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Computer algebra systems are revolutionizing the teaching, the learning, and the exploration of science. Not only can students and researchers work through mathematical models more efficiently and with fewer errors than with pencil and paper, they can also easily explore, both analytically and numerically, more complex and computationally intensive models. Aimed at science and engineering undergraduates at the sophomore/junior level, this introductory guide to the mathematical models of science is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, mathematics, physics, and chemistry. The topics are organized into the Appetizers dealing with graphical aspects, the Entrees concentrating on symbolic computation, and the Desserts illustrating numerical simulation. The heart of the text is a large number of computer algebra recipes based on the Maple 10 software system. These have been designed not only to provide tools for problem solving, but also to stimulate the reader’s imagination. Associated with each recipe is a scientific model or method and an interesting or amusing story (accompanied with a thought-provoking quote) that leads the reader through the various steps of the recipe. This text is the first of two volumes.  The advanced guide, aimed at junior/senior/graduate level students, deals with more advanced differential equation models.

Physics --- Mathematical models. --- Computer-assisted instruction. --- Mathematics. --- Computer science --- Computer simulation. --- Computer software. --- Physics. --- Applied mathematics. --- Engineering mathematics. --- Mathematical Modeling and Industrial Mathematics. --- Symbolic and Algebraic Manipulation. --- Appl.Mathematics/Computational Methods of Engineering. --- Mathematical Methods in Physics. --- Mathematical Software. --- Simulation and Modeling. --- Models, Mathematical --- Simulation methods --- Engineering --- Engineering analysis --- Mathematical analysis --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Software, Computer --- Computer systems --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Model-integrated computing --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Science --- Mathematics --- 519.67 --- 681.3*G --- 681.3*I12 --- 681.3*I12 Algorithms: algebraic algorithms; nonalgebraic algorithms; analysis of algorithms (Algebraic manipulation; computing methodologies) --- Algorithms: algebraic algorithms; nonalgebraic algorithms; analysis of algorithms (Algebraic manipulation; computing methodologies) --- 681.3*G Mathematics of computing --- Mathematics of computing --- 519.67 Machine, graphical and other methods of computational mathematics --- Machine, graphical and other methods of computational mathematics --- Computer-assisted instruction --- Algebra --- Mathematical physics. --- Mathematical and Computational Engineering. --- Data processing. --- Physical mathematics --- Computer --- Assisted instruction. --- Computer science—Mathematics.