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VTU NOTES
Subject code
BMATE101
Semester
1st

## Module - 1

Introduction to polar coordinates and curvature relating to EC & EE 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 EC & EE 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 EE & EC 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 to Integral Calculus in EC & EE Engineering applications.
Multiple Integrals: Evaluation of double and triple integrals, evaluation of double integrals by change of order of integration, changing into polar coordinates. Applications to find Area and Volume by a double integral.Problems.
Beta and Gamma functions: Definitions, properties, relation between Beta and Gamma functions.
Problems.

## Module - 5

Introduction of linear algebra related to EC & EE 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.