Introduction to numerical programming : a practical guide for scientists and engineers using Python and C/C++

Select an Action

Place Hold(s)
Add to My Lists
Email
Print

Title:

Personal Author:

Beu, Titus A., author

Series:

Series in computational physics

Publication Information:

Boca Raton : CRC Press, Taylor & Francis Group, 2015

Physical Description:

xix, 653 pages : illustrations ; 26 cm.

ISBN:

9781466569676

Abstract:

"This book introduces numerical programming using Python and C/C++, emphasizing methods used in physics and engineering. Its helps readers develop the ability to navigate relevant algorithms, knowledge of coding design, and efficient scientific programming skills. It requires minimal background in mathematics, leading readers from elementary methods to complex algorithms useful in modern programming. It incorporates examples and real code throughout, as well as problem sets, to facilitate a hands-on learning experience. "--provided by publisher

Subject Term:

Physics -- Data processing

Engineering -- Data processing

Computer programming

Python (Computer program language)

C++ (Computer program language)

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010343224	QC52 B48 2015	Open Access Book	Book	Searching... Unknown

On Order

Summary

Makes Numerical Programming More Accessible to a Wider Audience

Bearing in mind the evolution of modern programming, most specifically emergent programming languages that reflect modern practice, Numerical Programming: A Practical Guide for Scientists and Engineers Using Python and C/C++ utilizes the author's many years of practical research and teaching experience to offer a systematic approach to relevant programming concepts. Adopting a practical, broad appeal, this user-friendly book offers guidance to anyone interested in using numerical programming to solve science and engineering problems. Emphasizing methods generally used in physics and engineering--from elementary methods to complex algorithms--it gradually incorporates algorithmic elements with increasing complexity.

Develop a Combination of Theoretical Knowledge, Efficient Analysis Skills, and Code Design Know-How

The book encourages algorithmic thinking, which is essential to numerical analysis. Establishing the fundamental numerical methods, application numerical behavior and graphical output needed to foster algorithmic reasoning, coding dexterity, and a scientific programming style, it enables readers to successfully navigate relevant algorithms, understand coding design, and develop efficient programming skills. The book incorporates real code, and includes examples and problem sets to assist in hands-on learning.

Begins with an overview on approximate numbers and programming in Python and C/C++, followed by discussion of basic sorting and indexing methods, as well as portable graphic functionality Contains methods for function evaluation, solving algebraic and transcendental equations, systems of linear algebraic equations, ordinary differential equations, and eigenvalue problems Addresses approximation of tabulated functions, regression, integration of one- and multi-dimensional functions by classical and Gaussian quadratures, Monte Carlo integration techniques, generation of random variables, discretization methods for ordinary and partial differential equations, and stability analysis

This text introduces platform-independent numerical programming using Python and C/C++, and appeals to advanced undergraduate and graduate students in natural sciences and engineering, researchers involved in scientific computing, and engineers carrying out applicative calculations.

Author Notes

Titus Adrian Beu, professor of theoretical and computational physics at the University "Babes-Bolyai" from Cluj-Napoca, Romania, has been active in the broader field of computational physics for more than 30 years. His research topics have evolved from Tokamak plasma and nuclear reactor calculations in the 1980s, collision theory and molecular cluster spectroscopy in the 1990s, to fullerenes and nanofluidics simulations in recent years. Development of ample computer codes has been at the core of all research projects the author has conducted. In parallel, he has lectured on general programming techniques and advanced numerical methods, general simulation methods, and advanced molecular dynamics.

Series Preface	p. xi
Preface	p. xiii
Author	p. xvii
Acknowledgments	p. xix
1 Approximate Numbers	p. 1
1.1 Sources of Errors in Numerical Calculations	p. 1
1.2 Absolute and Relative Errors	p. 2
1.3 Representation of Numbers	p. 4
1.4 Significant Digits	p. 5
1.5 Errors of Elementary Operations	p. 7
References and Suggested Further Reading	p. 10
2 Basic Programming Techniques	p. 11
2.1 Programming Concepts	p. 11
2.2 Functions and Parameters	p. 12
2.3 Passing Arguments to Python Functions	p. 15
2.4 Passing Arguments to C/C++ Functions	p. 17
2.5 Arrays in Python	p. 19
2.6 Dynamic Array Allocation in C/C++	p. 19
2.7 Basic Matrix Operations	p. 24
References and Suggested Further Reading	p. 30
3 Elements of Scientific Graphics	p. 31
3.1 The Tkinter Package	p. 31
3.2 The Canvas Widget	p. 32
3.3 Simple Tkinter Applications	p. 35
3.4 Plotting Functions of One Variable	p. 39
3.5 Graphics Library graphlib.py	p. 44
3.6 Creating Plots in C++ Using the Library graphlib.py	p. 57
References and Suggested Further Reading	p. 61
4 Sorting and Indexing	p. 63
4.1 Introduction	p. 63
4.2 Bubble Sort	p. 64
4.3 Insertion Sort	p. 66
4.4 Quicksort	p. 70
4.5 Indexing and Ranking	p. 71
4.6 Implementations in C/C++	p. 75
4.7 Problems	p. 78
References and Suggested Further Reading	p. 84
5 Evaluation of Functions	p. 85
5.1 Evaluation of Polynomials by Horner's Scheme	p. 85
5.2 Evaluation of Analytic Functions	p. 88
5.3 Continued Fractions	p. 91
5.4 Orthogonal Polynomials	p. 94
5.5 Spherical Harmonics-Associated Legendre Functions	p. 98
5.6 Spherical Bessel Functions	p. 102
5.7 Implementations in C/C++	p. 105
5.8 Problems	p. 113
References and Suggested Further Reading	p. 125
6 Algebraic and Transcendental Equations	p. 127
6.1 Root Separation	p. 127
6.2 Bisection Method	p. 129
6.3 Method of False Position	p. 132
6.4 Method of Successive Approximations	p. 134
6.5 Newton's Method	p. 139
6.6 Secant Method	p. 142
6.7 Birge-Vieta Method	p. 144
6.8 Newton's Method for Systems of Nonlinear Equations	p. 147
6.9 Implementations in C/C++	p. 151
6.10 Problems	p. 157
References and Suggested Further Reading	p. 168
7 Systems of Linear Equations	p. 169
7.1 Introduction	p. 169
7.2 Gaussian Elimination with Backward Substitution	p. 169
7.3 Gauss-Jordan Elimination	p. 179
7.4 LU Factorization	p. 187
7.5 Inversion of Triangular Matrices	p. 195
7.6 Cholesky Factorization	p. 197
7.7 Tridiagonal Systems of Linear Equations	p. 203
7.8 Block Tridiagonal Systems of Linear Equations	p. 207
7.9 Complex Matrix Equations	p. 208
7.10 Jacobi and Gauss-Seidel Iterative Methods	p. 209
7.11 Implementations in C/C++	p. 213
7.12 Problems	p. 223
References and Suggested Further Reading	p. 231
8 Eigenvalue Problems	p. 233
8.1 Introduction	p. 233
8.2 Diagonalization of Matrices by Similarity Transformations	p. 234
8.3 Jacobi Method	p. 235
8.4 Generalized Eigenvalue Problems for Symmetric Matrices	p. 243
8.5 Implementations in C/C++	p. 246
8.6 Problems	p. 249
References and Suggested Further Reading	p. 264
9 Modeling of Tabulated Functions	p. 265
9.1 Interpolation and Regression	p. 265
9.2 Lagrange Interpolation Polynomial	p. 268
9.3 Neville's Interpolation Method	p. 273
9.4 Cubic Spline Interpolation	p. 276
9.5 Linear Regression	p. 283
9.6 Multilinear Regression Models	p. 287
9.7 Nonlinear Regression: The Levenberg-Marquardt Method	p. 293
9.8 Implementations in C/C++	p. 301
9.9 Problems	p. 309
References and Suggested Further Reading	p. 331
10 Integration of Functions	p. 333
10.1 Introduction	p. 333
10.2 Trapezoidal Rule; A Heuristic Approach	p. 333
10.3 The Newton-Cotes Quadrature Formulas	p. 335
10.4 Trapezoidal Rule	p. 337
10.5 Simpson's Rule	p. 339
10.6 Adaptive Quadrature Methods	p. 341
10.7 Romberg's Method	p. 344
10.8 Improper Integrals: Open Formulas	p. 348
10.9 Midpoint Rule	p. 352
10.10 Gaussian Quadratures	p. 354
10.11 Multidimensional Integration	p. 361
10.12 Adaptive Multidimensional Integration	p. 369
10.13 Implementations in C/C++	p. 372
10.14 Problems	p. 384
References and Suggested Further Reading	p. 393
11 Monte Carlo Method	p. 395
11.1 Introduction	p. 395
11.2 Integration of Functions	p. 396
11.3 Importance Sampling	p. 399
11.4 Multidimensional Integrals	p. 402
11.5 Generation of Random Numbers	p. 408
11.6 Implementations in C/C++	p. 415
11.7 Problems	p. 417
References and Suggested Further Reading	p. 426
12 Ordinary Differential Equations	p. 427
12.1 Introduction	p. 427
12.2 Taylor Series Method	p. 429
12.3 Euler's Method	p. 431
12.4 Runge-Kutta Methods	p. 434
12.5 Adaptive Step Size Control	p. 440
12.6 Methods for Second-Order ODEs	p. 447
12.7 Numerov's Method	p. 454
12.8 Shooting Methods for Two-Point Problems	p. 457
12.9 Finite-Difference Methods for Linear Two-Point Problems	p. 466
12.10 Implementations in C/C++	p. 471
12.11 Problems	p. 481
References and Suggested Further Reading	p. 507
13 Partial Differential Equations	p. 509
13.1 Introduction	p. 509
13.2 Boundary-Value Problems for Elliptic Differential Equations	p. 511
13.3 Initial-Value Problems for Parabolic Differential Equations	p. 525
13.4 Time-Dependent Schrodinger Equation	p. 542
13.5 Initial-Value Problems for Hyperbolic Differential Equations	p. 553
13.6 Implementations in C/C++	p. 559
13.7 Problems	p. 567
References and Suggested Further Reading	p. 585
Appendix A Dynamic Array Allocation in C/C++	p. 587
Appendix B Basic Operations with Vectors and Matrices	p. 591
Appendix C Embedding Python in C/C++	p. 599
Appendix D The Numerical Libraries numxlib.py and numxlib. h	p. 605
Appendix E The Graphics Library graphlib.py Based on Tkinter	p. 611
Appendix F The C++ Interface to the Graphics Library graphlib.py	p. 627
Appendix G List of Programs by Chapter	p. 637
Index	p. 641

Available:*

On Order

Summary

Summary

Author Notes

Table of Contents