An introduction to ordinary differential equations and systems of ordinary differential equations, including new analytical methods to solve nonlinear equations, mathematical modeling, computer programming, computer graphics with MAPLE, and applications in science and engineering. "... a new textbook that will thoroughly revolutionize the teaching and learning of differential equations with the vital goal of student retention always in sight." Dr. Randolph Rach, original coauthor of the Adomian's Decomposition Method. ¿ New modern analytical methods to solve nonlinear differential equations, such as the Adomian Decomposition Method, which overcomes most restrictions of existing methods (e.g., no need for a grid, specialized software, complex discretization, special smoothing, handling of large matrices, small perturbation, numerical instability, linearization, etc.). ¿ Integrated, balanced presentation of model development, solution methods, computer implementation, and analysis of system's response. ¿ Designed to increase engineering and science student retention. ¿ Mathematical and computer modeling with Maple. No prior knowledge of Maple required. ¿ Emphasis on problem solving over mathematical rigorousness. ¿ Clear and simple presentation of concepts with multitude of examples: 125 solved examples, 70 computer programs, 146 proposed problems, 17 illustrations, 118 computer graphs, answers to problems, detailed bibliography. ¿ Preference of general, systematic, analytical methods over complex numerical methods. ¿ Self contained. Except for calculus, all necessary background is included.