ME 681




Course details

Course No: ME 681

Instructor: Basant Lal Sharma

Department: Mechanical Engineering

Units: (L-T-P-D-U) 3-0-0-0-4

Schedule: LEC: MWF 11:00-12:00 L6


Email: bls at

Phone: 6173

Main BookS

Books for General Reading

1. Kreyszig, E., Advanced Engineering Mathematics1 , John Wiley & Sons.

2. Courant, R., Hilbert, D., Methods of Mathematical Physics, Vol. 1, 2. John Wiley & Sons.

3. Dasgupta, B., Applied Mathematical Methods. Dorling Kindersley.

4. Simmons, G. F., Differential equations, with applications and historical notes. McGraw-Hill.

5. Jeffrey, A., Advanced Engineering Mathematics. Harcourt/Academic Press.

Books for Details

1. Halmos, P. R., Finite-dimensional vector spaces. Springer-Verlag.

2. Golub, G. H., Loan, C. F. V., Matrix computations, Johns Hopkins University Press.

3. Gel’fand, I. M., Lectures on Linear algebra. Interscience Publishers.

4. Bowen, R. M., Wang, C.-C., Introduction to vectors and tensors: I, II. Springer-Verlag.

5. Birkhoff, G. and Gian-Carlo Rota, Ordinary differential equations. Ginn.

6. Bender, C. M. and Orszag, S. A., Advanced mathematical methods for scientists and engineers,


7. Petrovskii, I. G., Lectures on Partial Differential Equations, Interscience Publishers.

8. Bracewell, R., The Fourier Transform and Its Applications. McGraw Hill.

9. Gelfand, I. M., Fomin, S. V., Calculus of variations. Prentice-Hall.

Useful links

Wiki, Menger, Mathworld, Derivative


Course Summary

  1. Properties of Vector Algebra, Vector space, subspace, basis, null and

  2. range space, invertibility and matrix representation; Cartesian Tensor

  3. notation and vector analysis; Matrices and Matrix algebra, Echelon

  4. form, orthogonalization; Eigen values and eigenvectors of a linear

  5. operator; First and second order ODEs, Linear Differential equations

  6. with constant coefficients and equi dimensional equations; Second

  7. order linear homogenous differential equations and their                    

  8. solutions; Methods of Taylor and Frobenius, Laplace and Fourier

  9. transforms, Fourier series; Legendre and Bessel functions; Sturm

  10. Louville Problem; classification of PDEs; Analytical solution of linear

  11. PDEs.

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