Ronald B. Guenther – författare

Sturm-Liouville problems arise naturally in solving technical problems in engineering, physics, and more recently in biology and the social sciences. These problems lead to eigenvalue problems for ordinary and partial differential equations. Sturm-Liouville Problems: Theory and Numerical Implementation addresses, in a unified way, the key issues that must be faced in science and engineering applications when separation of variables, variational methods, or other considerations lead to Sturm-Liouville eigenvalue problems and boundary value problems.

Sturm-Liouville problems arise naturally in solving technical problems in engineering, physics, and more recently in biology and the social sciences. These problems lead to eigenvalue problems for ordinary and partial differential equations. Sturm-Liouville Problems: Theory and Numerical Implementation addresses, in a unified way, the key issues that must be faced in science and engineering applications when separation of variables, variational methods, or other considerations lead to Sturm-Liouville eigenvalue problems and boundary value problems.

An Introduction to Numerical Methods: A MATLAB® Approach, Fifth Edition continues to offer readers an accessible and practical introduction to numerical analysis. It presents a wide range of useful and important algorithms for scientific and engineering applications, using MATLAB to illustrate each numerical method with full details of the computed results so that the main steps are easily visualized and interpreted. This edition also includes new chapters on Approximation of Continuous Functions and Dealing with Large Sets of Data.

Features:

An Introduction to Numerical Methods: A MATLAB® Approach, Fifth Edition continues to offer readers an accessible and practical introduction to numerical analysis. It presents a wide range of useful and important algorithms for scientific and engineering applications, using MATLAB to illustrate each numerical method with full details of the computed results so that the main steps are easily visualized and interpreted. This edition also includes new chapters on Approximation of Continuous Functions and Dealing with Large Sets of Data.

Features:

Aspects of Integration: Novel Approaches to the Riemann and Lebesgue Integrals is comprised of two parts. The first part is devoted to the Riemann integral, and provides not only a novel approach, but also includes several neat examples that are rarely found in other treatments of Riemann integration. Historical remarks trace the development of integration from the method of exhaustion of Eudoxus and Archimedes, used to evaluate areas related to circles and parabolas, to Riemann’s careful definition of the definite integral, which is a powerful expansion of the method of exhaustion and makes it clear what a definite integral really is.

The second part follows the approach of Riesz and Nagy in which the Lebesgue integral is developed without the need for any measure theory. Our approach is novel in part because it uses integrals of continuous functions rather than integrals of step functions as its starting point. This is natural because Riemann integrals of continuous functions occur much more frequently than do integrals of step functions as a precursor to Lebesgue integration. In addition, the approach used here is natural because step functions play no role in the novel development of the Riemann integral in the first part of the book. Our presentation of the Riesz-Nagy approach is significantly more accessible, especially in its discussion of the two key lemmas upon which the approach critically depends, and is more concise than other treatments.

Features

Aspects of Integration: Novel Approaches to the Riemann and Lebesgue Integrals is comprised of two parts. The first part is devoted to the Riemann integral, and provides not only a novel approach, but also includes several neat examples that are rarely found in other treatments of Riemann integration. Historical remarks trace the development of integration from the method of exhaustion of Eudoxus and Archimedes, used to evaluate areas related to circles and parabolas, to Riemann’s careful definition of the definite integral, which is a powerful expansion of the method of exhaustion and makes it clear what a definite integral really is.

The second part follows the approach of Riesz and Nagy in which the Lebesgue integral is developed without the need for any measure theory. Our approach is novel in part because it uses integrals of continuous functions rather than integrals of step functions as its starting point. This is natural because Riemann integrals of continuous functions occur much more frequently than do integrals of step functions as a precursor to Lebesgue integration. In addition, the approach used here is natural because step functions play no role in the novel development of the Riemann integral in the first part of the book. Our presentation of the Riesz-Nagy approach is significantly more accessible, especially in its discussion of the two key lemmas upon which the approach critically depends, and is more concise than other treatments.

Features

Introduction to the Potential Theory for the Time-Dependent Stokes System is made up of two parts. The first part deals with a careful presentation of the principles on which the physical problems are based. The fluids under consideration are assumed to be incompressible and the equations so obtained are nonlinear. The linear problems are obtained by introducing characteristic parameters and so determining which terms can be neglected. The authors feel it is important that when a mathematical problem is solved, one knows precisely which problem has actually been solved. The second part deals with the mathematical treatment of the problems derived in the first part. These equations are linear and time dependent. The first step is the construction of a fundamental solution for the equations involved. They are analogous to the fundamental solutions for the potential and heat equations commonly found in the mathematical and engineering literature. The fundamental solution is used as in classical potential theory to construct solutions to initial and certain boundary value problems for the linear Stokes equations.

Features

Introduction to the Potential Theory for the Time-Dependent Stokes System is made up of two parts. The first part deals with a careful presentation of the principles on which the physical problems are based. The fluids under consideration are assumed to be incompressible and the equations so obtained are nonlinear. The linear problems are obtained by introducing characteristic parameters and so determining which terms can be neglected. The authors feel it is important that when a mathematical problem is solved, one knows precisely which problem has actually been solved. The second part deals with the mathematical treatment of the problems derived in the first part. These equations are linear and time dependent. The first step is the construction of a fundamental solution for the equations involved. They are analogous to the fundamental solutions for the potential and heat equations commonly found in the mathematical and engineering literature. The fundamental solution is used as in classical potential theory to construct solutions to initial and certain boundary value problems for the linear Stokes equations.

Features