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M2 Notes For Mechanical Engineering Stream | BMATM201 VTU Notes

Subject code

Module - 1

Integral Calculus: Introduction to Integral Calculus in Mechanical 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 Mechanical 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

Partial Differential Equations: Importance of partial differential equations for Mechanical Engineering applications Formation of PDE’s by elimination of arbitrary constants and functions. Solution of nonhomogeneous PDE by direct integration. Homogeneous PDEs involving derivatives with respect to one independent variable only. Solution of Lagrange’s linear PDE.Derivation of one-dimensional heat equation and wave equation.

Module - 4

Numerical Methods -1 Importance of numerical methods for discrete data in the field of Mechanical 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 Mechanical 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.