#### 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.