Week 1: Review of Linear Algebra and Several Variable Calculus.
Week 2: Picard-Lindeloff Theorem for Existence and Uniqueness of Solution, Continuous Dependence on Initial Data.
Week 3: Linear System: Fundamental Existence Theorem and Uniqueness theorem, Solution Subspace, Linear Independence and Wronskian.
Week 4: Matrix Exponential: Convergence, Properties. Matrix Exponential for Diagonlizable Matrix, Fundamental Matrix, Generalized Eigenvalues, Matrix Exponential for non-Diagonlizable Matrix.
Week 5: Phase Plane Analysis: Phase Portrait, Fixed point and Linearization, Reversible System.
Week 6: Comparison Principle, Maximum Principle and Oscillation theory.
Week 7: Periodic System, Floquet theory, Hill’s equation.
Week 8: Limit Cycle: Closed Orbit, Poincare Map, Poincare-Bendixson theorem.
Week 9: Sturm-Liouville Theory for second order equations. Properties of the eigenfunctions, Spectrum of Linear Operators.
Week 10: Linearization and Stable Manifold Theorem.
Week 11: Stability in Lyapunov Sense, Lyapunov Direct Method.
Week 12: Limit Cycle and Poincare Bendixson Theorem.
DOWNLOAD APP
FOLLOW US