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VTU NOTES
Subject code
BMATE201
Semester
2nd

## Module - 1

Integral Calculus: Introduction to Integral Calculus in EC & EE Engineering

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 - 2

Vector Calculus: Introduction to Vector Calculus in EC & EE Engineering.

Scalar and vector fields. Gradient, directional derivative, curl and divergence – physical interpretation, solenoidal and irrotational vector fields. Problems.Curvilinear coordinates: Scale factors, base vectors, Cylindrical polar coordinates, Spherical polar coordinates, transformation between cartesian and curvilinear systems, orthogonality. Problems.

## Module - 3

Laplace Transform: Importance of Laplace Transform for EC & EE engineering applications.

Existence and Uniqueness of Laplace transform (LT), transform of elementary functions, region of convergence. Properties–Linearity, Scaling, t-shift property, s-domain shift, differentiation in the domain, division by t, differentiation and integration in the time domain. LT of special functions periodic functions (square wave, saw-tooth wave, triangular wave, full & half wave rectifier), Heaviside Unit step function, Unit impulse function.

Inverse Laplace Transforms: Definition, properties, evaluation using different methods, convolution theorem (without proof), problems, and applications to solve ordinary differential equations.

## Module - 4

Numerical Methods -1 Importance of numerical methods for discrete data in the field of EC & EE engineering.

Solution of algebraic and transcendental equations – Regula-Falsi and Newton-Raphson methods (only formulae). Problems. Finite differences, Interpolation using Newton’s forward and backward difference formulae, Newton’s divided difference formula and Lagrange’s interpolation formula (All formulae without proof). Problems.

Numerical integration: Trapezoidal, Simpson’s (1/3)rd and (3/8)th rules(without proof). Problems.

## Module - 5

Numerical Methods -2:Introduction to various numerical techniques for handling EC & EE Engineering applications.

Numerical Solution of Ordinary Differential Equations (ODE’s): Numerical solution of ordinary differential equations of first order and first degree – Taylor’s series method, Modified Euler’s method, Runge-Kutta method of fourth order and Milne’s predictor-corrector formula (No derivations of formulae). Problems.