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In this book, vector differential calculus is considered, which extends the basic concepts of (ordinary) differential calculus, such as, continuity and differentiability to vector functions in a simple and natural way. The new concepts of gradient, divergence and curl are introduced. Line, surface and volume integrals which occur frequently in connection with physical and engineering problems are defined. Three important vector integral theorems, Gauss divergence theorem, Greens theorem in plane and Stokes theorem are discussed. The idea of Laplace transform to develop some useful results has been introduced also demonstrated how the Laplace transform technique is used in solving a class of problems in differential equations. Fourier series is an infinite series representation of a periodic function in terms of sines and cosines of an angle and its multiples. How Fourier series is useful to solve ordinary and partial differential equations particularly with periodic functions appearing as non-homogeneous terms has been discussed. This book comprises previous question papers problems at appropriate places and also previous GATE questions at the end of each chapter for the benefit of the students.
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