This topic will be reviewed in the second chapter

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Unformatted text preview: ectors and matrices with real or complex entries. (This topic will be reviewed in the second chapter.) Familiarity is also needed with the basics of vector calculus, including the gradient, divergence and curl, and the integral theorems which relate them to each other. Finally, one needs ability to carry out lengthy calculations with confidence. Needless to say, all of these skills are necessary for a thorough understanding of the mathematical i language that is an essential foundation for the sciences and engineering. Moreover, the subject of partial differential equations should not be studied in isolation, because much intuition comes from a thorough understanding of applications. The individual branches of the subject are concerned with the special types of partial differential equations which which are needed to model diffusion, wave motion, equilibria of membranes and so forth. The behavior of physical systems often suggest theorems which can be proven via rigorous mathematics. (This last point, and the book itself, can be best appreciated by those who have taken a course in rigorous mathematical proof, such as a course in mathematic...
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