Science: (C, C++, and MATLAB) by B. S. Grewal, ISBN-13: 978-1683921288

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Numerical Methods in Engineering and Science: (C, C++, and MATLAB) by B. S. Grewal, ISBN-13: 978-1683921288

[PDF eBook eTextbook]

• Publisher: ‎ Mercury Learning and Information (September 4, 2018)
• Language: ‎ English
• 950 pages
• ISBN-10: ‎ 1683921283
• ISBN-13: ‎ 978-1683921288

This book is intended as an introduction to numerical methods for scientists and engineers. Providing an excellent balance of theoretical and applied topics, it shows the numerical methods used with C, C++, and MATLAB.

* Provides a balance of theoretical and applied topics
* Shows the numerical methods used with C, C++, and MATLAB

Chapter 1 Approximations and Errors
in Computation 1
1.1 Introduction 1
1.2 Accuracy of Numbers 2
1.3 Errors 3
1.4 Useful Rules for Estimating Errors 4
Exercises 1.1 7
1.5 Error Propagation 8
1.6 Error in the Approximation of a Function 11
1.7 Error in a Series Approximation 13
1.8 Order of Approximation 14
1.9 Growth of Error 15
Exercises 1.2 16
1.10 Objective Type of Questions 17
Exercises 1.3 17
Chapter 2 Solution of Algebraic and Transcendental Equations 19
2.1 Introduction 20
2.2 Basic Properties of Equations 20
Exercises 2.1 25
2.3 Transformation of Equations 25
2.4 Synthetic Division of A Polynomial By A Linear Expression 29
Exercises 2.2 32
2.5 Iterative Methods 32
2.6 Graphical Solution of Equations 33
Exercises 2.3 37
2.7 Rate of Convergence 38
2.8 Bisection Method 38
2.9 Method of False Position or Regula-Falsi Method or
Interpolation Method 43
2.10 Secant Method 47
2.11 Iteration Method 50
Exercises 2.4 56
2.12 Newton-Raphson Method 57
2.13 Some Deductions From Newton-Raphson Formula 63
Exercises 2.5 66
2.14 Muller’s Method 68
Exercises 2.6 70
vi • CONTENTS
2.15 Roots of Polynomials Equations 70
Exercises 2.7 75
2.16 Multiple Roots 75
2.17 Complex Roots 77
2.18 Lin-Bairstow’s Method 78
2.19 Graeffe’s Root Squaring Method 84
Exercises 2.8 88
2.20 Comparison of Iterative Methods 89
2.21 Objective Type of Questions 90
Exercises 2.9 90
Chapter 3 Solution of Simultaneous Algebraic Equations 93
3.1 Introduction t to Determinants 93
Exercises 3.1 99
3.2 Introduction To Matrices 100
Exercises 3.2 113
3.3 Solution of Linear Simultaneous Equations 114
3.4 Direct Methods of Solution 115
Exercises 3.3 130
3.5 Iterative Methods of Solution 131
Exercises 3.4 145
3.6 Ill-Conditioned Equations 146
Exercises 3.5 148
3.7 Comparison of Various Methods 149
3.8 Solution of Non-Linear Simultaneous Equations 149
Exercises 3.6 152
3.9 Objective Type of Questions 153
Exercises 3.7 153
Chapter 4 Matrix Inversion and Eigenvalue Problem 155
4.1 Introduction 155
4.2 Matrix Inversion 156
4.3 Gauss Elimination Method 156
4.4 Gauss-Jordan Method 157
4.5 Factorization Method 159
4.6 Partition Method 162
4.7 Iterative Method 165
Exercises 4.1 166
4.8 Eigenvalues and Eigenvectors 168
4.9 Properties of Eigenvalues 171
4.10 Bounds for Eigenvalues 172
CONTENTS • vii
4.11 Power Method 174
Exercises 4.2 178
4.12 Jacobi’s Method 179
4.13 Given’s Method 183
4.14 House-Holder’s Method 186
Exercises 4.3 189
4.15 Objective Type of Questions 190
Chapter 5 Empirical Laws and Curve-Fitting 193
5.1 Introduction 193
5.2 Graphical Method 194
5.3 Laws Reducible to the Linear Law 195
Exercises 5.1 199
5.4 Principle of Least Squares 200
5.5 Method of Least Squares 202
Exercises 5.2 208
5.6 Fitting A Curve of the Type 209
5.7 Fitting of Other Curves 212
5.8 Most Plausible Values of Unknowns 216
Exercises 5.3 218
5.9 Method of Group Averages 219
5.10 Laws Containing Three Constants 222
Exercises 5.4 226
5.11 Method of Moments 228
Exercises 5.5 230
5.12 Objective Type of Questions 231
Exercises 5.6 231
Chapter 6 Finite Differences 233
6.1 Introduction 233
6.2 Finite Differences 234
6.3 Differences of A Polynomial 240
Exercises 6.1 241
6.3 Factorial Notation 242
6.5 Reciprocal Factorial Function 246
6.6 Inverse Operator of  247
6.7 Effect of an Error on a Difference Table 248
Exercises 6.2 251
6.8 Other Difference Operators 252
6.9 Relations Between the Operators 252
6.10 To Find One or More Missing Terms 257
Exercises 6.3 263
6.11 Application to Summation of Series 265
Exercises 6.4 268
6.12 Objective Type of Questions 269
Exercises 6.5 269
Chapter 7 Interpolation 273
7.1 Introduction 274
7.2 Newton’s Forward Interpolation Formula 274
7.3 Newton’s Backward Interpolation Formula 276
Exercises 7.1 283
7.4 Central Difference Interpolation Formulae 286
7.5 Gauss’s Forward Interpolation Formula 287
7.6 Gauss’s Backward Interpolation Formula 288
7.7 Stirling’s Formula 289
7.8 Bessel’s Formula 290
7.9 Laplace-Everett’s Formula 291
7.10 Choice of an Interpolation Formula 292
Exercises 7.2 304
7.11 Interpolation with Unequal Intervals 306
7.12 Lagrange’s Interpolation Formula 306
Exercises 7.3 311
7.13 Divided Differences 313
7.14 Newton’s Divided Difference Formula 314
7.15 Relation Between Divided and Forward Differences 315
Exercises 7.4 319
7.16 Hermite’s Interpolation Formula 320
Exercises 7.5 325
7.17 Spline Interpolation 326
Exercises 7.6 331
7.18 Double Interpolation 331
7.19 Inverse Interpolation 332
7.20 Lagrange’s Method 332
7.21 Iterative Method 334
Exercises 7.7 336
7.22 Objective Type of Questions 337
Exercises 7.8 337
Chapter 8 Numerical Differentiation and Integration 339
8.1 Numerical Differentiation 339
8.2 Formulae for Derivatives 340
8.3 Maxima and Minima of a Tabulated Function 352
Exercises 8.1 355
CONTENTS • ix
8.4 Numerical Integration 358
8.5 Newton-Cotes Quadrature Formula 359
Exercises 8.2 369
8.6 Errors in Quadrature Formulae 372
8.7 Romberg’s Method 375
8.8 Euler-Maclaurin Formula 380
8.9 Method of Undetermined Coefficients 383
8.10 Gaussian Integration 385
Exercises 8.3 390
8.11 Numerical Double Integration 392
Exercises 8.4 393
8.12 Objective Type of Questions 394
Exercises 8.5 394
Chapter 9 Difference Equations 397
9.1 Introduction 397
9.2 Definition 398
9.3 Formation of Difference Equations 399
Exercises 9.1 401
9.4 Linear Difference Equations 401
9.5 Rules for Finding the Complementary Function 402
Exercises 9.2 406
9.6 Rules for Finding the Particular Integral 407
Exercises 9.3 411
9.7 Difference Equations Reducible to Linear Form 412
Exercises 9.4 414
9.8 Simultaneous Difference Equations with Constant Coefficients 414
Exercises 9.5 415
9.9 Application to Deflection of a Loaded String 415
Exercises 9.6 417
9.10 Objective Type of Questions 417
Exercises 9.7 417
Chapter 10 Numerical Solution of Ordinary
Differential Equations 419
10.1 Introduction 420
10.2 Picard’s Method 421
10.3 Taylor’s Series Method 424
Exercises 10.1 429
10.4 Euler’s Method 429
10.5 Modified Euler’s Method 432
Exercises 10.2 437
x • CONTENTS
10.6 Runge’s Method 438
10.7 Runge-Kutta Method 440
Exercises 10.3 447
10.8 Predictor-Corrector Methods 448
10.9 Milne’s Method 448
Exercises 10.4 455
10.10 Adams-Bashforth Method 456
Exercises 10.5 462
10.11 Simultaneous First Order Differential Equations 463
10.12 Second Order Differential Equations 468
Exercises 10.6 472
10.13 Error Analysis 473
10.14 Convergence of a Method 476
10.15 Stability Analysis 476
Exercises 10.7 479
10.16 Boundary Value Problems 479
10.17 Finite-Difference Method 480
10.18 Shooting Method 485
Exercises 10.8 487
10.19 Objective Type of Questions 488
Exercises 10.9 488
Chapter 11 Numerical Solution of
Partial Differential Equations 491
11.1 Introduction 491
11.2 Classification of Second Order Equations 492
Exercises 11.1 493
11.3 Finite Difference Approximations to Partial Derivatives 494
11.4 Elliptic Equations 495
11.5 Solution of Laplace’s Equation 496
11.6 Solution of Poisson’s Equation 508
Exercises 11.2 511
11.7 Solution of Elliptic Equations by Relaxation Method 513
Exercises 11.3 520
11.8 Parabolic Equations 521
11.9 Solution of One Dimensional Heat Equation 522
11.10 Solution of Two Dimensional Heat Equation 530
Exercises 11.4 534
11.11 Hyperbolic Equations 535
11.12 Solution of Wave Equation 535
Chapter 12 Linear Programming 547
12.1 Introduction 548
12.2 Formulation of the Problem 548
Exercises 12.11 552
12.3 Graphical Method 555
12.4 Some Exceptional Cases 562
Exercises 12.2 566
12.5 General Linear Programming Problem 569
12.6 Canonical and Standard Forms of L.P.P. 570
12.7 Simplex Method 573
Exercises 12.3 577
12.8 Working Procedure of the Simplex Method 578
Exercises 12.4 589
12.9 Artificial Variable Techniques 591
12.10 Exceptional Cases 599
Exercises 12.5 602
12.11 Duality Concept 603
Exercises 12.6 606
12.12 Duality Principle 607
Exercises 12.7 612
12.13 Dual Simplex Method 613
Exercises 12.8 618
12.14 Transportation Problem 619
12.15 Working Procedure for Transportation Problems 621
12.16 Degeneracy in Transportation Problems’ 627
Exercises 12.9 629
12.17 Assignment Problem 632
Exercises 12.10 639
12.18 Objective Type of Questions 642
Exercises 12.11 642
Chapter 13 A Brief Review of Computers 645
13.1 Introduction 645
13.2 Structure of a Computer 646
13.3 Computer Representation of Numbers 647
13.4 Floating Point Representation of Numbers 649
13.5 Computer Calculations 652
Exercises 13.1 655
13.6 Program Writing 655
xii • CONTENTS
Chapter 14 Numerical Methods Using C Language 657
14.1 Introduction 657
14.2 An Overview of “C” Features 658
14.3 Bisection Method (Section 2.7) 674
14.4 Regula-Falsi Method (Section 2.8) 676
14.5 Newton Raphson Method (Section 2.11) 679
14.6 Muller’s Method (Section 2.13) 681
14.7 Multiplication of Matrices [Section 3.2 (3)4] 684
14.8 Gauss Elimination Method [Section 3.4(3)] 687
14.9 Gauss-Jordan Method [Section 3.4(4)] 689
14.10 Factorization Method [Section 3.4(5)] 691
14.11 Gauss-Seidal Iteration Method [Section 3.5(2)] 695
14.12 Power Method (Section 4.11) 699
14.13 Method of Least Squares (Section 5.5) 703
14.14 Method of Group Averages (Section 5.9) 706
14.15 Method of Moments (Section 5.11) 708
14.16 Newton’s Forward Interpolation Formula (Section 7.2) 711
14.17 Lagrange’s Interpolation Formula (Section 7.12) 714
14.18 Newton’s Divided Difference Formula (Section 7.14) 716
14.19 Derivatives Using Forward Difference Formulae [Section 8.2 (1)] 718
14.20 Trapezoidal Rule (Section 8.5—I) 724
14.21 Simpson’s Rule (Section 8.5—II) 726
14.22 Euler’s Method (Section 10.4) 727
14.23 Modified Euler’s Method (Section 10.5) 729
14.24 Runge-Kutta Method (Section 10.7) 732
14.25 Milne’s Method (Section 10.9) 734
14.26 Adams-Bashforth Method (Section 10.10) 736
14.27 Solution of Laplace Equation (Section 11.5) 740
14.28 Solution of Heat Equation (Section 11.9) 745
14.29 Solution of Wave Equation (Section 11.12) 748
14.30 Linear Programming—Simplex Method (Section 12.8) 750
Exercises 14.1 754
Chapter 15 Numerical Methods Using C++ Language 757
15.1 Introduction 757
15.2 An Overview of C++ Features 758
15.3 Bisection Method (Section 2.7) 776
15.4 Regula-Falsi Method (Section 2.8) 778
15.5 Newton Raphson Method (Section 2.11) 780
15.6 Muller’s Method (Section 2.13) 781
15.7 Multiplication of Matrices [Section 3.2 (3)4] 784
15.8 Gauss Elimination Method [Section 3.4 (3)] 786
CONTENTS • xiii
15.9 Gauss-Jordan Method [Section 3.4 (4)] 788
15.10 Factorization Method [Section 3.4 (5)] 790
15.11 Gauss-Seidal Iteration Method [Section 3.5 (2)] 793
15.12 Power Method (Section 4.11) 796
15.13 Method of Least Squares (Section 5.5) 799
15.14 Method of Group Averages (Section 5.9) 801
15.15 Method of Moments (Section 5.11) 803
15.16 Newton’s Forward Interpolation Formula (Section 7.2) 805
15.17 Lagrange’s Interpolation Formula (Section 7.12) 807
15.18 Newton’s Divided Difference Formula (Section 7.14) 808
15.19 Derivatives Using Forward Difference Formulae
(Section 8.2) 809
15.20 Trapezoidal Rule (Section 8.5—I) 813
15.21 Simpson’s Rule (Section 8.5—II) 814
15.22 Euler’s Method (Section 10.4) 815
15.23 Modified Euler’s Method (Section 10.5) 816
15.24 Runge-Kutta Method (Section 10.7) 818
15.25 Milne’s Method (Section 10.9) 819
15.26 Adams-Bashforth Method 821
15.27 Solution of Laplace’s Equation (Section 11.5) 823
15.28 Solution of Heat Equation (Section 11.9) 827
15.29 Solution of Wave Equation (Section 11.12) 829
15.30 Linear Programming—Simplex Method (Section 12.8) 830
Exercises 15.1 834
Chapter 16 Numerical Methods Using MATLAB 837
16.1 Introduction 837
16.2 An Overview of MATLAB Features 838
16.3 Bisection Method (Section 2.7) 844
16.4 Regula-Falsi Method (Section 2.8) 846
16.5 Newton Raphson Method (Section 2.11) 848
16.6 Muller’s Method (Section 2.13) 849
16.7 Multiplication of Matrices [Section 3.2 (3)4] 850
16.8 Gauss Elimination Method [Section 3.4 (3)] 851
16.9 Gauss-Jordan Method [Section 3.4 (4)] 852
16.10 Factorization Method [Section 3.4 (5)] 853
16.11 Gauss Siedel Iteration Method [Section 3.5 (2)] 856
16.12 Power Method (Section 4.11) 858
16.13 Method of Least Squares (Section 5.5) 860
16.14 Method of Group Averages (Section 5.9) 861
16.15 Method of Moments (Section 5.11) 863
16.16 Newton’s Forward Interpolation Formula (Section 7.2) 864
16.17 Lagrange’s Interpolation Formula (Section 7.12) 866
16.18 Newton’s Divided Difference Formula (Section 7.14) 867
16.19 Derivatives Using Forward Difference Formula
[Section 8.2] 868
16.20 Trapezoidal Rule (Section 8.5-1) 870
16.21 Simpson’s Rule (Section 8.5-II) 871
16.22 Euler’s Method (Section 10.4) 871
16.23 Modified Euler’s Method (Section 10.5) 872
16.24 Runge-Kutta Method (Section 10.7) 873
16.25 Milne’s Method (Section 10.9) 874
16.26 Adams-Bashforth Method (Section 10.10) 876
16.27 Solution of Laplace’s Equation (Section 11.5) 877
16.28 Solution of Heat Equation (Section 11.9) 881
16.29 Solution of Wave Equation (Section 11.12) 882
16.30 Linear Programming-Simplex Method (Section 12.8) 884
Exercises 16.1 887
Appendix A Useful Information 891
I Basic Information and Errors 891
II Solution of Algebraic and Trancendental Equations 892
III Solution of Simultaneous Algebraic Equations 893
IV Finite Differences and Interpolation 895
V Interpolation 895
VI Numerical Differentiation 897
VII Numerical Integration 898
VIII Number Solution of ordinary Differential Equations 900
IX Number Solution of Partial Differential Equations 901
Appendix B Answers to Exercises 903
Appendix C Bibliography 929
Index 931

B. S. Grewal (late), had written numerous articles and books about mathematics and had received several awards and grants during his career.

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