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Synopsis The present publication is written to meet the requirements of undergraduate and postgraduate students of several Indian Universities. The topics included in the text are according to the new pattern of University Grants Commission. The subject matter both as regards the arrangement of chapters as well the contents of each chapter has been so graded, proceeding from simple to more difficult topics, that a student may follow the course with great ease and interest. The publication covers Limits, Continuity and Differentiability; Functions of Several Variables, Partial Differentiation; Envelopes and Evolutes; Maxima, Minima, Lagarange’s Multipliers; Intermediate Forms; Beta and Gamma Functions, Multiple Integrals; Sequences and Convergence of a Series. It is believed that the publication will be of great value not only to the students but also to the teachers.