Differential Calculus -1: determination of nth order derivatives ofStandard functions - Problems. Leibnitz’s theorem (without proof)- problems.Polar Curves - angle between the radius vector and tangent,angle between two curves, Pedal equation of polar curves.Derivative of arc length - Cartesian, Parametric and Polar forms(without proof) - problems. Curvature and Radius ofCurvature – Cartesian, Parametric, Polar and Pedal forms(without proof) -problems
Differential Calculus -2Taylor’s and Maclaurin’s theorems for function of onevariable(statement only)- problems. Evaluation of Indeterminateforms.Partial derivatives – Definition and simple problems, Euler’stheorem(without proof) – problems, total derivatives, partialdifferentiation of composite functions-problems. Definition andevaluation of Jacobians
Vector Calculus:Derivative of vector valued functions, Velocity, Acceleration andrelated problems, Scalar and Vector point functions. Definition ofGradient, Divergence and Curl-problems. Solenoidal andIrrotational vector fields. Vector identities - div(ɸA), curl (ɸA ),curl( grad ɸ), div(curl A).
Integral Calculus:Reduction formulae - I Sinnx dx, I Cosn x dx , I Sinmx Cosnx dx, (mand n are positive integers), evaluation of these integrals withstandard limits (0 to π/2) and problems.Differential Equations ;Solution of first order and first degree differential equations– Exact, reducible to exact and Bernoulli’s differential equations.Orthogonal trajectories in Cartesian and polar form. Simple problems on Newton\'s law of cooling.
Linear Algebra Rank of a matrix by elementary transformations, solutionof system of linear equations - Gauss-elimination method, Gauss–Jordan method and Gauss-Seidel methodEigen values and Eigen vectors, Rayleigh’s power method to findthe largest Eigen value and the corresponding Eigen vector.Linear transformation, diagonalisation of a square matrix .Reduction of Quadratic form to Canonical form