Mathematical modeling
Prof. Dr. Gerrit Lohmann
Gerrit.Lohmann@awi.de
Tel: 0471-4831-1758 / 1750
24. April- 24. July 2006: Monday 11-13, Room S3032
This lecture is about concepts of mathematical modeling, and about the kinds of techniques that are useful for modeling. It covers exact and approximate analytical techniques, numerical methods, and model inference based on observations. A focus will be on applications across a broad range of Earth System Modeling and Analysis. It discusses the general components of the modeling process and highlights the potential of modeling in practice. A part of the lecture provides case studies, with examples, exercises, and projects.
Literature:
- The nature of mathematical modeling, N. Gershenfeld, Cambridge University Press, Cambridge, 2003, 344 pp. link for applications
- Applied Mathematical Modeling: A Multidisciplinary Approach; von D. R. Shier, K. T. Wallenius, pp. 443, CRC PrILlc, ISBN 1584880481
- Imboden, D. und Koch, S. (2003).Systemanalyse - Einführung in die mathematische Modellierung natürlicher Systeme Springer-Verlag, Berlin Heidelberg.
- Script for part of the course Mathematical modeling, G. Lohmann, 2006
Preliminary Schedule:
1) 24.4. Introduction, Aim of modelling, Linear differential equations, Laplace transformation
2) 8.5. Types of Models, Examples: Exponential & Logistic equations, Newton's cooling, Numerical schemes
3) 15.5. Practical applications with R: Ordinary differential equations
Here are the examples:
- lesson_14May_commands.R
- EulerForward_1storder.R
- EulerForward_1storder_generalized.R
- EulerForward_2storder_generalized.R
- EulerForward_1storder_LogisticE.R
- EulerForward_2storder_LogisticE.R
4) 22.5. ODE continued
5) 29.5. Examples, Stability theory, Bifurcations
6) 12.6. Partial differential equations with applications in Earth System Science, Diffusion and advection
- Bifurcation ppt
- VL6Minutes.doc
- Diff_adv_solv ppt
- Stability doc
- numerics 1 pdf
- numerics 2 pdf (not used)
- numerics 3 pdf (not used)
7) 19.6. Practical units: Partial differential equations
- numerics pdf (from the last lesson)
- work sheet
- Diffusion_explicit.R
- AdVDiffusion_leapfrog.R
8) 26.6. Master and Fokker-Planck Equation, Bownian Motion
9) 3.7. continued: Master and Fokker-Planck Equation, Bownian Motion
10) 10.7. Practical units: Applications for stochastic systems
- work sheet
- brown_oneparticle.R
- 2D_Diffusion.R
- brown_multipleparticle.R
- brown_multipleparticle_potential.R
11) 17.7. Linear time series analysis, Statistical Modelling, Significance testing
- VL11 ppt1 (5,3 MB), ppt2 (7,3 MB), ppt3 (8,6 MB)
- some background material pdf1
- some background material pdf2
12) 24.7. Practical units: Spectrum, wavelet, EOF, SSA
for fun:
Practical unit (left over, not during the lesson 7): Difference equations, Logistic map and Chaos, Bifurcations
How to get the Credit Points / Schein?
Projects with R, Practical work within the lessons
Help of Thomas Laepple (Thomas.Laepple@awi.de)
Oral exam: List of catchwords: repeat lessons 1)-12) !!!
Day: 4 August 2006; 8:30, Room S3032