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"In order to emphasize the relationships and cohesion between analytical and numerical techniques, Ordinary Differential Equations in Theory and Practice presents a comprehensive and integrated treatment of both aspects in combination with the modeling of relevant problem classes. This text is uniquely geared to provide enough insight into qualitative aspects of ordinary differential equations (ODEs) to offer a thorough account of quantitative methods for approximating solutions numerically, and to acquaint the reader with mathematical modeling, where such ODEs often play a significant role.Although originally published in 1995, the text remains timely and useful to a wide audience. It provides a thorough introduction to ODEs, since it treats not only standard aspects such as existence, uniqueness, stability, one-step methods, multistep methods, and singular perturbations, but also chaotic systems, differential-algebraic systems, and boundary value problems. The authors aim to show the use of ODEs in real life problems, so there is an extended chapter in which not only the general concepts of mathematical modeling but also illustrative examples from various fields are presented. A chapter on classical mechanics makes the book self-contained."

"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."

"Suatu virus jenis Corona pertama kali terdeteksi di Wuhan, Cina pada akhir tahun 2019, yang selanjutnya disebut sebagai SARS-CoV-2. Penyakit menular yang disebabkan oleh virus SARS-CoV-2 ini kemudian diberi nama Coronavirus Disease 2019, yang kemudian disingkat menjadi COVID-19. Per tanggal 29 Januari 2022, tercatat sebanyak kurang lebih 900.000 kasus terkonfirmasi positif COVID-19 hanya di DKI Jakarta, sebagai episentrum penyebaran COVID-19 di Indonesia. Sejak saat itu, berbagai disiplin ilmu mencoba memberikan kontribusi dalam upaya pengendalian dan pemahaman bagaimana penyakit COVID-19 menyebar, salah satunya melalui pendekatan matematika. Berbagai pendekatan matematika telah diperkenalkan, salah satunya menggunakan pendekatan sistem persamaan diferensial biasa. Dalam skripsi ini, akan dilakukan pendekatan yang sama di mana populasi manusia akan dibagi berdasarkan status kesehatannya untuk mengetahui bagaimana COVID-19 dapat menyebar. Beberapa hal dipertimbangkan dalam pengkonstruksian model antara lain keberadaan individu terinfeksi dengan maupun tanpa gejala, proses infeksi secara tidak langsung melalui kontak dengan permukaan terkontaminasi, dan beberapa upaya yang telah diterapkan oleh Pemerintah Kota DKI Jakarta diantaranya aturan pemberlakuan isolasi mandiri dan perawatan khusus di rumah sakit bagi populasi terinfeksi. Dari model matematika tersebut, skripsi yang dikerjakan akan mengulas penurunan model, analisis model secara analitik maupun numerik, dan pemberian intepretasi. Data yang digunakan dalam skripsi akan mengacu pada data kasus aktif COVID-19 di DKI Jakarta sejak tanggal 30 November 2020 sampai tanggal 31 Maret 2021.

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A type of Corona virus was first detected in Wuhan, China by the end of 2019, hereinafter referred to as SARS-CoV-2. Infectious diseases caused by the SARS-CoV-2 virus was later given the name Coronavirus Disease 2019, which then shortened to COVID-19. As of January 29, 2022, there were about 900,000 positive confirmed cases of COVID-19 only in DKI Jakarta, as the epicenter of the spread of COVID-19 in Indonesia. Since then, various disciplines trying to contribute to overcome and understand how COVID-19 is spreading, one of which is through a mathematical approach. Various mathematical approaches have been introduced, one of them uses the approach system of ordinary differential equations. In this thesis, the same approach will be taken where the human population will be divided according to their health status to know how COVID-19 can spread. Some discussions included in the construction of the model, among others, are the presence of infected symptomatic or asymptomatic individuals, indirect virus transmission through contact with contaminated surface, and several interventions that have been implemented by the DKI Jakrta City Government, including the rules for implementing self-isolation and hospitalization for the infected population. From the mathematical model, the thesis will review the derivation of the model, analyse the model both analytically and numerically, and give the interpretation. The data used in the thesis will refer to the data on active COVID-19 cases in DKI Jakarta from 30 November 2020 to 31 March 2021."

"Offers an alternative to the "rote" approach of presenting standard categories of differential equations accompanied by routine problem sets. The exercises presented amplify and provide perspective for the material, often giving readers opportunity for ingenuity. Little or no previous acquaintance with the subject is required to learn usage of techniques for constructing solutions of differential equations in this reprint volume."