##### BMATM201 Mathematics for Mechanical Engg Stream

#### Syllabus Copy

## Module - 1

**Integral Calculus**

Introduction to Integral Calculus in Mechanical 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 double integral.Problems. Beta and Gamma functions: Definitions, properties, relation between Beta and Gamma functions. Problems. Self-Study: Volume by triple integration, Center of gravity. Applications: Applications to mathematical quantities (Area, Surface area, Volume), Analysis of probabilistic models.

## Module - 2

**Vector Calculus**

Introduction to Vector Calculus in Mechanical Engineering applications. Vector Differentiation: Scalar and vector fields. Gradient, directional derivative, curl and divergence – physical interpretation, solenoidal and irrotational vector fields. Problems. Vector Integration: Line integrals, Surface integrals. Applications to work done by a force and flux. Statement of Greenâ€™s theorem and Stokeâ€™s theorem. Problems. Self-Study: Volume integral and Gauss divergence theorem. Applications: Heat and mass transfer, oil refinery problems, environmental engineering, velocity and acceleration of moving particles, analysis of streamlines.

## Module - 3

**Partial Differential Equations (PDEs)**

Importance of partial differential equations for Mechanical Engineering application. 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. Self-Study: Solution of the one-dimensional heat equation and wave equation by the method of separation of variables. Applications: Vibration of a rod/membrane.

## 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 Newtonâ€™s forward and backward difference formulae, Newtonâ€™s divided difference formula and Lagrangeâ€™s interpolation formula (All formulae without proof). Problems. Numerical integration: Trapezoidal, Simpson’s (1/3)rd and (3/8)th rules(without proof). Problems. Self-Study: Bisection method, Lagrangeâ€™s inverse Interpolation. Applications: Finding approximate solutions to solve mechanical engineering problems involving numerical data.

## Module - 5

**Numerical Methods -2**

Introduction to various numerical techniques for handling Mechanical Engineering applications. Numerical Solution of Ordinary Differential Equations (ODEs): Numerical solution of ordinary differential equations of first order and first degree – Taylorâ€™s series method, Modified Eulerâ€™s method, Runge-Kutta method of fourth order and Milneâ€™s predictorcorrector formula (No derivations of formulae). Problems. Self-Study: Adam-Bashforth method. Applications: Finding approximate solutions to solve mechanical engineering problems.