Scientific computing is the study of how to use computers effectively to solve problems that arise from the mathematical modeling of phenomena in science and engineering. It is based on mathematics, numerical and symbolic/algebraic computations and visualization. This book serves as an introduction to both the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes; we explain both the theory behind these algorithms and how they must be implemented in order to work reliably in finite-precision arithmetic. The book includes many programs written in Matlab and Maple ? Maple is often used to derive numerical algorithms, whereas Matlab is used to implement them. The theory is developed in such a way that students can learn by themselves as they work through the text. Each chapter contains numerous examples and problems to help readers understand the material “hands-on”.

This book offers an introduction to the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes. Includes numerous complete, ready-to-run programs in Matlab and Maple.

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Scientific computing is the study of how to use computers effectively to solve problems that arise from the mathematical modeling of phenomena in science and engineering. It is based on mathematics, numerical and symbolic/algebraic computations and visualization. This book serves as an introduction to both the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes; we explain both the theory behind these algorithms and how they must be implemented in order to work reliably in finite-precision arithmetic. The book includes many programs written in Matlab and Maple ? Maple is often used to derive numerical algorithms, whereas Matlab is used to implement them. The theory is developed in such a way that students can learn by themselves as they work through the text. Each chapter contains numerous examples and problems to help readers understand the material “hands-on”.

Why Study Scientific Computing? Gander, Walter (et al.) Pages 1-8 Finite Precision Arithmetic Gander, Walter (et al.) Pages 9-60 Linear Systems of Equations Gander, Walter (et al.) Pages 61-112 Interpolation Gander, Walter (et al.) Pages 113-179 Nonlinear Equations Gander, Walter (et al.) Pages 181-259 Least Squares Problems Gander, Walter (et al.) Pages 261-385 Eigenvalue Problems Gander, Walter (et al.) Pages 387-486 Differentiation Gander, Walter (et al.) Pages 487-515 Quadrature Gander, Walter (et al.) Pages 517-582 Numerical Ordinary Differential Equations Gander, Walter (et al.) Pages 583-671 Iterative Methods for Linear Systems Gander, Walter (et al.) Pages 673-815 Optimization Gander, Walter (et al.) Pages 817-886