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This is the third volume of a series of four volumes covering all stages of development of the Calculus, from the last year at school to degree standard. The books are written for students of science and engineering as well as for specialist mathematicians, and are designed to bridge the gap between the works used in schools and more advanced studies, with their emphasis on rigour. The volume treats of the theory of functions of more than one variable. Partial differentiation and multiple integrals are explained in detail. Each section has examples; at the end of each chapter there are problems from school-leaving and open scholarship examinations. This volume is most suitable for the first or second year at British universities.