Abdulhakeem Yusuf
Summary: The following topics were covered during the period of stay
1. GENERAL FIRST-ORDER EQUATION i. General Introduction of ODE ii. iii. Equivalence of an Initial Value Problem Existence & Uniqueness Theorem
2. LINEAR SYSTEM OF FIRST-ORDER EQUATION i. Characrerisation of the Fundamental Matrix ii. iii. iv. v. vi. vii. Properties of Linear Systems Adjoint systems Homogeneous and non-homogeneous system Autonomous Differential equations LINEAR SYSTEMS WITH PERIODIC COEFFICIENTS THEORY OF OSCILLATION
3. STABILITY THEORY i. Lyapunov Theory ii. iii. iv. v. vi. vii. viii. SECOND METHOD OF LYAPUNOV Eularian derivatives BOUNDEDNESS OF SOLUTIONS Lyapunov stability in switched and hybrid system Extension and generalisation Connections to optimal control General Applications
4. STURM-LIOUVILLE PROBLEMS i. Regular Sturm-Liouville Problem ii. iii. iv. Periodic Sturm-Liouville problem Self Adjoint operators Quantum systems v. vi. vii. Special functions as solutions Weight function and inner product Numerical methos.
5. Machine learning (ML) and ODEs i. Neural ordinary differential Equations ii. iii. iv. v. vi. vii. Optimization and ODEs Dynamical systems perspectives in ML Stochastics Differential Equations ODES in Representations learning Time series modeling with ODEs Physics informed neural networks
Control theory and reinforcement learning.