According to Biju Patnaik University of Technology (BPUT) Orissa Syllabus] Primarily intended for the first year undergraduate students of all the branches of engineering, this textbook covers the complete syllabus prescribed in Biju Patnaik University of Technology (BPUT), Orrisa. Organized in two parts, Part I (For first semester) begins with the mathematical formulation of practical problems that leads to differential equations of the first order and their application to electrical circuits. It also includes different techniques for the solution of differential equations of second order, Legendre’s equation and Bessel’s equations. It concludes with a brief account of matrices, including some special matrices, and their applications to the solution of linear algebraic equations. Part II (For second semester) covers Laplace transformations and their use in getting solution to differential equations, Fourier series expansion of arbitrary functions, differential operators such as gradient, divergence and curl, and applications of line integrals and surface integrals in physical problems. KEY FEATURES 1 Illustrative examples (more than 300) to emphasize clearly the principles involved in the topics discussed. 2 Large number of exercises to reinforce the understanding of the subject 3 Two recent BPUT question papers at the end 4 270 short answer questions to grasp the fundamental concepts involved