Core Course Structure and Syllabus

Dept. of Mechanical Engineering

M Tech (Common to All the Streams: MD, MSE, FTE, CM, AP)

SEMESTER-I

SEMESTER-II: NIL

SEMESTER-III

SEMESTER-IV

ME501 Advanced Engineering Mathematics

Linear Algebra: Introduction to vector space, linear independence, solution of simultaneous linear systems, uniqueness and existence, Algebraic eigenvalue problem, similarity transformation, Introduction of linear transformation, Gram-Schmidt orthonormalization

Multivariate Calculus: Differential geometry, parametric representation, Frenet-Serret frame, directional derivative, Grad, Div and Curl, introduction to tensor algebra, equation of line, plane, surface, Line integral, path independence, Divergence theorem, Stokes’ theorem, Green’s theorem in a plane

Ordinary Differential Equation: First order equations, integrating factor, orthogonal trajectories, Existence and uniqueness, Second order equations with constant coefficients, The Cauchy-Euler equation, Method of undetermined coefficients, variation of parameters,matrix method, Sturm-Liouville problems, trigonometric Fourier series

Integral Transform: Fourier series, Fourier integral, Fourier and Laplace transform, standard rules, Dirac-delta and Heaviside function, convolution, solution of ODEs

Partial differential equation: Linear equations, superposition, separation of variable, Second order wave equation, Unsteady heat conduction equation, Laplace equation

Probability and Statistics: Probability Distribution, Bayes Theorem, Parameter Estimation, Testing of Hypothesis, Goodness of Fit

Texts/References

1. Erwin Kreyszig, Advanced Engineering Mathematics, Wiley, 10th edition, 2011.
2. R. K. Jain and S.R.K Iyengar, Advanced Engineering Mathematics, Narosa Publishing House, 5th edition, 2016.
3. Gilbert Strang, Linear Algebra, Cengage learning, 4th edition, 2006.
4. Shepley L. Ross, Differential Equations, Wiley, 4th edition, 1989.
5. David Poole, Linear Algebra A Modern Introduction, Thomson, 4th edition, 2019.
6. Thomas and Finney, Calculus and Analytic Geometry, Narosa Publishing House, 2010.
7. Georgi P. Tolstov, Fourier Series, Dover Publications, Inc, 2012.
8. Ronald N. Bracewell, The Fourier Transform and its Applications, McGrawHill, 2004.
9. Michael Greenberg, Advanced Engineering Mathematics, 2nd edition, Pearson, 1998.

ME502 Engineering Computing Laboratory

Review of C/C++; Programming assignments for numerical methods like Euler Method for 1st-order ODE, Gaussian Quadrature using C/C++; Review of Matlab and programming assignments for numerical differential and integration; Plotting functions: plot, bar, log-log, plotyy, polar, semilogx, semilogy, stairs, stem; Handling axis, title, legends, x and y label; Subplot; Three dimensional line plots, Surface mesh, Contour plots; Gauss Elimination Method

References

1. Y. P. Kanetkar, Let Us C, BPB, 16th edition, 2018.

2. B. Gottfried and J. Chhabra, Programming with C, Tata Mcgraw Hill, 4th Edition, 2018.

3. RudraPratap, Getting Started with Matlab, Oxford University Press, 7th edition, 2016.

4. Stormy Attaway, Matlab: A Practical Introduction to Programming and Problem Solving, Butterworth-Heinemann Elsevier, 5th edition, 2018.

ME503Technical Writing

Modes of technical communication: Reports, Technical papers, book chapters, Manuals, Posters. Structure of a technical document. Copyright issues in technical writing: existing laws, open sources, permission procedure. How to write a good technical paper?,Proper procedure in citing already published works,Referencing styles. Common mistakes of English in scientific documents. Proper way of writing and citing equations. Proper use of figures and tables. Writing a good review paper. Writing of abstract, synopsis, cover letters, responses, discussion and keywords

References

1. Alred, G. J., Brusaw, C. T., &Oliu, W. E. Handbook of technical writing. 9th edition. Bedford/St. Martin, 2009
2. Parija, S.C. & Kate, V. (Ed.), Writing and publishing a scientific research paper, Springer/Singapore, 2017

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