Mathematics-I for Mechanical Engineering stream (BMATM101)

Mathematics-I for Mechanical Engineering stream

Course Code: BMATM101 
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

Calculus :Introduction to polar coordinates and curvature relating toMechanical engineering.Polar coordinates, Polar curves, angle between the radius vector and the tangent, angle between two curves. Pedal equations. Curvature and Radius of curvature - Cartesian, Parametric, Polar and Pedal forms. Problems.

Self-study: Center and circle of curvature, evolutes and involutes.

Applications: Applied Mechanics, Strength of Materials, Elasticity.

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Module-2 

Series Expansion and Multivariable Calculus: 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.

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Module-3

Ordinary Differential Equations (ODEs) of First Order:Introduction to first-order ordinary differential equations pertaining to the applications for Mechanical engineering.Linear and Bernoulli’s differential equations. Exact and reducible to exact differential equationsIntegrating factors on 1/𝑁(𝜕𝑀/𝜕𝑦 −𝜕𝑁/𝜕𝑥) 𝑎𝑛𝑑 1/𝑀(𝜕𝑁/𝜕𝑥 −𝜕𝑀/𝜕𝑦). Orthogonal trajectories, Newton’s law of cooling.

Nonlinear differential equations: Introduction to general and singular solutions,solvable for p only,Clairaut’s equations, reducible to Clairaut’s equations - Problems.

Self-Study: Applications of ODEs: L-R circuits. Solvable for x and y.

Applications: Rate of Growth or Decay, Conduction of heat.

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Module-4

Ordinary Differential Equations of Higher Order: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.

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Module-5

Linear Algebra :Introduction of linear algebra related to Mechanical engineering applications.Elementary row transformationofa matrix, Rank of a matrix. Consistency and solution of a system of linear equations - Gauss-elimination method, Gauss-Jordan method and approximate solution by Gauss-Seidel method. Eigenvalues and Eigenvectors, Rayleigh’s power method to find the dominant Eigenvalue and Eigenvector.

Self-Study: Solution of a system of equations by Gauss-Jacobi iterative method. Inverse of a square matrix by Cayley- Hamilton theorem.

Applications of Linear Algebra: Network Analysis, Balancing equations.

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Important Links:

1. Click here to download Star Making Questions

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,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 – HillBook Co., New York, 6th Ed., 2017.

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

6. H. K. Dass and Er. Rajnish Verma: “Higher Engineering Mathematics” S. ChandPublication, 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., 6thEd., 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