Perturbation methods are old and powerful. Solutions are provided as formulas rather than numbers or pictures, so the skill of the person (or machine!) reading the formula is essential. This unique book presents several classical methods to solve perturbation problems using backward error analysis. This lessens the likelihood of blunders because ......
Linear algebra and ordinary differential equations (ODEs) are foundational postcalculus mathematics. The goal of this text is to help students master both subject areas in a one-semester course. The linear algebra necessary for applications is developed first and continually referenced when solving ODEs. The discussion of ODEs focuses on solving ......
This textbook focuses on computational methods for inverse problems that are governed by partial differential equations (PDEs). The author considers deterministic and Bayesian formulations and highlights how traditional tools from deterministic inversion can be integrated into solution methods for Bayesian inverse problems. Advanced topics such as ......
If you have a basic knowledge of C and want to deepen your understanding, specifically for use in scientific computing, this unique book is for you. Scientific Computing in Modern C is the first book to discuss scientific computing from a software perspective. It covers a broad range of topics - the finer points of C , specific idioms of C ......
And Related Problems of Mathematical Physics, Engineering, and Life Sciences
This book is the first to offer a systematic methodology for solving nonlinear ordinary differential equations (ODEs) using power series, specifically those arising in mathematical physics. It provides tools to eliminate the tedious manipulation of infinite series, enabling recursive computation of all terms. The authors also present a structured ......
This book is a self-contained introduction to quantum algorithms with an emphasis on quantum optimization, that is, quantum algorithms to solve optimization problems. The book provides all the tools necessary to understand the benefits and drawbacks of quantum optimization algorithms, paying particular attention to provable guarantees and ......
From the Euclidean Space and the Circle to Lie Groups
Coordination, consensus, and synchronization are found in diverse natural phenomena and engineering applications. Examples are flocking birds, illuminating fireflies, a school of fish, and distributed control and sensing. The simplest of such problems are set in the Euclidean spaces and the circle. Consensus and Synchronization: From the Euclidean ......
The shape of the Earth was a significant scientific question in the eighteenth century. When it was discovered that the Earth was flattened at the poles, scientists sought to understand the cause, leading to the study of the gravitational attraction of celestial spheroids. The solution drew upon Newton's law of universal gravitation, which used ......
This book analyzes a variety of results related to the modeling, analysis, estimation, and control design and the applications of different configurations of tubular reactors of two classes of partial differential equations (hyperbolic and parabolic), both linear and nonlinear. The advantages of using the tubular reactor case to study distributed ......
