Mathematics-II for Mechanical Engineering stream (BMATM201)

Mathematics-II for Mechanical Engineering stream

Course Code: BMATM201
CIE Marks:50
Course Type(Theory/Practical/Integrated )
Integrated SEE Marks:50
Total Marks 100
Teaching Hours/Week (L:T:P: S) 2:2:2:0 Exam Hours 03
Total Hours of Pedagogy 40 hours Theory + 10 to 12 Lab slots
Credits:04

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.

Click here to download Module-1

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 Green’s theorem and Stoke’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.

Click here to download Module-2

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.

Click here to download Module-3(To be updated soon)

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.

Self-Study: Bisection method, Lagrange’s inverse Interpolation.

Applications: Finding approximate solutions to solve mechanical engineering problems involving numerical data.

Click here to download Module-4

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 - Taylor’s series method, Modified Euler’s method, Runge-Kutta method of fourth order and Milne’s predictorcorrector formula (No derivations of formulae). Problems.

Self-Study: Adam-Bashforth method.

Applications: Finding approximate solutions to solve mechanical engineering problems.

Click here to download Module-5

Important Links:

1. Click here to download Star Making Questions(With solutions)

2. Click here to download MQP with Solution-1

3. Click here to download MQP with Solution-2

4. Click here to download Module1 Question Bank

5. Click here to download Module2 Question Bank

6. Click here to download Module3 Question Bank (To be Updated Soon)

7. Click here to download Module4 Question Bank

8. Click here to download Module5 Question Bank

Suggested Learning Resources:

Text Books

1. B. S. Grewal: “Higher Engineering Mathematics”, Khanna Publishers, 44thEd., 2021.

2. E. Kreyszig: “Advanced Engineering Mathematics”, John Wiley & Sons, 10thEd., 2018.Reference Books

1. V. Ramana: “Higher Engineering Mathematics” McGraw-Hill Education, 11th Ed., 2017

2. Srimanta Pal & Subodh C.Bhunia: “Engineering Mathematics” Oxford University Press,3 rdEd., 2016.

3. N.P Bali and Manish Goyal: “A Textbook of Engineering Mathematics” Laxmi Publications, 10thEd., 2022.

4. C. Ray Wylie, Louis C. Barrett: “Advanced Engineering Mathematics” McGraw – Hill Book Co., New York, 6th Ed., 2017.

5. Gupta C.B, Sing S.R and Mukesh Kumar: “Engineering Mathematic for Semester I and II”, Mc-Graw Hill Education(India) Pvt. Ltd 2015.

6. H.K. Dass and Er. Rajnish Verma: “Higher Engineering Mathematics” S.Chand Publication, 3rd Ed.,2014.

7. James Stewart: “Calculus” CengagePublications, 7thEd., 2019.

Web links and Video Lectures (e-Resources):

 http://nptel.ac.in/courses.php?disciplineID=111

 http://www.class-central.com/subject/math(MOOCs)

 http://academicearth.org/

 VTU e-Shikshana Program

 VTU EDUSAT Program