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Textbook
Q1 Topics
1. Modelling concepts
1.1. Model classification
1.2. Model decisions
1.3. Uncertainty Classification
1.4. Verification, Calibration and Validation
1.5. Goodness of Fit
2. Numerical Modelling
2.1. Revision of Concepts
2.2. The First Derivative
2.3. Finite Difference Method
2.4. Taylor Series Expansion
Exercises on Taylor expansion
2.5. Numerical Integration
2.6. Initial Value Problem for ODE: single-step methods
2.7. Implicit methods for nonlinear ODE
2.8. Multi-step and multi-stage methods
2.9. Boundary-value Problems: second-order ODE
3. Univariate Continuous Distributions
3.1. PDF and CDF
3.2. Empirical Distributions
3.3. Non-Gaussian distributions
3.4. Parametric Distributions
Uniform distribution
Gaussian distribution
Lognormal distribution
Gumbel distribution
Exponential distribution
Beta distribution
Summary of parametric distributions
3.5. Location, Shape and Scale: Consistent Parameterization
3.6. Fitting a Distribution
Method of moments
Maximum Likelihood Estimation
Goodness of Fit
4. Multivariate Distributions
4.1. Discrete events
4.2. Continuous Random Variables
4.3. Covariance and correlation coefficient
4.4. Multivariate Gaussian distribution
5. Uncertainty Propagation
5.1. Transforming random variables
5.2. Mean and Variance propagation laws
5.3. Linear propagation of mean and covariance
5.4. Monte Carlo simulations for uncertainty propagation
6. Observation theory
6.1. Introduction
6.2. Least-squares estimation
Notebook exercise: fitting different models
6.3. Weighted least-squares estimation
Notebook exercise: playing with the weights
6.4. Best linear unbiased estimation
Estimation of a single sample vs many samples
6.5. Precision and confidence intervals
Notebook: factors influencing precision
6.6. Maximum Likelihood Estimation
6.7. Non-linear least-squares estimation
Notebook Gauss-Newton iteration for GNSS Trilateration
6.8. Model testing
6.9. Hypothesis testing for Sensing and Monitoring
Notebook exercise: which melting model is better?
Notebook exercises: is my null hypothesis good enough?
6.10. Notation and formulas
Programming
1. Getting Started!
1.1. Computers
1.2. Environments and Environment Managers
1.3. Command Line Interface
1.4. Files and Folders
2. Sharing code in reports
2.1. File Paths
2.2. Markdown
3. Version control with Git
3.1. Version Control
3.2. Jupyter notebooks and git
3.3. Branching and merging
3.4. Merge conflicts
4. Large language models
4.1. Effective prompting
4.2. Generating code exercise
4.3. Debugging errors exercise
4.4. The importance of human-in-the-Loop
Miscellaneous
References
Changelog
Credits and License
Repository
Open issue
Index
