BMATS101 Mathematics for CSE Stream
syllabus Copy
Module - 1
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.
Self-study: Center and circle of curvature, evolutes and involutes.
Applications: Computer graphics, Image processing.
Module - 2
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.
Self-study: Euler’s theorem and problems. Method of Lagrange’s undetermined multipliers with
single constraint.
Applications: Series expansion in computer programming, Computing errors and approximations.
Module - 3
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 1𝑁(𝜕𝑀𝜕𝑦−𝜕𝑁𝜕𝑥)𝑎𝑛𝑑1𝑀(𝜕𝑁𝜕𝑥𝑀𝜕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.
Self-Study: Applications of ODEs, Solvable for x and y.
Applications of ordinary differential equations: Rate of Growth or Decay, Conduction of heat.
Module - 4
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.
Self-Study: Divisibility, GCD, Properties of Prime Numbers, Fundamental theorem of Arithmetic.
Applications: Cryptography, encoding and decoding, RSA applications in public key encryption.
Module - 5
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.
Self-Study: Solution of system of equations by Gauss-Jacobi iterative method. Inverse of a square matrix by Cayley- Hamilton theorem.
Applications: Boolean matrix, Network Analysis, Markov Analysis, Critical point of a network system. Optimum solution.