Thursday 26 December 2019

Engineering Mathematics-I


Welcome to Mathematics World

Dr. Sonendra Gupta


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Course File July-Dec. 2022

Module-1
Rolle’s theorem, Mean Value theorems, Expansion of functions by Maclaurin’s and Taylor’s for one variable; Taylor’s theorem for the function of two variables, Partial Differentiation, Maxima & Minima (two and three variables), Method of Lagrange's Multipliers. 

Topics

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Rolle’s theorem

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Mean Value theorems

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Maclaurin’s Series or Theorem

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Taylor Series or Theorem in one variable

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Partial Differentiation

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Euler’s theorem for Homogeneous function

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Composite Function and Total Differential Coefficients

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Jacobians and their properties with Functionally dependence conditions

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Maxima & Minima of two variables and Lagrange's sufficient condition

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Maxima & Minima of three variables

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Method of Lagrange's Multipliers

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Taylor Theorem for two variables function 

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Tangent and Normal

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Radius of Curvature

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Circle of Curvature

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Curve Tracing

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Approximation of Errors

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Module-2

Definite Integral as a limit of a sum and Its application in summation of series; Beta and Gamma functions and their properties; Applications of definite integrals to evaluate surface areas and volumes of revolutions. Multiple Integral, Change the order of the integration, Applications of multiple integral for calculating area and volumes of the curves.


 





















































 

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