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Abstrak :
This book offers engineering students an introduction to the theory of partial differential equations and then guiding them through the modern problems in this subject. Divided into two parts, in the first part readers already well-acquainted with problems from the theory of differential and integral equations gain insights into the classical notions and problems, including differential operators, characteristic surfaces, Levi functions, Green’s function, and Green’s formulas. Readers are also instructed in the extended potential theory in its three forms: the volume potential, the surface single-layer potential and the surface double-layer potential. Furthermore, the book presents the main initial boundary value problems associated with elliptic, parabolic and hyperbolic equations. The second part of the book, which is addressed first and foremost to those who are already acquainted with the notions and the results from the first part, introduces readers to modern aspects of the theory of partial differential equations.

Abstrak :
This book is designed to serve as a textbook for a course on ordinary differential equations, which is usually a required course in most science and engineering disciplines and follows calculus courses. The book begins with linear algebra, including a number of physical applications, and goes on to discuss first-order differential equations, linear systems of differential equations, higher order differential equations, Laplace transforms, nonlinear systems of differential equations, and numerical methods used in solving differential equations. The style of presentation of the book ensures that the student with a minimum of assistance may apply the theorems and proofs presented. Liberal use of examples and homework problems aids the student in the study of the topics presented and applying them to numerous applications in the real scientific world. This textbook focuses on the actual solution of ordinary differential equations preparing the student to solve ordinary differential equations when exposed to such equations in subsequent courses in engineering or pure science programs. The book can be used as a text in a one-semester core course on differential equations, alternatively it can also be used as a partial or supplementary text in intensive courses that cover multiple topics including differential equations.

Abstrak :
Online collaboration tools adalah aplikasi yang mendukung penggunanya untuk bekerja sama dengan rekan kerja atau tim dalam menyelesaikan pekerjaan dengan fungsinya antara lain dapat digunakan untuk berdiskusi & berkomunikasi, menyimpan proyek bersama, serta mengerjakan proyek secara bersama-sama. Pada Maret 2020, pandemi COVID-19 telah masuk ke Indonesia yang menyebabkan adanya kebijakan pembatasan sosial dengan salah satu kebijakannya adalah perubahan dari work from office menjadi work from home untuk beberapa perusahaan. Pada masa tersebut, penggunaan online collaboration tools untuk bekerja pun meningkat karena sebagai salah satu alternatif agar tetap bisa bekerja sama dengan tim. Penelitian ini bertujuan untuk menganalisis faktor-faktor yang memengaruhi pengguna dalam bekerja menggunakan online collaboration tools di saat masa pandemi COVID-19 telah berakhir dan untuk memprediksi apakah pengguna masih tetap melanjutkan penggunaannya. Penelitian ini mengadopsi teori technology affordance, task technology fit dan post acceptance model. Model penelitian meliputi 1) technology affordance (collaborative affordance, communication affordance, sharing resources affordance), 2) task-technoogy fit (utilization, task characteristics, perceived task technology fit), 3) post acceptance model (confirmation, perceived usefulness, satisfaction, continuance intention). Analisis data dilakukan menggunakan metode PLS-SEM dengan 404 responden valid. Hasil analisis nya menemukan bahwa faktor technology affordance, task-technology fit, confirmation, perceived usefulness, dan satisfaction membawa pengaruh terhadap intensi pengguna dalam melanjutkan penggunaan. Penelitian ini memberikan implikasi teoreties karena ada nilai keterbaruan dalam konteks online collaboration tools, serta implikasi praktis bagi pengembang aplikasi dan perusahaan tempat bekerja yang akan atau sedang menggunakan online colaboration tools. ......Online Collaboration Tools is an application that supports its users to work together with colleagues or a team in completing work with its functions, being used to discuss & communicate, save projects, and work on projects together. In March 2020, the COVID-19 pandemic entered Indonesia which resulted in a social violation policy with one of the policies being a change from working from the office to working from home for several companies. At that time, the use of online collaboration tools for work also increased because it was an alternative to being able to work with the team. This study aims to analyze the factors that influence users to work using online collaboration tools when the COVID-19 pandemic has ended and to predict whether users will continue to use them. This study adopts the theory of technology affordances, task technology fit, and post acceptance model. The research model includes 1) technology affordances (collaborative affordance, communication affordance, sharing resources affordance), 2) task-technology fit (utilization, task characteristics, perceived task technology fit), 3) post-acceptance model (confirmation, perceived usefulness, satisfaction, continuance intention). Data analysis was carried out using the PLS-SEM method with 404 valid respondents. The results of the analysis found that technology affordance, task-technology fit, confirmation, perceived usefulness, and satisfaction factors influenced the user’s intention to continue using it. This research provides theoretical implications because there is a novelty value in the context of online collaboration tools, as well as practical implications for application developers and workplace companies that will or are currently using online collaboration tools.

Abstrak :
Effective dynamics of stochastic partial differential equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors’ experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension.

Abstrak :
Approximate global convergence and adaptivity for coefficient inverse problems is the first book in which two new concepts of numerical solutions of multidimensional Coefficient Inverse Problems (CIPs) for a hyperbolic Partial Differential Equation (PDE) are presented. Two central questions for CIPs are addressed, how to obtain a good approximations for the exact solution without any knowledge of a small neighborhood of this solution, and how to refine it given the approximation. The book also combines analytical convergence results with recipes for various numerical implementations of developed algorithms. The developed technique is applied to two types of blind experimental data, which are collected both in a laboratory and in the field. The result for the blind backscattering experimental data collected in the field addresses a real world problem of imaging of shallow explosives.

Abstrak :
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples. The book is organized into two main sections and a set of appendices. Part I addresses steady-state boundary value problems, starting with two-point boundary value problems in one dimension, followed by coverage of elliptic problems in two and three dimensions. It concludes with a chapter on iterative methods for large sparse linear systems that emphasizes systems arising from difference approximations. Part II addresses time-dependent problems, starting with the initial value problem for ODEs, moving on to initial boundary value problems for parabolic and hyperbolic PDEs, and concluding with a chapter on mixed equations combining features of ODEs, parabolic equations, and hyperbolic equations. The appendices cover concepts pertinent to Parts I and II. Exercises and student projects, developed in conjunction with this book, are available on the book webpage along with numerous MATLAB m-files. Readers will gain an understanding of the essential ideas that underlie the development, analysis, and practical use of finite difference methods as well as the key concepts of stability theory, their relation to one another, and their practical implications. The author provides a foundation from which students can approach more advanced topics and further explore the theory and/or use of finite difference methods according to their interests and needs.