MA3264 ----- Mathematical Modeling
(Semester 2 2011/2012)
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)
- 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
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Review