## Mathematical Modeling

Math 4428

Spring 2018

Objectives:

During this course, students will develop their skill in analyzing optimization, dynamical, and probabilistic models. These skills include:

Handouts:

Syllabus

Schedule

Homework:

Notes:

Projects:

Matlab code:

During this course, students will develop their skill in analyzing optimization, dynamical, and probabilistic models. These skills include:

- Translating a real-world problem into a mathematical model
- Determining a solution or possible solutions to the mathematical model
- Relating mathematical findings back to the real-world application
- Assessing the quality of the model and determining ways to improve the model
- Working with a team to analyze, interpret, and communicate the solution to a problem using optimization, dynamical systems, or probabilistic techniques

Handouts:

Syllabus

Schedule

Homework:

- One variable optimization - introduction to modeling, sensitivity analysis
- Multivariable optimization - unconstrained optimization, Lagrange multipliers
- Computational methods for optimization - Newton's Method, linear programming
- Introduction to dynamical models
- Analyzing dynamical models - phase portraits and cobweb plots
- Analyzing dynamical models - bifurcations, numerical approximations, and chaos
- Introduction to probability models
- Stochastic models - Markov chains, Markov processes, Monte Carlo simulation

Notes:

Projects:

- Guidelines
- Presentation rubric
- Project descriptions:

Matlab code:

- Optimization:
- Dynamical systems:
- Whaling
- Lorenz system (script, solver)
- Backward Euler and Van der Pol's oscillator

- Probability: