Numerical Data Fitting in Dynamical Systems

Preface

1: Introduction

2: Mathematical Foundations
1. Optimality Criteria
2. Sequential Quadratic Programming Methods
3. Least Squares Methods
4. Numerical Solution of Ordinary Differential Equations
5. Numerical Solution of Differential Algebraic Equations
6. Numerical Solution of One-Dimensional Partial Differential Equations
7. Laplace Transforms
8. Automatic Differentiation
9. Statistical Interpretation of Results

3: Data Fitting Models
1. Explicit Model Functions
2. Laplace Transforms
3. Steady State Equations
4.Ordinary Differential Equations
5. Partial Differential Equations
6. Optimal Control Problems

4: Numerical Experiments
1. Test Environment
2. Numerical Pitfalls
3. Testing the Validity of Models
4. Performance Evaluation

5: Case Studies
1. Linear Pharmacokinetics
2. Receptor-Ligand Binder Study
3. Robot Design
4. Multibody System of a Truck
5. Binary Distillation Column
6. Acetylene Reactor
7. Transdermal Application of Drugs
8. Groundwater Flow
9. Cooling a Hot Strip Mill
10. Drying Maltodextrin in a Convection Oven
11. Fluid Dynamics of Hydro Systems

Appendix A: Software Installation
1. Hardware and Software Requirements
2. System Setup
3. Packing List

Appendix B: Test Examples
1. Explicit Model Functions
2. Laplace Transforms
3. Steady State Equations
4. Ordinary Differential Equations
5. Differential Algebraic Equations
6. Partial Differential Equations
7. Partial Differential Algebraic Equations

Appendix C: The PCOMP Language

Appendix D: Generation of Fortran Code
1. Model Equations
2. Execution of Generated Code

References

Index