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:

Introduction of series expansion and partial differentiation in Computer Science & Engineering applications. Taylor’s and Maclaurin’s series expansion for one variable (Statement only) – problems. Indeterminate forms – L’Hospital’s rule-Problems. Partial differentiation, total derivative – differentiation of composite functions. Jacobian and problems. Maxima and minima for a function of two variables. Problems.

Ordinary Differential Equations (ODEs) of First Order:

Introduction to first-order ordinary differential equations pertaining to the applications for Computer Science & Engineering. Linear and Bernoulli’s differential equations. Exact and reducible to exact differential equations – Integrating factors on 1/𝑁(𝜕𝑀/𝜕𝑦 −𝜕𝑁/𝜕𝑥) 𝑎𝑛𝑑 1/𝑀(𝜕𝑁/𝜕𝑥 −𝜕𝑀/𝜕𝑦). Orthogonal trajectories, L-R & C-R circuits. Problems.

Non-linear differential equations: Introduction to general and singular solutions, Solvable for p only, Clairaut’s equations,reducible to Clairaut’s equations. Problems.

Modular Arithmetic:

Introduction of modular arithmetic and its applications in Computer Science and Engineering. Introduction to Congruences, Linear Congruences, The Remainder theorem, Solving Polynomials, Linear Diophantine Equation, System of Linear Congruences, Euler’s Theorem, Wilson Theorem and Fermat’s little theorem. Applications of Congruences-RSA algorithm.

Linear Algebra:

Introduction of linear algebra related to Computer Science &Engineering. Elementary row transformationofa matrix, Rank of a matrix. Consistency and Solution of system of linear equations – Gauss-elimination method, Gauss-Jordan method and approximate solution by Gauss-Seidel method. Eigenvalues and Eigenvectors, Rayleigh’s power method to find the dominant Eigenvalue and Eigenvector.