BMATM201: Mathematics for MES-II syllabus ME Stream Chemistry Group 2022 Scheme

Mathematics for MES-II detailed syllabus for ME Stream Chemistry Group 2022 Scheme curriculum has been taken from the VTUs official website and presented for the ME Stream Chemistry Group students. For course code, course name, duration, number of credits for a course and other scheme related information, do visit full semester subjects post given below.

For ME Stream Chemistry Group 2nd Sem scheme and its subjects, do visit ME Stream Chemistry Group 2nd Sem 2022 Scheme scheme. The detailed syllabus of mathematics for mes-ii is as follows.

Course Objectives:

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Teaching-Learning Process

Pedagogy (General Instructions): These are sample Strategies, which teachers can use to accelerate the attainment of the various course outcomes.

1. In addition to the traditional lecture method, different types of innovative teaching methods may be adopted so that the delivered lessons shall develop students’ theoretical and applied mathematical skills.
2. State the need for Mathematics with Engineering Studies and Provide real-life examples.
3. Support and guide the students for self-study.
4. You will also be responsible for assigning homework, grading assignments and quizzes, and documenting students’ progress.
5. Encourage the students to group learning to improve their creative and analytical skills.
6. Show short related video lectures in the following ways:
   • As an introduction to new topics (pre-lecture activity).
   • As a revision of topics (post-lecture activity).
   • As additional examples (post-lecture activity).
   • As an additional material of challenging topics (pre-and post-lecture activity).
   • As a model solution of some exercises (post-lecture activity).

Module 1:

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Module 2:

Vector Calculus(8 hours) 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. (RBT Levels: L1, L2 and L3)

Module 3:

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Module 4:

Numerical Methods -1(8 hours) 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. (RBT Levels: L1, L2 and L3)

Module 5:

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List of Laboratory Experiments

(2 hours/week per batch/ batch strength 15) 10 lab sessions + 1 repetition class + 1 Lab Assessment

1. Program to compute surface area, volume and centre of gravity
2. Evaluation of improper integrals
3. Finding gradient, divergent, curl and their geometrical interpretation
4. Verification of Green’s theorem
5. Solution of one-dimensional heat equation and wave equation
6. Solution of algebraic and transcendental equations by Regula-Falsi and Newton-Raphson method
7. Interpolation/Extrapolation using Newton’s forward and backward difference formula
8. Computation of area under the curve using Trapezoidal, Simpson’s (1/3)rd and (3/8)th rule
9. Solution of ODE of first order and first degree by Taylor’s series and Modified Euler’s method
10. Solution of ODE of first order and first degree by Runge-Kutta 4th order and Milne’s predictor-corrector method

Suggested Software’S: Mathematica/MatLab/Python/Scilab

Course Outcomes:

(Course Skill Set) At the end of the course the student will be able to:

1. Apply the knowledge of multiple integrals to compute area and volume.
2. Understand the applications of vector calculus refer to solenoidal, irrotational vectors, line integral and surface integral.
3. Demonstrate partial differential equations and their solutions for physical interpretations.
4. Apply the knowledge of numerical methods in solving physical and engineering phenomena.
5. Get familiarize with modern mathematical tools namely Mathematica/MatLab/Python/Scilab

Text Books:

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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, 3rdEd., 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

Activity-Based Learning

(Suggested Activities in Class)/Practical-Based Learning

• Quizzes
• Assignments
• Seminar

For detailed syllabus of all other subjects of ME Stream Chemistry Group, 2022 Scheme curriculum do visit ME Stream Chemistry Group 2nd Sem subject syllabuses for 2022 Scheme.

For all ME Stream Chemistry Group results, visit VTU ME Stream Chemistry Group all semester results direct link.