Mathematics and Computational Methods for Aviation Engineering Applications

课程简介

/ Indicative Syllabus Differential equations - ordinary differential equations; partial differential equations; numerical methods Dynamical systems – fixed point; stability; discrete-event systems; finite- dimensional dynamical systems; infinite-dimensional dynamical system Convexity and convex functions – affine and convex sets; hyperplanes; convex functions and its properties; conjugate function, quasiconvex functions, log-concave and log-convex functions; convexity with respect to generalised inequalities Convex optimisation problem – convex optimisation; linear optimisation; quadratic optimisation problems; geometric programming; vector optimisation Duality – The Lagrange dual function; the Lagrange dual problem; geometric interpretation; saddle-point interpretation; optimality condition; perturbation and sensitivity analysis. -- 1 of 3 -- Statistical estimation – Parametric distribution estimation; non-parametric distribution estimation Uncertainty modelling - Stochastic Linear Programming, stochastic integer programmes, and approximation and sampling methods (e.g., Monte Carlo methods and sample average approximation; Robust optimisation, min- max/max-min optimisation, decomposition methods for two-stage robust optimisation problems. Algorithms for unconstrained minimisation – unconstrained minimisation problems; descent methods; gradient descent method; steepest descent method. Interior-point methods – Inequality constrained minimisation problems; logarithmic barrier function and central path; Primal-dual interior-point methods.

目标

1. To provide students with understanding and knowledge about the advanced mathematics in aviation engineering. 2. To develop students’ capability to conduct numerical analysis and design optimisation methods in solving mathematical modelling in the context of aviation and air transportation. 3. To provide students with in-depth and the state-of-the-art modelling methods in aviation domain.

先修要求

/ Co-requisite/ Exclusion Nil

Teaching Pattern

Methodology 1. The teaching and learning methods include lectures/tutorials, projects and homework assignments. 2. The lectures/tutorials aim at providing students with integrated knowledge of mathematics in air transportation, air mobility, safety and reliability modelling in aviation. 3. Homework assignments and quiz are used to allow students to reflect on and deepen their knowledge of a selected topic. Teaching/Learning Methodology Intended subject learning outcomes a b c d 1. Lectures/tutorials √ √ √ √ 2. Homework assignments √ √ √ √