Cavite State University - CCAT Campus - Library

Includes bibliographical references and index

Approximate NumbersSources of Errors in Numerical CalculationsAbsolute and Relative ErrorsRepresentation of NumbersSignificant DigitsErrors of Elementary OperationsReferences and Suggested Further ReadingBasic Programming TechniquesProgramming ConceptsFunctions and ParametersPassing Arguments to Python FunctionsPassing Arguments to C/C++ FunctionsArrays in PythonDynamic Array Allocation in C/C++Basic Matrix OperationsReferences and Suggested Further ReadingElements of Scientific GraphicsThe Tkinter PackageThe Canvas WidgetSimple Tkinter ApplicationsPlotting Functions of One VariableGraphics Library graphlib.pyCreating Plots in C++ Using the Library graphlib.pyReferences and Suggested Further ReadingSorting and IndexingIntroductionBubble SortInsertion SortQuicksortIndexing and RankingImplementations in C/C++ProblemsReferences and Suggested Further ReadingEvaluation of FunctionsEvaluation of Polynomials by Horner's SchemeEvaluation of Analytic FunctionsContinued FractionsOrthogonal PolynomialsSpherical Harmonics Associated Legendre FunctionsSpherical Bessel FunctionsImplementations in C/C++ProblemsReferences and Suggested Further ReadingAlgebraic and Transcendental EquationsRoot SeparationBisection MethodMethod of False PositionMethod of Successive ApproximationsNewton's MethodSecant MethodBirge-Vieta MethodNewton's Method for Systems of Nonlinear EquationsImplementations in C/C++ProblemsReferences and Suggested Further ReadingSystems of Linear EquationsIntroductionGaussian Elimination with Backward SubstitutionGauss-Jordan EliminationLU FactorizationInversion of Triangular MatricesCholesky FactorizationTridiagonal Systems of Linear EquationsBlock Tridiagonal Systems of Linear EquationsComplex Matrix EquationsJacobi and Gauss-Seidel Iterative MethodsImplementations in C/C++ProblemsReferences and Suggested Further ReadingEigenvalue ProblemsIntroductionDiagonalization of Matrices by Similarity TransformationsJacobi MethodGeneralized Eigenvalue Problems for Symmetric MatricesImplementations in C/C++ProblemsReferences and Suggested Further ReadingModeling of Tabulated FunctionsInterpolation and RegressionLagrange Interpolation PolynomialNeville's Interpolation MethodCubic Spline InterpolationLinear RegressionMultilinear Regression ModelsNonlinear Regression: The Levenberg-Marquardt MethodImplementations in C/C++ProblemsReferences and Suggested Further ReadingIntegration of FunctionsIntroductionTrapezoidal Rule; A Heuristic ApproachThe Newton-Cotes Quadrature FormulasTrapezoidal RuleSimpson's RuleAdaptive Quadrature MethodsRomberg's MethodImproper Integrals: Open FormulasMidpoint RuleGaussian QuadraturesMultidimensional IntegrationAdaptive Multidimensional IntegrationImplementations in C/C++ProblemsReferences and Suggested Further ReadingMonte Carlo MethodIntroductionIntegration of FunctionsImportance SamplingMultidimensional IntegralsGeneration of Random NumbersImplementations in C/C++ProblemsReferences and Suggested Further ReadingOrdinary Differential EquationsIntroductionTaylor Series MethodEuler's MethodRunge-Kutta MethodsAdaptive Step Size ControlMethods for Second-Order ODEsNumerov's MethodShooting Methods for Two-Point ProblemsFinite-Difference Methods for Linear Two-Point ProblemsImplementations in C/C++ProblemsReferences and Suggested Further ReadingPartial Differential EquationsIntroductionBoundary-Value Problems for Elliptic Differential EquationsInitial-Value Problems for Parabolic Differential EquationsTime-Dependent Schroedinger EquationInitial-value Problems for Hyperbolic Differential EquationsImplementations in C/C++ProblemsReferences and Suggested Further ReadingAppendicesIndex

"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
"This book is devoted to the general field of numerical programming, with emphasis on methods specific to computational physics and engineering. While tremendous advances of computer performances have been achieved in recent years, numerical methods still remain virtually inexhaustible resources for extending the range of challenging real-life problems made tractable. Along these lines, the book sets as its primordial goal to contribute to fostering interest in numerical programming by making computations accessible and appealing to broader categories of scientists and engineers. I have written this book for advanced undergraduate and graduate students in natural sciences and engineering, with the aim of being suited as curriculum material for a one- or two-semester course in numerical programming based on Python or C/C++. The book may also be used for independent study or as a reference material beyond academic studies. It may be useful, for instance, as an introductory text for researchers preparing to engage in scientific computing, or engineers needing effective numerical tools for applicative calculations. I have placed emphasis on the rigorous, yet accessible presentation of the fundamental numerical methods, which are complemented with implementations and applications, highlighting specific numerical behavior and often featuring graphical output. Although the material requires basic knowledge of calculus, linear algebra, and differential equations, it does not assume previous acquaintance with numerical techniques, leading the reader all the way from elementary algorithms to elaborate methods of relevance for modern numerical programming"-- Provided by publisher

English text.