Differential Calculus-1: Review of elementary differential calculus, Polar curves - angle between theradius vector and tangent, angle between two curves, pedal equation. Curvature and radius of curvature- Cartesian and polar forms; Centre and circle of curvature (All without proof-formulae only) -applications to evolutes and involutes. (RBT Levels:Ll & L2)
Differential Calculus-2: Taylor's and Maclaurin's series expansions for one variable (statements only), indeterminate forms - L'Hospital's rule. Partial differentiation; Total derivatives-differentiation of composite functions. Maxima and minima for a function of two variables; Method of Lagrange multipliers with one subsidiary condition.Applications of maxima and minima with illustrative examples.Jacobians-simple problems. (RBT Levels:Ll & L2)
Integral Calculus:Review of elementary integral calculus. Multiple integrals: Evaluation of double and triple integrals. Evaluation of double integrals- change of order of integration and changing into polar co ordinates.Applicationsto find areavolume and centre of gravity Beta and Gamma functions: Definitions, Relation between beta and gamma functions and simple problems. (RBT Levels:Ll & L2)
Ordinary differendal equations (ODE's) of first order: Exact and reducible to exact differential equations. Bernoulli's equation. Applications of ODE's-orthogonal trajectories,Newton's law of cooling and L R circuits.Nonlinear differential equations:Introduction to general andsingular solutions ; Solvable for p only; Clairaut's and reducible to Clairaut's equations only. (RBT Levels:Ll,Ll & L3)
Linear Algebra:Rank of a matrix-echelon form. Solution of system of linear equations-consistency. Gauss-elimination method, Gauss- Jordan method and Approximate solution by Gauss-Seidel method. Eigenvalues and eigenvectors Rayleigh'spower method. Diagonalization of a square matrix of order two. (RBT Levels :Lt, L2 & L3)