IIMT University, UP, Computer Engineering Semester 1, Engineering Mathematics-I Syllabus

ETAS-111 Engineering Mathematics-I

UNIT-1 Matrix 
Matrix introduction, Special Type of Matrices, Elementary Transformations, Rank of Matrix (Echelon form, Normal form), Linear system of equations (Homogenous and Non- Homogenous), consistency and inconsistency of linear systems, Characteristic roots and vectors (Eigen values and Eigen vectors), Cayley-Hamilton Theorem, Applications of matrices.

UNIT- 2 Differential Calculus-I 
Successive Differentiation, nth order differential coefficients, Leibnitz’s theorem, Partial Differentiation, Partial derivatives of 1st order and higher orders, Homogenous Functions, Euler’s theorem on Homogenous Functions, Relations between Second order derivatives of homogenous functions, Deductions from Euler’s theorem, Composite Function, Asymptotes, Curve Tracing (Cartesian and Polar Coordinates)

UNIT- 3 Differential Calculus-II 
Expansion of functions of several variables, Taylor’s and Maclaurin’s Theorems for two variables, Jacobian, Properties of Jacobian, Results on Jacobian, Jacobian of Implicit functions, Functional Dependence, Maxima and minima of functions of two variables, Lagrange’s Methods of Multipliers.

UNIT- 4 Multiple Integrals 
Multiple Integrals (double and triple), Change of order of integration, change of variables, Volumes and Surface areas by multiple integrals (Cartesian and Polar coordinates), Beta and Gamma functions, Dirichlet’s integral and extension of Dirichlet’s integral.

UNIT- 5 Vector Calculus 
Vector Point Function, Gradient, Divergence, Curl and their physical interpretation, Vector identities, Directional Derivatives, Line, Surface and Volume Integrals, Green’s, Stocke’s and Gauss divergence theorem (statement and application)

Text Books:
1. Grewal B.S., Higher Engineering Mathematics, Khanna Publishers.
2. Prasad C., Engineering Mathematics for Engineers, Prasad Mudralaya.
3. Dass H.K., Engineering Mathematics Vol-I, S. Chand.

Reference Books:
1. Kreyszig E., Advanced Engineering Mathematics, Wiley Eastern.
2. Piskunov N, Differential & Integral Calculus, Moscow Peace Publishers
3. Narayan Shanti, A Text book of Matrices, S. Chand