I059785_award_certificate

Feb 27, 20150 likes117 views

This certificate acknowledges that Kundan Kumar successfully published a research paper titled "A Parabola Symmetrical to y=x Line" in January 2015. The paper was reviewed and published by the International Journal of Scientific & Engineering Research.

CERTIFICATE of PUBLICATION
THIS ACKNOWLEDGES THAT
KUNDAN KUMAR
HAS SUCCESSFULLY PUBLISHED RESEARCH PAPER
|
Members | IJSER Review Board Panel | www.ijser.org
WWW.IJSER.ORG
JANUARY
2015
A Parabola Symmetrical to y=x
Line

This document provides information about coordinate geometry and various geometric concepts that can be represented using a Cartesian coordinate system. It includes: 1) An introduction to coordinate geometry and Cartesian coordinate systems. 2) Equations and properties of lines, including finding slopes, angles between lines, parallel/perpendicular lines, and intersections. 3) Equations and properties of circles, including center-radius form, diameter form, tangents, and normals. 4) Worked examples and exercises on finding equations of lines and circles given information about points, slopes, radii, etc.

engineeringmathematics-iv_unit-vKundan Kumar

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engineeringmathematics-iv_unit-ivKundan Kumar

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engineeringmathematics-iv_unit-iiiKundan Kumar

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The document provides an overview of complex integration, including: 1) Definitions of complex line integrals and applications in engineering. 2) Cauchy's integral theorem and formula, used to evaluate line integrals. 3) Taylor and Laurent series expansions of analytic functions. 4) The residue theorem, used to evaluate integrals along closed paths via residues of singularities enclosed by the path.

engineeringmathematics-iv_unit-iKundan Kumar

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B.Tech-II_Unit-VKundan Kumar

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This document provides an overview of topics in vector integration, including line integrals, surface integrals, and volume integrals. It includes examples of calculating each type of integral. The key theorems covered are Green's theorem, Stokes' theorem, and Gauss's theorem of divergence. Green's theorem relates a line integral around a closed curve to a double integral over the enclosed region. Stokes' theorem relates a line integral around a closed curve to a surface integral over the enclosed surface. Gauss's theorem relates the surface integral of the normal component of a vector field over a closed surface to the volume integral of the divergence of the vector field over the enclosed volume.

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This document provides an overview of vector differentiation, including gradient, divergence, curl, and related concepts. It begins with definitions of scalar and vector point functions. It then defines the vector differential operator Del and explores using it to calculate the gradient of a scalar function, directional derivatives, and normal derivatives. The document also covers divergence and curl, providing their definitions and formulas. Examples are given for calculating gradient, divergence, curl, and directional derivatives. The document concludes with exercises and references for further reading.

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