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Precize Engineering Mathematics-I

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Differential Calculus, Integral Calculus, Partial Derivatives and its applications, Multiple Integrals, Vector Calculus and its applications

Description

Differential Calculus : Curve tracing: Tracing of Standard Cartesian; Parametric and Polar curves; Curvature of Cartesian, Parametric and Polar curves.
Integral Calculus : Rectification of standard curves; Areas bounded by standard curves; Volumes and surfaces of revolution of curves; Applications of integral calculus to find centre of gravity and moment of inertia.
Partial Derivatives : Function of two or more variables; Partial differentiation; Homogeneous functions and Euler’s theorem; Composite functions; Total derivative; Derivative of an implicit function; Change of variable; Jacobians.
Applications of Partial Differentiation : Tangent and normal to a surface; Taylor’s and Maclaurin’s series for a function of two variables; Errors and approximations; Maxima and minima of function of several variables; Lagrange’s method of undetermined multipliers.
Multiple Integrals : A brief introduction of cylinder, cone and standard conicoids. Double and triple integral and their evaluation, change of order of integration, change of variable, Application of double and triple integration to find areas and volumes.
Vector Calculus : Scalar and vector fields, differentiation of vectors, velocity and acceleration. Vector differential operators: Del, Gradient, Divergence and Curl, their physical interpretations. Formulae involving Del applied to point functions and their products. Line, surface and volume integrals.
Application of Vector Calculus : Flux, Solenoidal and Irrotational vectors. Gauss Divergence theorem. Green’s theorem in plane, Stoke’s theorem (without proofs) and their applications.