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This is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. The book covers both well-established techniques and recently developed procedures, including the classical series solution method, diverse perturbation methods, pioneering asymptotic methods, and the latest homotopy methods. It gives a complete description of the methods without going deep into rigorous mathematical aspects. Detailed examples illustrate the application of the methods to solve real-world problems.