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Q1 Topics
1. Numerical Modelling
1.1. Approximating derivatives
1.2. Initial Value Problem for ODE: single-step methods
1.3. Accuracy and stability of numerical methods
1.4. Implicit methods for nonlinear ODE
1.5. Multi-step and multi-stage methods
1.6. Boundary-value Problems: second-order ODE
2. Multivariate Distributions
2.1. Contingency tables
2.2. Discrete events
2.3. Continuous Random Variables
2.4. Covariance and correlation coefficient
2.5. Multivariate Gaussian distribution
3. Uncertainty Propagation
3.1. Transforming random variables
3.2. Mean and Variance propagation laws
3.3. Linear propagation of mean and covariance
3.4. Monte Carlo simulations for uncertainty propagation
4. Observation theory
4.1. Introduction
4.2. Least-squares estimation
Notebook exercise: fitting different models
4.3. Weighted least-squares estimation
Notebook exercise: playing with the weights
4.4. Best linear unbiased estimation
Estimation of a single sample vs many samples
4.5. Precision and confidence intervals
Notebook: factors influencing precision
4.6. Non-linear least-squares estimation
Notebook Gauss-Newton iteration for GNSS Trilateration
4.7. Model testing
4.8. Hypothesis testing for Sensing and Monitoring
Notebook exercise: which melting model is better?
Notebook exercises: is my null hypothesis good enough?
4.9. Notation and formulas
Programming topics Q1
1. Getting Started!
1.1. Computers
1.2. Environments and Environment Managers
1.3. Command Line Interface
1.4. Files and Folders
2. Version Control with Git
2.1. Version Control
2.2. Jupyter Notebooks and Git
2.3. Branching and Merging
2.4. Merge Conflicts
3. Sharing code in reports
3.1. File Paths
3.2. Markdown
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
Appendix
I. Modelling Concepts
I.i. Model Classification
I.ii. Model Decisions
I.iii. Uncertainty Classification
I.iv. Verification, Calibration and Validation
I.v. Goodness of Fit
II. Numerical Modelling
II.i. Revision of Concepts
II.ii. Taylor Series Expansion
Exercises on Taylor expansion
II.iii. Numerical Integration
III. Univariate Continuous Distributions
III.i. PDF and CDF
III.ii. Empirical Distributions
III.iii. Non-Gaussian distributions
III.iv. Parametric Distributions
Uniform distribution
Gaussian distribution
Lognormal distribution
Gumbel distribution
Exponential distribution
Beta distribution
Summary of parametric distributions
III.v. Location, Shape and Scale: Consistent Parameterization
III.vi. Fitting a Distribution
Method of moments
Maximum Likelihood Estimation
Goodness of Fit
IV. Observation Theory
IV.i. Vectors and matrices
IV.ii. Vector spaces
IV.iii. System of linear equations
Miscellaneous
References
Changelog
Credits and License
Repository
Open issue
Index
