ME 681

 

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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



MY CONTACT

Email: bls at iitk.ac.in

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,

McGraw-Hill.

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.

Course FlyerME681_2010_files/ME681.pdfshapeimage_7_link_0

MATHEMATICS FOR ENGINEERS