Santhanam Krishnan

parseval's identity reduction formula integration by parts properties of definite integral nature of canonical form. rank signature index order conversion from quadratic to canonical form quadratic form and canonical form denationalization of a matrix by orthogonal transf orthogonal transformation of symmetric matrix pairwise orthogonal orthogonal matrix properties of eigen values cayley- hamilton theorem & applications eigen vector eigen value some types of matrices convergent and divergent of integration improper integral irrational function integration rational partial fraction substitution method of integration problem based on properties definite and indefinite integrals basic concepts of integration differentiation of implicit functions. constraint maxima & minima ( lagrangian multiplier maxima & minima (extreme values) stationary points taylor's expansion jacobian total differentiation partial differentiation convex upward & convex downward - first & second d local maxima & minima absolute maxima & minima decreasing functions increasing turning points critical points/ stationary points differential calculus maxima minima cosine transforms properties of fourier transform and fourier sine convolution of two functions cosine transform inverse fourier sine fourier sine inverse fourier transform fourier transform fourier integral formula complex form of fourier series half range cosine & sine series root mean square 2pi) (0 pi) (-pi l) (-l 2l) fourier series in the intervals (0 change of interval euler's formula for fourier coefficients even & odd functions fourier series dirichlet's condition periodic function type iv when f(x y) = e^(ax+by)g(x y) type iii when f(x y) = x^r y^s type ii when f(x y) = sin(ax+b) or cos(ax+b) type i when f(x y) = e^(ax+by) f(z^mp z^m q)=0 f(x^mp y^n q)=0 z=px+qy+f(pq)-clariaut form f(x y z p q)=0 f(y p q)=0 f(x p q)=0 f(z p q)=0 f(p q)=0 method of lagrangian multipliers method of grouping lagrangian linear equation solution to pde pp +qq = r laplace transformation of periodic and anti-period change of scale solving differential equation final value and initial value laplace table convolution integration differentiation first and second shifting theorem linearity properties of laplace transform inverse transform laplace transform evaluation various types of complex integrals. cauchy's residue theorem singularities and zeros laurent's series maclaurin’s series taylor's series cauchy's integral formula for derivatives cauchy's integral formula cauchy's integral theorem simultaneous first order linear differential equat method of variation of parameters legendre's equation euler cauchy's equation linear functions with constant variables bernoulli's theorem definite integrals integration of irrational algebraic functions integration of rational algebraic functions methods of integration bilinear transformation construction of analytic function harmonic function analytic function gauss divergence theorem stoke's theorem green's theorem volume integral surface integral lineintegral directional derivative scalarpotential conservative workdone irrotational solenoidal curl div grad latin square two way calssification one way classification various method to solve ode by numerical methods numerical differentiation & integration interpolation solution of equation - numerical method testing of hypothesis