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 -2
Taylor’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 and Irrotational vector fields. Vector identities - div(ɸA), curl (ɸA ),curl( grad ɸ), div(curl A).
Integral Calculus:
Reduction formulae - (m and 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. Simpleproblems 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