The book Introduction to Numerical Methods is designed for students and researchers who want to learn the practical application of modern scientific computing techniques. Avoiding an encyclopedic and heavily theoretical presentation, it covers fundamental issues and methods in depth, explains the reasons for the success and failure of numerical software, and describes new and easily understandable approaches and techniques.

The authors adopt an algorithmic approach, focusing on techniques that can be easily applied in engineering, computer science, and mathematics for industrial applications. They emphasize the latest methods, issues, and software while providing the theoretical foundations in a detailed manner, so those who are called to apply the techniques will be able to successfully design solutions to unusual problems.

They show how algorithms work in practice, anticipating that the reader will gradually become familiar with the programming environment of MATLAB® as they learn the material presented in the book. They provide many different exercises in each chapter and review questions aimed at self-assessment.

The book Introduction to Numerical Methods is addressed to undergraduate students as well as students beginning their graduate studies. It is also suitable for researchers from other scientific fields who wish to learn the basic concepts and ideas of scientific computing.

Contents of the book:

• Numerical algorithms
• Rounding errors
• Nonlinear equations in one variable
• Introduction to linear algebra
• Linear systems: direct methods
• Linear least squares problems
• Linear systems: iterative methods
• Eigenvalues and singular values
• Nonlinear systems and optimization
• Polynomial interpolation
• Piecewise polynomial interpolation
• Optimal approximation
• Fourier transform
• Numerical differentiation
• Numerical integration
• Differential equations