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# Book Details # Mathematics - I (Vector Differential Calculus, Vector Integral Calculus)

 Course Code : ULZ0222 Author : uLektz University : General for All University Regulation : 2017 Categories : Electrical & Electronics Format : ePUB3 (DRM Protected) Type : eBook

FREE

Description :Mathematics - I (Vector Differential Calculus, Vector Integral Calculus) of ULZ0222 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 INFINITE SERIES

1.1 Infinite series: Tests for convergence of series (Comparison, Ratio, Root, Integral, Raabe's, logarithmic)

1.2 Alternating series, Absolute convergence, Conditional convergence

###### UNIT - II DIFFERENTIAL & INTEGRAL CALCULUS OF SINGLE VARIABLE

2.1 Differential & Integral Calculus of single variable: Taylor's & MaClaurin's expansion, Radius of curvature, Tracing of some standard curves

2.2 Applications of definite integral to Area, Arc length, Surface area and volume (in cartesian, parametric and polar co-ordinates)

###### UNIT - III CALCULUS OF SEVERAL VARIABLES

3.1 Calculus of several variables: Partial differentiation, Euler's theorem

3.2 Total differential, Taylor's theorem

3.3 Maxima-Minima, Lagrange's method of multipliers

3.4 Application in estimation of error and approximation

###### UNIT - IV MULTIPLE INTEGRALS

4.1 Multiple Integrals: Double integral (Cartesian and polar co-ordinates), Change of order of integration

4.2 Triple integrals (Cartesian, cylindrical and spherical co-ordinates)

4.3 Beta and Gamma functions, Applications of multiple integration in area and volume

###### UNIT - V VECTOR DIFFERENTIAL CALCULUS

5.1 Vector Differential Calculus: Continuity and differentiability of vector functions, Scalar and Vector point function

5.2 Gradient, Directional Derivative, Divergence, Curl and their applications

###### UNIT - VI VECTOR INTEGRAL CALCULUS

6.1 Vector Integral Calculus: Line integral, Surface integral and Volume integral

6.2 Applications to work done by the force, Applications of Green's, Stoke's and Gauss divergence theorems