1. Project and presentation preparation Applied Math 115 Practice your presentation, stay on schedule Correct organization: a brief introduction and motivation, a description of the model and equations, an analysis of the results, and a conclusion slide We wont be able to run Matlab during presentations

2. Suggestions for slide style Verify that figures/ equations look good on projector (can try in classroom after hours) –use minimum font size of 20-24 point, –Use same font size especially in plots axes, titles and legend (FontSize Matlab command) –Avoid too thin plot lines (LineWidth Matlab command) –avoid too crowded slides All plots need to be clearly & completely labeled/ legend/ titled

3. Presentation style Use less slides (again, most of you ok on this) Know what to present: –Omit or shorten obvious results/ model description –include only interesting & surprising outcomes Include a short conclusion slide: list only the interesting formulation/ results Choose notations/ parameter names wisely (e.g. P and R rather than P and p)

4. How to build a model Model building is iterative! 1.Add new elements to an already-existing model one at a time 2.Ask yourself what is the main problem with the results (e.g. population dies) 3.Fix it and back to step 2 4.Add complications only if essential Examine qualitative features of your model first –consider extreme scenarios: how does model/ new term act when each parameter and/ or variable goes to infinity? to zero? negative values?

5. Model formulation For third and final projects: model a specific problem motivated by your interests or by something you ran into during your everyday experience, rather than model some abstract scenario. It is always a good idea to acquire or use data for motivating, tuning or testing the model, yet that is not required. Use various modeling tools that are available to you now 1.PDEs: e.g. wave eqn (see traffic) or diffusion eqn) 2.Markov process/ equation for PDF 3.Optimization principles 4.Cellular automata 5.ODEs; Delay differential equations

6. Model Analysis Scenarios vs parameter sensitivity perform a parameter sensitivity study with respect to all uncertain parameters. Plot/ contour results vs parameters when possible. Do one(!) scenario based on a creative idea for extending the model or applying it. Analyze carefully & in detail. Analysis is more than running ODE45 a few times and showing graphs Do a fixed point analysis; linear stability analysis (algebraic if possible; numerical if not), calculate statistics…

7. We are here Always attempt to do something unusual/ novel in model formulation/ analysis. Creativity Seek help when things go wrong or just to get feedback. Enjoy!