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Course number and title: EEM208C Topics in Functional Analysis for Applied Mathematics and Engineering
Credits: 4
Instructor(s)-in-charge: Not offered in 2011-12
Course type: Lecture
Required or Elective: A Signals and Systems course.
Course Schedule:
Lecture: 4 hrs/week
Outside Study: 8 hrs/week
Course Assessment:
Homework: Several assignments
Grading Policy: Typically, 30% homework, 30% midterm, 40% final.
Course Prerequisites: EEM208B
Catalog Description: Semigroups of linear operators over Hilbert spaces; generator and resolvent, generation theorems, Laplace inversion formula. Dissipative operators and contraction semigroups. Analytic semigroups and spectral representation. Semigroups with compact resolvents. Parabolic and hyperbolic systems. Controllability and stabilizability. Spectral theory of different operators, PDEs, generalized functions.  
Textbook and any related course material:
A.V. Balakrishnan, Applied Functional Analysis, 2nd Edition, Springer .
Course Website
Topics covered in the course:
Closed Linear Operators.
Definitions and General Properties of Semigroups of Operators.
Generation of Semigroups, Resolvent, Laplace Inversion Formula.
Semigroups of Hilbert Spaces Operators, Contraction Semigroups and Dissipative Operators. Elementary Examples.
Compact Semigroups.
Semigroups with Compact Resolvents. Analytic Semigroups.
Cauchy Problems. Parabolic and Hyperbolic systems. Applications.
Controllability and Observability, State space reduction.
Stability and Stabilizability.
Introduction to Boundary Input Problems.
Will this course involve computer assignments? NO Will this course have TA(s) when it is offered? NO

:: Last modified: February 2013 by J. Lin ::

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