BMATM101: Mathematics for ME Streams-I syllabus ME Stream Chemistry Group 2022 Scheme

Mathematics for ME Streams-I 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 1st Sem scheme and its subjects, do visit ME Stream Chemistry Group 1st Sem 2022 Scheme scheme. The detailed syllabus of mathematics for me streams-i 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:

Series Expansion and Multivariable Calculus (8 hours) Introduction to series expansion and partial differentiation in the field of Mechanical engineering applications. Taylor’s and Maclaurin’s series expansion for one variable (Statement only) – problems. Indeterminate forms – L’Hospital’s rule, Problems. Partial differentiation, total derivative – differentiation of composite functions. Jacobian and problems. Maxima and minima for a function of two variables-Problems. Self-study:Euler’s theorem and problems. Method of Lagrange’s undetermined multipliers with a single constraint.
Applications: Computation of stress and strain, Errors and approximations in manufacturing process, Estimating the critical points and extreme values, vector calculus. (RBT Levels: L1, L2 and L3)

Module 3:

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Module 4:

Ordinary Differential Equations of Higher Order(8 hours) Importance of higher-order ordinary differential equations in Mechanical engineering applications. Higher-order linear ODEs with constant coefficients – Inverse differential operator, method of variation of parameters, Cauchy’s and Legendre homogeneous differential equations – Problems.
Self-Study: Formulation and solution of oscillations of a spring. Finding the solution by the method of undetermined coefficients.
Applications: Applications to oscillations of a spring, Mechanical systems and Transmission lines. (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 2D plots for Cartesian and polar curves 2 Finding angle between polar curves, curvature and radius of curvature of a given curve 3 Finding partial derivatives and Jacobian 4 Applications to Maxima and Minima of two variables 5 Solution of first-order ordinary differential equation and plotting the solution curves 6 Solutions of Second-order ordinary differential equations with initial/ boundary conditions 7 Solution of differential equation of oscillations of spring with various load 8 Numerical solution of system of linear equations, test for consistency and graphical representation 9 Solution of system of linear equations using Gauss-Seidel iteration 10 Compute eigenvalues and eigenvectors and find the largest and smallest eigenvalue by Rayleigh power 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 calculus to solve problems related to polar curves.
2. Learn the notion of partial differentiation to compute rate of change of multivariate functions.
3. Analyze the solution of linear and non-linear ordinary differential equations.
4. make use of matrix theory for solving the system of linear equations and compute eigenvalues and eigenvectors.
5. 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, 3rd Ed., 2016.
3. N.P Bali and Manish Goyal: “A Textbook of Engineering Mathematics” Laxmi Publications, 10th Ed., 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” Cengage Publications, 7thEd., 2019.
8. David C Lay: “Linear Algebra and its Applications”, Pearson Publishers, 4th Ed., 2018.
9. Gareth Williams: “Linear Algebra with Applications”, Jones Bartlett Publishers Inc., 6th Ed., 2017.
10. Gilbert Strang: “Linear Algebra and its Applications”, Cengage Publications, 4th Ed., 2022.

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 1st Sem subject syllabuses for 2022 Scheme.

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