Calculus: Introduction to polar coordinates and curvature relating to Computer Science and Engineering. Polar coordinates, Polar curves, angle between the radius vector and the tangent, angle between two curves. Pedal equations. Curvature and Radius of curvature – Cartesian, Parametric, Polar and Pedal forms. Problems.

Series Expansion and Multivariable Calculus: Taylor’s and Maclaurin’s series expansion for one variable (Statement only) – problems. Indeterminate forms – L'Hospital’s rule. Partial differentiation, total derivative, Jacobian, maxima and minima for functions of two variables.

Ordinary Differential Equations (ODEs): Introduction to first-order ODEs in CSE. Linear and Bernoulli equations. Exact and reducible to exact differential equations. Orthogonal trajectories, L-R & C-R circuits.
Non-linear Differential Equations: Clairaut’s equations, general and singular solutions.

Modular Arithmetic: Introduction and applications in CSE. Congruences, Linear Congruences, Remainder theorem, Euler’s theorem, Wilson Theorem, Fermat’s Little Theorem. RSA algorithm.

Linear Algebra: Elementary row transformation, Rank of matrix, Gauss elimination, Gauss-Jordan, Gauss-Seidel method, Eigenvalues, Eigenvectors, Rayleigh power method.