Dynamical System Theory for Engineers: Large Scale Stability

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Large Scale Stability: Bounded Solutions

Covers large scale stability with a focus on bounded solutions and their implications.

Multivariable Integral Calculus

Covers multivariable integral calculus, including rectangular cuboids, subdivisions, Douboux sums, Fubini's Theorem, and integration over bounded sets.

Linear Algebra: Matrix Operations

Covers matrix operations and properties, including eigenvalues and eigenvectors.

Real Analysis: Sequences and Limits

Covers real sequences, induction, limits, and convergence in mathematical analysis.

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

High Order Methods: Space Discretisation

Covers high order methods for space discretisation in linear differential systems.

Dynamical Systems: Equilibrium Points and Stability

Covers dynamical systems, equilibrium points, stability analysis, and phase plots using examples like the pendulum system.

Hyperbolic Problems: Transport Equation

Covers hyperbolic problems and the transport equation, emphasizing the importance of weak solutions and the conservative transport equation.

Sobolev Spaces in Higher Dimensions

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Introduction to Quantum Chaos

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.