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# Book Details # ENGINEERING MATHEMATICS

 Course Code : ULZ0232 Author : uLektz University : General for All University Regulation : 2017 Categories : Engineering Mathematics Format : ePUB3 (DRM Protected) Type : eBook

FREE

Description :ENGINEERING MATHEMATICS of ULZ0232 covers the latest syllabus prescribed by General for All University for regulation 2017. 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