Mathematical Methods in Systems Engineering – EE5412
Title : Mathematical Methods in Systems Engineering
Course No : EE5412
- 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 :
- Mathematical Analysis by Tom M. Apostol, Narosa Publishing House, 1993.
- Calculus on Manifolds by Michael Spivak, W. A. Benjamin, Inc., 1965.
- Finite-dimensional Vector Spaces by Paul R. Halmos, D Van Nostrand Company, Inc., 1942.