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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
Q2 Topics
1. Numerical Methods for PDEs
1.1. Introduction to PDEs
1.2. Diffusion Equation
1.3. Advection Equation
1.4. Advection-diffusion equation
2. Finite Element Method
2.1. Strong form of the 1D Poisson equation
2.2. From strong to weak form
2.3. From weak to discrete form
2.4. Finite element implementation
2.5. Elements and shape functions
2.6. Numerical integration
2.7. Poisson equation in 2D
2.8. Isoparametric mapping
3. Signal Processing
3.1. Fourier Series
Square wave example
3.2. Complex Fourier Series
3.3. Fourier Transform
3.4. Sampling
3.5. Discrete Fourier Transform
3.6. Spectral Estimation
3.7. Supplementary Videos
4. Time Series Analysis
4.1. Time series components
Components of time series
4.2. Noise and stochastic model
4.3. Modelling and Estimation
Time series modelling
4.4. Time Series Stationarity
4.5. Autocovariance function
4.6. Autoregressive process
Fit AR(p) model (Optional)
4.7. Autocorrelation and PSD
4.8. Forecasting
Forecasting example
4.9. Appendix on Moving Average (optional)
5. Optimization
5.1. Optimization origins
5.2. Optimization basics
5.3. Taxonomy of optimization models
5.4. Example Linear Programming
Implementation in Python
5.5. Augmented form of a mathematical program
5.6. SIMPLEX method
Exercise 1: Simple Exercise
Exercise 2: Cargo airplane (Optional)
Cargo Airplane: Implementation in Python (Optional)
5.7. Integer problems and solving with Branch-and-Bound
5.8. Some constraints that take advantage of integer/binary variables
5.9. Genetic Algorithm
5.10. Exercise: Airlines Problem (Optional)
5.11. Road Network Design Problem
Python implementation with mixed integer linear program
Python implementation with genetic algoritm
6. Machine Learning
6.1. Introduction and k-Nearest Neighbors
6.2. Decision Theory
6.3. Linear Basis Function Models and Regularization
6.4. Stochastic Gradient Descent
6.5. Feedforward Neural Networks
6.6. Review and Quiz
7. Extreme Value Analysis
7.1. Concept of Extremes
Return Period
Sampling Techniques
7.2. Block Maxima & GEV
Block Maxima
Asymptotic Model
GEV Distribution
Return Period & Design Life
7.3. Peak Over Threshold & GPD
Peak Over Threshold (POT)
Intermezzo: Poisson
Threshold & Declustering
GPD: Introduction
GPD:
m
Return Levels
Return Period & Design Life
7.4. Supplementary Material
Bernoulli and Binomial
EVA videos
8. Risk Analysis
8.1. Introduction to Risk Analysis
Definition of Risk
Steps in a Risk Analysis
Risk Curve
8.2. Risk Evaluation
Decision Analysis
Cost Benefit Analysis
Economic Optimization
Optimization Example
Safety Standards
8.3. Exercises
FN Curve
Dam and River
Paint System
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
5. Object-oriented programming
5.1. Classes and Object-Oriented Programming in Python
5.2. What are classes?
5.3. Encapsulation
5.4. Inheritance
5.5. Polymorphism
5.6. Exercise
6. Programming with large matrices
6.1. Assembly and np._ix
6.2. Sparse matrices with scipy.sparse
6.3. Solving systems of equations
7. Errors in Python
7.1. Error Types
7.2. The Python Traceback
8. Testing in Python
8.1. Assertions
8.2. Raising errors
8.3. Handling errors: the
try
-
except
block
8.4. Unit Testing
9. Week 2.4: Gurobi installation
10. Week 1.6: Errors
10.1. Introduction
10.2. Error Types
10.3. The Python Traceback
10.4. Raising errors
10.5. Handling Errors
10.6. Assertions
11. Week 1.8: SymPy
11.1. SymPy
Miscellaneous
References
Changelog
Credits and License
Repository
Open issue
Index
