Ebook: Elements of Scientific Computing

Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. This book is a gentle introduction to such computational methods where the techniques are explained through examples. It is our goal to teach principles and ideas that carry over from field to field. You will learn basic methods and how to implement them. In order to gain the most from this text, you will need prior knowledge of calculus, basic linear algebra and elementary programming.

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Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. This book is a gentle introduction to such computational methods where the techniques are explained through examples. It is our goal to teach principles and ideas that carry over from field to field. You will learn basic methods and how to implement them. In order to gain the most from this text, you will need prior knowledge of calculus, basic linear algebra and elementary programming.

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Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. This book is a gentle introduction to such computational methods where the techniques are explained through examples. It is our goal to teach principles and ideas that carry over from field to field. You will learn basic methods and how to implement them. In order to gain the most from this text, you will need prior knowledge of calculus, basic linear algebra and elementary programming.
Content:
Front Matter....Pages i-xii
Computing Integrals....Pages 1-29
Differential Equations: The First Steps....Pages 31-73
Systems of Ordinary Differential Equations....Pages 75-98
Nonlinear Algebraic Equations....Pages 99-145
The Method of Least Squares....Pages 147-193
About Scientific Software....Pages 195-272
The Diffusion Equation....Pages 273-357
Analysis of the Diffusion Equation....Pages 359-409
Parameter Estimation and Inverse Problems....Pages 411-421
A Glimpse of Parallel Computing....Pages 423-453
Back Matter....Pages 455-465

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Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. This book is a gentle introduction to such computational methods where the techniques are explained through examples. It is our goal to teach principles and ideas that carry over from field to field. You will learn basic methods and how to implement them. In order to gain the most from this text, you will need prior knowledge of calculus, basic linear algebra and elementary programming.
Content:
Front Matter....Pages i-xii
Computing Integrals....Pages 1-29
Differential Equations: The First Steps....Pages 31-73
Systems of Ordinary Differential Equations....Pages 75-98
Nonlinear Algebraic Equations....Pages 99-145
The Method of Least Squares....Pages 147-193
About Scientific Software....Pages 195-272
The Diffusion Equation....Pages 273-357
Analysis of the Diffusion Equation....Pages 359-409
Parameter Estimation and Inverse Problems....Pages 411-421
A Glimpse of Parallel Computing....Pages 423-453
Back Matter....Pages 455-465
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