Spring 2021
Prof. P Balamurugan
Author: Pranjal Gupta
Pre-requisite courses: None
Pre-requisite skills: None
Course Content: Aim of course: To familiarize students with models and theory of linear dynamical systems. Major Contents: ● Review of linear algebra: Systems of linear equations, Gaussian elimination, inverse of matrix and transpose. ● Review of Fields, Vector Spaces and Linear Transformations. Review of concepts of linear independence, basis, and fundamental subspaces associated with matrices and linear transformations, rank-nullity theorem, duality. ● Eigenvalues and eigenvectors of matrices and linear transformations, characteristic polynomials, Cayley-Hamilton Theorem, diagonalization. ● Concepts of dynamic systems and linear time invariant systems. Representation of linear dynamical systems using ordinary differential equations (ODEs) and linearization of non-linear dynamical systems. ● Solution methods of first order, second order and higher order ODEs and systems of ODEs. ● Solution methods of difference equations, existence and uniqueness theorems, Laplace and z-transforms. ● Transfer functions, concepts of stability, controllability and observability, canonical forms-Diagonal and Jordan forms. ● Applications, examples and case-studies involving simple linear systems. —
Coure Evaluation:
- Quizzes (2) = 15%
- Assignments (4) = 15%
- Lecture Scribing = 10%
- Midsem = 20%
- Endsem = 40%
Motivation behind taking the course: I wanted to do a course on linear dynamical systems because of their numerous applications in fields like control theory and finance. The course involved a comprehensive treatment of underlying mathematical concepts rather than directly jumping into the applications.
Information about Projects/Assignments: In this particular offering, there were 3 theory assignments and 1 in-class programming assignment. The programming assignment was straightforward, wherein we had to play around with numerical integration techniques in Python. The theory assignments were not lengthy and can be easily tackled if one is comfortable with MA106 and MA108 concepts.
Overall Course Difficulty: 3/5
Attendance Policy: None (may be due to online sem)
Professor’s Teaching Style: Prof. Balamurugan is known for going deep into the mathematics and this course was no exception. One can say that the course was MA106, MA108 and MA207 clubbed into one, although the professor had also planned to discuss some case studies on linear systems but wasn’t able to follow through because of time shortage. The course started from the very scratch expecting only basic knowledge of real analysis, and involved an extremely rigorous treatment of linear algebra and differential equation concepts (more rigorous than the aforementioned courses). Majority of the course was a theorem-proof conversation, except some classes in between which involved a programming aspect. The prof actively took interest in teaching the concepts and catered to all doubts asked in the class. The slides and scribes are well prepared and were really helpful during the exams.
Who can take this course?: Anyone who is ready to deal with hardcore mathematics