Practical Scientific Computing

Professor of Biotechnology, Vice Chancellor, Government College University, Faisalabad, Pakistan Dr. Victor Zalizniak was awarded his Masters in Physics at Krasnoyarsk State University, Russia before becoming a Research Fellow at the Centre for Scientific Computing at the Russian Academy of Sciences (Siberian Branch). He then moved to the Department of Aerospace Engineering at the Royal Melbourne Institute of Technology where he obtained his PhD. In 2001 he returned to the Department of Computer Science at his alma mater, Krasnoyarsk State University, where he continues to lecture, research and write in his particular fields of computational physics and mathematical physics. He is the author of several books on scientific computing including Essentials of Computational Physics Parts 1 and 2.

• PrefaceAcknowledgementsPart IChapter 1: Introduction1.1 Getting Started1.2 Interpreter1.3 ProgramChapter 2: Expressions2.1 Matrix2.2 Real Number2.3 Complex Number2.4 Boolean2.5 String2.6 Structure2.7 Cell2.8 Range Expression2.9 Boolean Expression2.10 Relational Expression2.11 Numerical ExpressionChapter 3: Statements3.1 Assignment Statement3.2 Loop Statements3.3 Conditional Statements3.4 Continue and Break StatementsChapter 4: Programming4.1 Program4.2 Function4.3 Procedure4.4 Java Programming4.5 C ProgrammingChapter 5: Architecture5.1 Front-end5.2 Back-end5.3 User Interface5.4 Gnuplot Interface5.5 Execution EngineChapter 6: Plotting6.1 Simple Function Plot (fplot)6.2 Two-Dimensional Plots6.3 Three-Dimensional PlotsPart IIChapter 7: Solving Nonlinear Equations7.1 Calculation of Roots with the use of Iterative Functions7.2 ExercisesChapter 8: Solving Systems of Linear Equations8.1 Linear Algebra Background8.2 Systems of Linear Equations8.3 Types of Matrices that arise from Applications and Analysis8.4 Error Sources8.5 Condition Number8.6 Direct Methods8.7 Iterative Methods8.8 ExercisesChapter 9: Computational Eigenvalue Problems9.1 Basic Facts concerning Eigenvalue Problems9.2 Localization of Eigenvalues9.3 Power Method9.4 Inverse Iteration9.5 Iteration with a Shift of Origin9.6 The QR Method9.7 ExercisesChapter 10: Introduction to Finite Difference Schemes for Ordinary Differential Equations10.1 Elementary Example of a Finite Difference Scheme10.2 Approximation and Stability10.3 Numerical Solution of Initial Value Problems10.4 Numerical Solution of Boundary Value Problems10.5 Error Estimation and Control10.6 ExercisesChapter 11: Interpolation and Approximation11.1 Interpolation11.2 Approximation of Functions and Data Representation11.3 ExercisesBibliography