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Q1 Topics
1. Modelling concepts
1.1. Model classification
1.2. Model decisions
1.3. Verification, Calibration and Validation
1.4. Goodness of Fit
2. Propagation of Uncertainty
2.1. Random vectors, covariance and correlation
2.2. Multivariate normal distribution
2.3. Uncertainty Classification
2.4. Mean and variance propagation laws
2.5. Linear propagation laws of mean and covariance
3. Observation theory
3.1. Introduction
3.2. Least-squares estimation
Notebook exercise: fitting different models
3.3. Weighted least-squares estimation
Notebook exercise: playing with the weights
3.4. Best linear unbiased estimation
3.5. Precision and confidence intervals
Notebook: factors influencing precision
3.6. Maximum Likelihood Estimation
3.7. Non-linear least-squares estimation
Notebook Gauss-Newton iteration for a point on a circle
3.8. Model testing
3.9. Hypothesis testing for Sensing and Monitoring
Notebook exercise: which melting model is better?
Notebook exercises: is my null hypothesis good enough?
3.10. Notation and formulas
4. Numerical Modelling
4.1. Revision of Concepts
4.2. The First Derivative
4.3. Finite Difference Method
4.4. Taylor Series Expansion
Exercises on Taylor expansion
4.5. Numerical Integration
4.6. Initial Value Problem for ODE: single-step methods
4.7. Multi-step and multi-stage methods
4.8. Boundary-value Problems: second-order ODE
4.9. Treatment of Partial Differential Equations: a start
5. Univariate Continuous Distributions
5.1. PDF and CDF
5.2. Empirical Distributions
5.3. Parametric Distributions
Revisiting Gaussian distribution
Non-Gaussian distributions
Uniform distribution
Exponential distribution
Gumbel distribution
Lognormal distribution
Summary of parametric distributions
5.4. Fitting a Distribution
Method of moments
Maximum Likelihood Estimation
Goodness of Fit
5.5. Parameterization of continuous distributions
6. Multivariate Distributions
6.1. Discrete events
6.2. Continuous Random Variables
6.3. Gaussian distribution
6.4. Non-Gaussian Distributions
6.5. Designing with Probability
One Random Variable
Two Random Variables
Q2 Topics
1. PDEs and the Finite Volume Method
1.1. Getting Started
1.2. Finite Volume Method
1.3. Advection
1.4. Unstructured meshes
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. Components of time series
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
4.7. Forecasting
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
Week 1.1: Getting Started!
Computers and Environments
Computers
Computing Environments
Software Installation
Install Miniconda
Hidden Files
Command Line Interface (CLI)
Environment Variables (Windows)
Visual Studio
Extensions
Files and Folders
Python Warmup
Week 1.2: Python Topics
Week 1.3: VS Code Live Share!
Visual Studio Live Share
Week 1.4: Version control with Git!
Version Control
Install git
Git workflow
Git on GitHub
Making Commits to the Remote Repository (Web IDE)
Git in VS code
Cloning a Repository
Making Commits to the Local Repository
Fetch and Pull from the Remote Repository
Week 1.5: Collaboration with Git!
Branching and merging
Forking
Merge conflicts
Week 1.6: Errors
Introduction
Error Types
The Python Traceback
Raising errors
Handling Errors
Assertions
Week 1.7: OOP
Classes and Object-Oriented Programming in Python
Week 1.8: SymPy
SymPy
Week 2.4: Gurobi installation
Fundamental Concepts
1. Vectors and matrices
2. Vector spaces
3. System of linear equations
4. Multivariate differentiation
5. Taylor series
6. Probability axioms
7. Random variables
8. Expectation (mean) and variance
9. Probability Tables
9.1. Normal
9.2. Chi-Squared
10. Probability in Python
11. Additional topics
Miscellaneous
References
Credits and License
Repository
Open issue
Index
