Title : Mathematical Methods in Systems Engineering
Course No :  EE5412
Credits :
Prerequisite :

Syllabus :

  • 1. Introduction to vector spaces: Systems of linear equations, Subspaces and bases, Orthogonal bases and orthogonal projections, Gram-Schmidt process, Linear models and least-squares problems, Eigenvalues and Eigenvectors, Symmetric and positive definite matrices.
  • 2. Functions on Euclidean space: Subsets of Euclidean space, Norms and inner product, Functions and continuity, Sequences and convergence.
  • 3. Calculus on Manifolds: Existence and uniqueness of solutions of ODEs, Derivatives, partial derivatives, Inverse and Implicit function theorem, Introduction to Manifolds, tangent bundle, vector fields, Lie brackets, distributions and Frobenius theorem

Text Books :

  1. Mathematical Analysis by Tom M. Apostol, Narosa Publishing House, 1993.
  1. Calculus on Manifolds by Michael Spivak, W. A. Benjamin, Inc., 1965.
  1. Finite-dimensional Vector Spaces by Paul R. Halmos, D Van Nostrand Company, Inc., 1942.

References :