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""Now in a thoroughly updated and revised fourth edition, this volume features new concepts and applications to assist readers in modeling and analyzing natural, social, and technological processes. It introduces key ideas in mathematical methods and modeling, focusing on the connections between mathematics and the applied and natural sciences. This edition emphasizes probability and stochastic differential equations and includes additional coverage of mathematics biology, including biochemical kinetics, epidemiology, viral dynamics, parasitic diseases, and more. New and revised exercises are incorporated throughout"--"

"The Trends in International Mathematics and Science Study (TIMSS) aims to provide a broad perspective forevaluating and improving education. This assessment also ranks the participant countries based on their performanceand makes inferences about factors affecting achievement and learning. However, the study may not function as it wasexpected because of differences in curricular, cultural, or language settings among countries. Consequently, thischallenges assumptions about measurement equivalency. The present study aims to assess the equivalency ofmathematics items on the TIMSS (2007) study across Australian and Indonesia. Students’ responses were subjected toRasch analysis to determine DIF items. The results revealed that many items of mathematics tests are problematicbecause they showed significant bias. The study also found that Australian students performed better and foundmathematics items on the test easier than their Indonesian counterparts did. Several factors such as curriculardifferences, methods used to solve mathematics problems, availability of textbooks and teachers’ quality might explainthe existence of DIF between the countries. These findings indicate that serious limitations of using TIMSS results incomparing the performance of students across countries. Thus, further empirical evidence is needed before TIMSS 2007results can be meaningfully used in research.The Trends in International Mathematics and Science Study (TIMSS) bertujuan menyediakan perspektif yang luasdalam mengevaluasi dan meningkatkan mutu pendidikan. TIMSS juga merangking negara-negara peserta studiberdasarkan kemampuan serta membuat prediksi tentang faktor-faktor yang memengaruhi capaian belajar siswamereka. Akan tetapi, karena perbedaan kurikulum, budaya atau bahasa dari negara-negara tersebut, TIMSS ini tidakberfungsi sebagaimana yang diharapkan. Akibatnya, kondisi ini menantang asumsi-asumsi tentang pengukuran yangekuivalen. Penelitian ini bertujuan untuk menguji keekuivalenan soal-soal matematika dari studi TIMSS 2007 denganmenggunakan jawaban siswa Australia dan Indonesia. Rasch analisis digunakan untuk menemukan soal-soal yang bias.Hasil analisis menujukkan bahwa banyak soal matematika dalam studi TIMSS 2007 bermasalah karena soal tersebutmemperlihatkan bias yang signifikan. Penelitian ini juga menemukan bahwa kemampuan siswa Australia lebih baik darisiswa Indonesia. Soal matematika terlihat lebih mudah bagi siswa Australia dibandingkan bagi siswa Indonesia.Perbedaan kurikulum sekolah, metode dalam pemecahan masalah dan ketersediaan buku dan kualitas guru didugasebagai faktor penyebab munculnya DIF item. Temuan-temuan dalam penelitian ini mengindikasikan adanyaketerbatasan yang serius dalam menggunakan hasil studi TIMSS untuk membandingkan negara-negara peserta studi.Oleh karena itu, bukti-bukti empiris lainnya sangat diperlukan sebelum hasil studi TIMSS 2007 dapat digunakandengan bermakna sebagai dasar penelitian."

"This textbook explores approximate solutions to general relativity and their consequences. It offers a unique presentation of Einstein's theory by developing powerful methods that can be applied to astrophysical systems. Beginning with a uniquely thorough treatment of Newtonian gravity, the book develops post-Newtonian and post-Minkowskian approximation methods to obtain weak-field solutions to the Einstein field equations. The book explores the motion of self-gravitating bodies, the physics of gravitational waves, and the impact of radiative losses on gravitating systems. It concludes with a brief overview of alternative theories of gravity. Ideal for graduate courses on general relativity and relativistic astrophysics, the book examines real-life applications, such as planetary motion around the Sun, the timing of binary pulsars, and gravitational waves emitted by binary black holes. Text boxes explore related topics and provide historical context, and over 100 exercises present challenging tests of the material covered in the main tex"