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Suitable of the first-semester course in undergraduate engineering and technology, the book presents the necessary mathematical concepts that engineers will be expected to know, namely matrices, three-dimensional analytical geometry, differential calculus, functions of several variables, and multiple integrals. The book uses an informal and user-friendly approach to provide students with a solid mathematical base for their subsequent years of study. Essential topics are covered clearly and concisely through detailed examples. Extensive exercises help students understand and build the confidence to apply mathematics to the solution of engineering problems in higher learning. Each chapter begins with a brief outline of essential theory, definitions and procedures. However, they are kept to the minimum, because problem-solving is extensively used to train students at this level. It is expected that students gain real understanding through seeing problems solved and then solving similar problems themselves. Learning by example is the method of this book. The book assumes in the reader little previous knowledge of topics dealt herewith. This also makes it appealing to a wide variety of readers with different mathematical backgrounds. About The Author C. Mohan is presently the Head, Department of Mathematics at Vel Tech Multi Tech Dr. Rangarajan Dr. Sakuntahala Engineering College, Chennai, and has been serving the college for more than a decade. He has been handling engineering mathematics including his other favorite subjects like probability and queuing theory, random processes, and discrete mathematics to undergraduate and postgraduate students of engineering. His field of interest in research is statistical processes. As a story writer and a poet, he has also published an anthology of poems, which he titled Deodate. Table of Contents Matrices What is a Matrix Linear Combination of Vectors Rank of a Matrix Characteristic Equation, Eigen Values and Eigen Vectors of Real Matrix Cayley-Hamilton (C-H) Theorem Applications of C-H Theorem Diagonalisation of Matrix Properties of Similarity Transformation Diagonalisation of a Square Matrix Computation of Power of a Square Matrix Working Rule to Diagonalise a n x n Matrix by Similarity Transformation Properties of Orthogonal Matrix Proofs Working Rule for Orthogonal Reduction of a n x n Symmetric Matrix Quadratic Form Linear Transformation of a Quadratic Form Index and Signature of the Quadratic form Two-Dimensional Analytical Geometry Beginning Three-dimensional Geometry Important Results Sphere Plane Section of a Sphere Orthogonal Spheres Equation of a Cone Right Circular Cone Equation of a Cylinder Right Circular Cylinder Differential Calculus Beginning Differential Calculus Definition of Curvature Formula for Radius of Curvature in Cartesian Coordinates Formula for Radius of Curvature in Parametric Coordinates Formula for Radius of Curvature in Polar Coordinates Centre of Curvature Evolutes and Envelopes Problems on Envelopes Functions of Several Variables Partial Derivatives Higher Orders of Partial Derivatives Rules of Partial Derivatives Eulers Theorem on Homogeneous Functions Total Differentiation Jacobians Properties of Jacobians Taylors Theorem for a Function of Two Variables Maxima and Minima for Function of Two Variables Multiple Integrals Double Integral Change of Order of Integration Change of Variables between Cartesian and Polar Coordinates Areas as a Double Integration (Cartesian Coordinates) Area as a Double Integral (Polar Coordinates) Triple Integration in Cartesian Coordinates Volume as a Triple Integral Model Question Paper