MA3264 —– Mathematical Modeling （outline）

May 5, 2019

(Semester 1 2013/2014)

Detailed Course Outline

  • Introduction (lectures 1–2)
    • Aim and history lecture 1
    • A few simple examples
    • What is a model lecture 2
    • The process of mathematical modeling
    • Model classification (some additional materials on mixture)
  • Optimization models (lectures 3–4)
    • Introduction lecture 3
    • One variable optimization (some additional materials on population)
    • Multivariable optimization lecture 4
    • Computational methods for optimization (some materials on simplex method 1, 2)
  • Discrete models (lecture 5 )
    • Introuction lecture 5
    • World population growth — data snooping
    • Linear models
    • Logistic models (some additional materials)
    • Two theorems on stability
  • Continuous models (lectures 6–10)
  • Probability models (lecture 11)
    • Introduction lecture 11
    • Discrete probability models
    • Continuous probability models
  • Models for population (lecture 12)
    • Introduction lecture 12
    • Population model: Malthus model
    • Population growth: Logistic model
    • Harvesting
    • Population of interacting species: Lotka-Volterra systems (some additional materials)
    • Age-dependent population models
  • Models for wave and oscillations (lectures 13-14)
    • Introduction lecture 13
    • Variable gravitational acceleration
    • The pendulum without damping (some additional materials)
    • The pendulum with damping
    • Mechanical vibrations lecture 14
    • Methods for solving second order ODEs
    • Numerical methods
  • More applications of mathematical modeling (lectures 15 –16)
  • Review