Ebook: Scientific Computing with MATLAB and Octave

This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer-based solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions using polynomials and construct accurate approximations for the solution of ordinary and partial differential equations. To make the format concrete and appealing, the programming environments Matlab and Octave are adopted as faithful companions. The book contains the solutions to several problems posed in exercises and examples, often originating from important applications. At the end of each chapter, a specific section is devoted to subjects which were not addressed in the book and contains bibliographical references for a more comprehensive treatment of the material.

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This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer-based solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions using polynomials and construct accurate approximations for the solution of ordinary and partial differential equations. To make the format concrete and appealing, the programming environments Matlab and Octave are adopted as faithful companions. The book contains the solutions to several problems posed in exercises and examples, often originating from important applications. At the end of each chapter, a specific section is devoted to subjects which were not addressed in the book and contains bibliographical references for a more comprehensive treatment of the material.
Content:
Front Matter....Pages I-XVI
What can’t be ignored....Pages 1-40
Nonlinear equations....Pages 41-74
Approximation of functions and data....Pages 75-106
Numerical differentiation and integration....Pages 107-128
Linear systems....Pages 129-179
Eigenvalues and eigenvectors....Pages 181-199
Ordinary differential equations....Pages 201-254
Numerical approximation of boundary-value problems....Pages 255-302
Solutions of the exercises....Pages 303-345
Back Matter....Pages 347-366

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This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer-based solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions using polynomials and construct accurate approximations for the solution of ordinary and partial differential equations. To make the format concrete and appealing, the programming environments Matlab and Octave are adopted as faithful companions. The book contains the solutions to several problems posed in exercises and examples, often originating from important applications. At the end of each chapter, a specific section is devoted to subjects which were not addressed in the book and contains bibliographical references for a more comprehensive treatment of the material.
Content:
Front Matter....Pages I-XVI
What can’t be ignored....Pages 1-40
Nonlinear equations....Pages 41-74
Approximation of functions and data....Pages 75-106
Numerical differentiation and integration....Pages 107-128
Linear systems....Pages 129-179
Eigenvalues and eigenvectors....Pages 181-199
Ordinary differential equations....Pages 201-254
Numerical approximation of boundary-value problems....Pages 255-302
Solutions of the exercises....Pages 303-345
Back Matter....Pages 347-366
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