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This textbook offers a comprehensive introduction to differential equations, covering both initial-value and boundary-value problems. It emphasizes problem-solving skills and applications in various fields, making it suitable for students in engineering, physics, and mathematics. The fourth edition includes a wealth of pedagogical aids, such as examples, explanations, and exercises, to enhance understanding. Understandable, step-by-step solutions are provided for every example. And this edition makes an even greater effort to show students how the mathematical concepts have relevant, everyday applications. Among the boundary-value related topics covered in this expanded text are: plane autonomous systems and stability; orthogonal functions; Fourier series; the Laplace transform; and elliptic, parabolic, and hyperparabolic partial differential equations, and their applications.
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