ME5010 Mathematical Methods for Engineers

Syllabus

Vectors, operations and operators, identities; Cartesian tensors: definition, notation, transformation matrix, orthogonal properties, order of a tensor, operations, contraction, quotient rule, vector identities and theorems in tensor form;First and second order ODEs, linear ODEs with constant coefficients; Laplace transforms; Second order linear homogenous differential equations and their solutions; Sturm-Liouville problem; Orthogonal functions; Gram-Schmidt procedure; PDEs: classification, analytical solution of linear PDEs, Fourier series, and Fourier transforms transformation of PDEs between different coordinate systems; Linear algebraic equations: matrix form, matrix operations, determinants, Cramer’s rule, inverse, singularity, inconsistent equations, Gauss elimination, Gauss-Seidel, LU decomposition, finding inverses, echelon form, general solution for under-determined systems, generalized inverses, least-squares solution for over-determined systems, eigen-values and eigenvectors, orthogonalization, singular value decomposition; Introduction to integral equations, classifications, solution methodology; Function, functional and an introduction to integral of calculus, Euler-Lagrange equation.

Evaluation

  1. Quiz 1: 15 points
  2. Quiz 2: 15 points
  3. Quiz 3: 15 points
  4. Class tests: 15 points
  5. Assignments: 20 points
  6. Project: 20 points

Books and references

  1. Erwin Kreyszig, "Advanced Engineering Mathematics," Wiley-India.
  2. Michael Greenberg, "Advanced Engineering Mathematics," Pearson.
Plain Academic