# Calculus & Linear Algebra for BE VTU Course 18 OBE & CBCS (I - COMMON - 18MAT11) (Decode)

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MODULE-1 Differential Calculus-1: Re'i7iew of eleωentary differential calculus, Polar cur'i7es anqle between the radius 'i7ector and tanqent. anqle between two cur'i7es, pedal equation. Cur'i7ature and radius of cur'i7ature- Cartesian and polar forms; Centre and circle of cur'i7ature (ΑΙΙ without proof-foπηulae only) -applications to evolutes and in'i7olιιtes. (Chapter - 1) MODULE-11 Differential Calculus-2 : Taylor's and Maclaurin's series exρansions for one varia{)]e (stateπ1ents only), indeterminate forms L'Hospital's rule. Partial differentiation; Total derivatives-differentiation of cornposite functions. Maxima and miniπ1a for a function of two variables; Method of Laqranqe rnultipliers with one subsidiary condition. Applications of maxima and minima with illustrative exaπφles. Jacobians-simple problems. (Chapter - 2) MODULE-111 Inte􀀫ral Calculus : Review of elementary inteQΠJI cθlculus. MuJtiple inteQωls : EvalωJtion of cJouble ancJ triρle inteQrθls. EvθlωHion of cfoub]e intelί!ΠJ!s- chBnlί!e of orcJer of intelί!ωtion Hncf chanlί!iΠ!ί! into μolar co-ordinates. Aρρlications to find areίl volume and centre of lί!Γavity. Beta ίlnd Gamma functions : Definitions, Relation 1Jetween {Jeta and qamma functions and simμle μro1J!ems. (Chapter - 3) MODULE-IV Ordinary differential equations (ODE's) of first order : Exact and redιιcible to exact differential equations. Bernoιιlli's equation. ApplicHtions of ODE's-orthoqonal trίljectorίes, Newton's !ίlw of coolinq ίlnd LR circuits. Nonlinear differential equatίons: Introductίon to qenerίll and sinqιιlar sο!ιιtίοηs : SolvHble for ρ only; Clairίlut's and reducible to Clίliraut's eqιιatίons only. (Chapter - 4) MODULE-V Linear Algebra : Rank of a matrix-echelon form. So!ution of system of linear equations -consistency. Gauss-elimination method. Gauss - Jordan method and Approximate solution by Gauss-Seidel method. EiSJen values and eiSJen vectors-RayleiSJh's power method. DiaSJonalizatίon of a square matrίx of order two. (Chapter - 5)

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