25872: Mathematical Methods in Engineering
Course Name: Mathematical Methods in Engineering
Course Number: 25872
Prerequisite(s): 22016 (General Math 2)
Co-requisite(s): -
Units: 2
Level: Undergraduate
Last Revision: Summer 2020

Description
The purpose of this course is to familiarize with linear algebra and its applications in electrical engineering.
 
Syllabus:
  • Vector and Vector Space: Field, vector space, linear dependence, linear independence, spanning a space, linear combination of vectors, change of basis in a space
  • Linear operators in a Vector Space: One to one operator, onto operator, domain space, null space, rank of matrix, matrix null, inner product, norm function, different types of norms, orthogonal vectors, orthogonal bases and Gram-Schmidt procedure, similarity transformation, similar matrices, linear operators, norm operators, system of linear equations, adjunct operators, unitary and orthogonal matrices and their properties
  • Eigenvectors and Eigenvalues: Eigenvectors, eigenvalues, diagonalization by similarity transformation, Jordan form, characteristics polynomial, minimum polynomials, positive definite, negative definite, positive semi definite and negative semi definite operators
  • Matrix Decomposition and its Applications:  Singular value decomposition, condition number, SVD, least square problem, SVD and pseudo inverse, QR, LU and Cholesky decompositions

References:
  • Gilbert Strang, Linear Algebra and Its Applications, Fourth edition
  • Carl D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, 2000
  • E. D. Nering, Linear Algebra and Matrix Theory
  • N. Loehr, Advanced Linear Algebra, Taylor and Francis (CRC) press, 2014


 
Last Update: 2024-06-09