# ENGINEERING MATHEMATICS-I

Course Code:RAS103

Author:uLektz

Regulation:2016

Categories:Engineering Mathematics

Format : ePUB3 (DRM Protected)

Type :eBook

Rs.189 Rs.28 Rs.85% off

Description :ENGINEERING MATHEMATICS-I of RAS103 covers the latest syllabus prescribed by Dr. A.P.J. Abdul Kalam Technical University, Uttar Pradesh for regulation 2016. Author: uLektz, Published by uLektz Learning Solutions Private Limited.

Note : No printed book. Only ebook. Access eBook using uLektz apps for Android, iOS and Windows Desktop PC.

##### Topics
###### UNIT - I DIFFERENTIAL CALCULUS – I

1.1 Successive Differentiation, Leibnitz’s theorem

1.2 Limit, Continuity and Differentiability of functions of several variables

1.3 Partial derivatives

1.4 Euler’s theorem for homogeneous functions

1.5 Total derivatives, Change of variables

1.6 Curve tracing: Cartesian and Polar coordinates

###### UNIT - II DIFFERENTIAL CALCULUS - II

2.1 Taylor’s and Maclaurin’s Theorem, Expansion of function of several variables

2.2 Jacobian

2.3 Approximation of errors, Extrema of functions of several variables

2.4 Lagrange’s method of multipliers (Simple applications)

###### UNIT - III MATRIX ALGEBRA

3.1 Types of Matrices, Inverse of a matrix by elementary transformations, Rank of a matrix (Echelon & Normal form)

3.2 Linear dependence, Consistency of linear system of equations and their solution, Characteristic equation

3.3 Eigen values and Eigen vectors

3.4 Cayley-Hamilton Theorem, Diagonalization

3.5 Complex and Unitary Matrices and its properties

###### UNIT - IV MULTIPLE INTEGRALS

4.1 Double and triple integrals, Change of order of integration, Change of variables, Application of integration to lengths

4.2 Surface areas and Volumes – Cartesian and Polar coordinates, Beta and Gamma functions, Dirichlet’s integral and its applications

###### UNIT - V VECTOR CALCULUS

5.1 Point function, Gradient, Divergence, Curl of a vector and their physical interpretations, Vector identities, Tangent and Normal, Directional derivatives

5.2 Line, Surface and Volume integrals, Applications of Green’s theorem, Applications of Stokes theorem, Applications of Gauss divergence theorem