ME 501

3-0-0-6

Masters

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**

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