2. Conceptual model

3. Examples: Heat flow on a wire Air flow around a plane’s wing Response to medication

4. Conceptual model Examples: Heat flow on a wire Air flow around a plane’s wing Response to medication Mathematical Model Equilibrium Equations Heuristics Simplifications Continuous Discrete Experiments, Statistics, Prediction

5. Conceptual model Examples: Heat flow on a wire Air flow around a plane’s wing Response to medication Equilibrium Equations Heuristics Simplifications Continuous Discrete Experiments, Statistics, Predictions Mathematical Model linear nonlinearODE other

6. Conceptual model Examples: Heat flow on a wire Air flow around a plane’s wing Response to medication Simplifications Continuous discrete Experiments, statistics, prediction Mathematical Model linear nonlinearODE other Ax=b Find A -1 x=A -1 b ?????

7. Conceptual model Examples: Heat flow on a wire Air flow around a plane’s wing Response to medication Simplifications Continuous discrete Experiments, statistics, prediction Mathematical Model linear nonlinearODE other Ax=b Find A -1 x=A -1 b ????? f(x) =0 Newton’s Method ????????

8. Conceptual model Examples: Heat flow on a wire Air flow around a plane’s wing Response to medication Simplifications Continuous discrete Experiments, statistics, prediction Mathematical Model linear nonlinearODE other Ax=b Find A -1 x=A -1 b ????? f(x) =0 Newton’s Method ???????? Euler’s Method ????????

9. Conceptual model Examples: Heat flow on a wire Air flow around a plane’s wing Response to medication Simplifications Continuous discrete Experiments, statistics, prediction linear nonlinearODE other Ax=b Find A -1 x=A -1 b ????? f(x) =0 Newton’s Method ???????? Euler’s Method ???????? Optimal control, PDEs, DAEs,… Mathematical Model

10. Conceptual model Examples: Heat flow on a wire Air flow around a plane’s wing Response to medication Simplifications Continuous discrete Experiments, statistics, prediction Mathematical Model linear nonlinearODE other Ax=b Find A -1 x=A -1 b ????? f(x) =0 Newton’s Method ???????? Euler’s Method ???????? Optimal control PDEs, DAEs,…

11. Conceptual model Examples: Heat flow on a wire Air flow around a plane’s wing Response to medication Simplifications Continuous discrete Experiments, statistics, prediction Mathematical Model linear nonlinearODE other Ax=b Find A -1 x=A -1 b ????? f(x) =0 Newton’s Method ???????? Euler’s Method ???????? Optimal control, PDEs, DAEs,… Computed Solution

12. Computed Solution Algorithms Programming Convergence Error Analysis Stability What can go wrong? Which algorithm works best on which type of problem?