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

  ---

• Optimization models (lectures 3--4)
  • Introduction lecture 3
  • One variable optimization
  • Multivariable optimization lecture 4
  • Computational methods for optimization

  ---

• Discrete models (lecture 5 )
  • Introuction lecture 5
  • World population growth -- data snooping
  • Linear models
  • Logistic models
  • Two theorems on stability

  ---

• Continuous models (lectures 6--10)
  • Introduction lecture 6
  • One variable models lecture 7
  • Nondimensionlization lecture 8
  • Methods for solving first order ODEs
  • Equilibrium and stability lecture 9
  • Bifurcation
  • Numerical methods
  • Multivariable models lecture 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
  • Age-dependent population models

  ---

• Models for wave and oscillations (lectures 13-14)

  • Introduction lecture 13
  • Variable gravitational acceleration
  • The pendulum without damping
  • The pendulum with damping
  • Mechanical vibrations lecture 14
  • Methods for solving second order ODEs
  • Numerical methods

  ---

• More applications of mathematical modeling (lectures 15 --16)

  • In chemistry lecture 15
  • In biology lecture 16
  • In engineering
  • In political sciences
  • In business
  • In social sciences

  ---

• Review