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"This textbook develops, analyzes, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified viewpoint. The author emphasizes finite difference and finite volume methods, specifically their principled derivation, stability, accuracy, efficient implementation, and practical performance in various fields of science and engineering. Smooth and nonsmooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is included as well.The author bridges theory and practice by developing algorithms, concepts, and analysis from basic principles while discussing efficiency and performance issues and demonstrating methods through examples and case studies from numerous application areas."

"Partial differential equations (PDEs) are essential for modeling many physical phenomena. This undergraduate textbook introduces students to the topic with a unique approach that emphasizes the modern finite element method alongside the classical method of Fourier analysis.Additional features of this new edition include broader coverage of PDE methods and applications, with new chapters on the method of characteristics, Sturmiouville problems, and Green functions, and a new section on the finite difference method for the wave equation. The author continues to emphasize Fourier series and finite element methods, which were the primary scope of the first edition."

"This introductory text on partial differential equations is the first to integrate modern and classical techniques for solving PDEs at a level suitable for undergraduates. The author successfully complements the classical topic of Fourier series with modern finite element methods. The result is an up-to-date, powerful, and flexible approach to solving PDEs, which both faculty and students will find refreshing, challenging, and rewarding. Linear algebra is a key component of the text, providing a framework both for computing solutions and for understanding the theoretical basis of the methods. Although techniques are emphasized over theory, the methods are presented in a mathematically sound fashion to develop a strong foundation for further study. Numerous exercises and examples involve meaningful experiments with realistic physical parameters, allowing students to use physical intuition to understand the qualitative features of the solutions."