This text demonstrates the power of mathematics to solve practical scientific and technical problems by formulating and finding solutions for models of these problems, especially by methods based upon the use of partial differential equations. Designed primarily for final-year undergraduates and graduate students, the book springs from the author's experience in teaching a course on this subject at first-year postgraduate level, and more generally from the work done since 1967 by the Oxford Study Groups with Industry. The text is combined with twenty-one carefully ordered problems taken from real situations, and students are encouraged to develop the skill of constructing their own models of new situations.
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