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VTU NOTES
Subject code
BMATS101
Semester
1st

## Module - 1

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.

## Module - 2

Introduction to series expansion and partial differentiation in the field of Computer Science and 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.

## Module - 3

Introduction to first-order ordinary differential equations about the applications for Computer Science and Engineering.

Linear and Bernoulli’s differential equations. Exact and reducible to exact differential equations integrating factors. Orthogonal trajectories, Newton’s law of cooling. Nonlinear differential equations: Introduction to general and singular solutions, solvable for p only, Clairaut’s equations, reducible to Clairaut’s equations – Problems.

## Module - 4

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.

## Module - 5

Introduction of linear algebra related to Computer Science and Engineering applications.

Elementary row transformation matrix, Rank of a matrix. Consistency and solution of a 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.