Engineering Mathematics-I

Unit I

Matrices: Elementary transformations, Inverse of a matrix, Rank of matrix, Solution of system of linear equations, Characteristic equation, Cayley-Hamilton theorem and its application, Linear dependence and independence of vectors, Eigen values and Eigen vectors, Complex matrices — Hermitian, Skew-Hermitian and Unitary matrices, Applications to engineering problems.

Unit II

Differential Calculus-I: Successive differentiation (nth order derivatives), Leibnitz theorem, Curve tracing, Partial derivatives, Euler's theorem for homogeneous functions, Total derivative, Change of variables.

Unit III

Differential Calculus-II: Expansion of functions by Taylor's and Maclaurin's theorems for functions of one and two variables, Maxima and minima of functions of several variables, Lagrange's method of multipliers, Jacobians, Approximation of errors.

Unit IV

Multiple Integration: Double integral, Triple integral, Change of order of integration, Change of variables, Beta and Gamma functions and their properties, Dirichlet's integral and its applications to area and volume, Liouville's extensions of Dirichlet's integral.

Unit V

Vector Calculus: Vector differentiation — Gradient, Curl and Divergence and their physical interpretation, Directional derivatives. Vector integration — Line integral, Surface integral, Volume integral, Gauss's Divergence theorem, Green's theorem and Stoke's theorem (without proof) and their applications.