Kaitlin Hill
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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:
  • 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:
  1. One variable optimization - introduction to modeling, sensitivity analysis
  2. Multivariable optimization - unconstrained optimization, Lagrange multipliers
  3. Computational methods for optimization - Newton's Method, linear programming
  4. Introduction to dynamical models
  5. Analyzing dynamical models - phase portraits and cobweb plots
  6. Analyzing dynamical models - bifurcations, numerical approximations, and chaos
  7. Introduction to probability models
  8. Stochastic models - Markov chains, Markov processes, Monte Carlo simulation

Notes:
  1. Optimization
  2. Dynamical systems
  3. Probability models

Projects:
  • Guidelines
  • Presentation rubric
  • Project descriptions:
    • Optimization
    • Dynamical systems
    • Probability

Matlab code:
  • Optimization​:
    • PC profit (1D - sensitivity analysis, 2D - Lagrange multipliers)
    • Newton's Method 
  • Dynamical systems:
    • Whaling
    • Lorenz system (script, solver)
    • Backward Euler and Van der Pol's oscillator
  • Probability:
    • Monte Carlo rain
    • Ponderosa pines and linear regression
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  • Home
  • CV
  • Research
    • Student projects
  • Publications
  • Teaching
    • Geogebra
    • MST 251
    • MST 354/654
  • Outreach