TB Engineering Mathematics -I

SYLLABUS- ENGINEERING MATHEMATICS-I,
Unit –1: Differential Calculus-I
Successive Differentiation, Leibnitz’s theorem, Limit, Continuity and Differentiability of
functions of several variables, Partial derivatives, Euler’s theorem for homogeneous functions,
Total derivatives, Change of variables, Curve tracing: Cartesian and Polar coordinates.
Unit–2: Differential Calculus-II
Taylor's and Maclaurin's Theorems, Expansion of function of several variables, Jacobian,
Approximation of errors, Extrema of functions of several variables, Lagrange’s method of
multipliers ( Simple applications).
Unit–3: Matrix Algebra
Types of Matrices, Inverse of a matrix by elementary transformations, Rank of a matrix (Echelon
& Normal form), Linear dependence, Consistency of linear system of equations and their solution,
Characteristic equation, Eigen values and Eigen vectors, Cayley-Hamilton Theorem, Diago-nalization,
Complex and Unitary Matrices and its properties.
Unit–4: Multiple Integrals
Double and triple integrals, Change of order of integration, Change of variables, Application of
integration to lengths, Surface areas and Volumes, Cartesian and Polar coordinates. Beta and
Gamma functions, Dirichlet’s integral and applications.
Unit–5: Vector Calculus
Point function, Gradient, Divergence and Curl of a vector and their physical interpretations,
Vector identities, Tangent and Normal, Directional derivatives. Line, Surface and Volume
integrals, Applications of Green’s, Stoke ’s and Gauss divergence theorems (without proof).