Differential Calculus-1: Review of elementary differential calculus, Polar curves - angle between the radius 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. (Chapter - 1)
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. (Chapter - 2)
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. Applications to find area volume and centre of gravity. Beta and Gamma functions : Definitions, Relation between beta and gamma functions and simple problems. (Chapter - 3)
Ordinary differential 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 LR circuits. Nonlinear differential equations: Introduction to general and singular solutions ; Solvable for p only; Clairaut's and reducible to Clairaut's equations only. (Chapter - 4)
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. Eigen values and eigen vectors-Rayleigh's power method. Diagonalization of a square matrix of order two. (Chapter - 5)