This book presents mathematical methods from both purely conceptual and computer-algebra-system perspectives. Part I follows the "paper and pencil" presentation of mathematical methods, emphasizing fundamental understanding and geometric intuition. In addition to a complete list of standard subjects, it introduces important contemporary topics such as nonlinear differential equations, chaos, and solitons. Part II uses Mathematica to cover the same topics as Part I, adopting a computer-oriented instructional approach. Using Mathematica frees students from laborious tasks, allowing them to focus entirely on concepts and to visualize the mathematical content more effectively. The focus of the text is on key ideas and basic technical and geometric insights, presented in a way that closely reflects how physicists and engineers actually think about mathematics.
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