Surface integral Problem 1 Vector Calculus Engineering Mathematics

#engineeringmathematics1 #engineeringmathsm2#vectorcalculus UNIT II VECTOR CALCULUS
Gradient and directional derivative - Divergence and curl - Vector identities - Irrotational and Solenoidal vector fields - Line integral over a plane curve - Surface integral - Area of a curved surface - Volume integral - Green’s, Gauss divergence and Stoke’s theorems - Verification and application in evaluating line, surface and volume integrals. UNIT - I MATRICES
Eigenvalues and Eigenvectors of a real matrix - Characteristic equation - Properties of Eigenvalues and Eigenvectors - Cayley - Hamilton theorem - Diagonalization of matrices by orthogonal
transformation - Reduction of a quadratic form to canonical form by orthogonal transformation - Nature of quadratic forms - Applications: Stretching of an elastic membrane.
UNIT - II DIFFERENTIAL CALCULUS MA3151 Syllabus Matrix and Calculus
Representation of functions - Limit of a function - Continuity - Derivatives - Differentiation rules (sum, product, quotient, chain rules) - Implicit differentiation - Logarithmic differentiation - Applications :
Maxima and Minima of functions of one variable.
UNIT - III FUNCTIONS OF SEVERAL VARIABLES MA3151 Syllabus Matrix and Calculus
Partial differentiation - Homogeneous functions and Euler’s theorem - Total derivative - Change of variables - Jacobians - Partial differentiation of implicit functions - Taylor’s series for functions of
two variables - Applications : Maxima and minima of functions of two variables and Lagrange’s method of undetermined multipliers.
UNIT - IV INTEGRAL CALCULUS MA3151 Syllabus Matrix and Calculus
Definite and Indefinite integrals - Substitution rule - Techniques of Integration: Integration by parts, Trigonometric integrals, Trigonometric substitutions, Integration of rational functions by partial
fraction, Integration of irrational functions - Improper integrals - Applications : Hydrostatic force and pressure, moments and centres of mass.
UNIT - V MULTIPLE INTEGRALS
Double integrals - Change of order of integration - Double integrals in polar coordinates - Area enclosed by plane curves - Triple integrals - Volume of solids - Change of variables in double and triple integrals - Applications : Moments and centres of mass, moment of inertia.

[@janhvinarayan1633]

thank u so much sir

[@akhileshv.r6271]

sir where is the introduction video ..?

[@TanishkaMudgal.]

good

[@keerthus921]

Sir .. please can you upload a different for this three integral (line, surface, volume).. please please please sir

[@yogisiva7033]

Sir can you please upload Laplace transform

[@saravanajothigandhirajan6570]

Sir pls upload green's theorem,gauss divergence and stoke's theorem related sums sir

[@maharajothi]

Na avunga ta katan but time illa nu sollitanga

[@user-kq2cx9xu7e]

What is k vector sir ????

[@jackshanvenujan3115]

HOW did you take dS as dx.dy plane? why not dydz or dxdz ?

[@mohamedanas8006]

I also have the same doubt

[@Funwithme4577]

In first octant x,y included so wo take dxdy ...and unit vec or remaining z is k then we take dot product of k with n..

[@Funwithme4577]

@@mohamedanas8006 check comment

[@mohamedanas8006]

​@@Funwithme4577 thanks bro

[@Maddy_cutz_pro]

But for limit of x for he doesn't put zero for y and simply taken but for limit of y he put zero to x ???

[@nilanisha5206]

For n cap why we are using k ?

[@prabasree9859]

Same doubt

[@Funwithme4577]

Because it's lying in first octant ..then reaming unit vec of Z is k so we take dot product of n cap with k

[@janhvinarayan1633]

because in xy plane perpendicular outwards vector is k cap