Data and Computing for Engineers

Data and computing skills are essential to all subdomains of modern (chemical) engineering, yet many students only receive ad-hoc training in these topics. Instead, CBE 20258 (undergraudate) and CBE 60258 (graduate) provides a systematic and rigorous introduction to the fundamentals of i) computing in Python; ii) mathematical modeling; iii) numerical methods for equation solving, integration, and optimization; iv) probability and statistics; and v) data analytics.

What am I going to get out of this class?

CBE 20258 (Sophomore)

At the end of the semester, you should be able to…

• Create mathematical models and apply computational methods to analyze systems using basic principles of chemical engineering (e.g., mass and energy balances, thermodynamic equilibrium, etc.)

• Analyze data and quantify uncertainty using standard statistical techniques and mathematical models grounded in engineering fundamentals

• Independently plan, implement, and debug short (100 to 300 lines) Python computer programs to analyze data, solve engineering mathematical models, and visualize results

CBE 40258 (Senior) / CBE 60258 (Graduate)

At the end of the semester, you should be able to…

• Numerically solve mathematical models relevant to chemical and biomolecular engineering research

• Analyze data and quantify uncertainty using modern data science (a.k.a., applied statistics) methods

• Think more critically demonstrated by independently planning, implementing, and debugging short Python computer programs

• Prepare education modules and publication quality data visualization

Content

Python Programming

• 1. Python Primer
  • 1.1. Welcome to Jupyter Notebooks and Vocareum
  • 1.2. Python Basics I: Variables, Strings, and Bugs
  • 1.3. Python Basics II: Loopy Logic
  • 1.4. Python Basics III: Lists, Dictionaries, and Enumeration
  • 1.5. Functions and Scope
  • 1.6. Recursion
  • 1.7. Pseudocode
  • 1.8. High/Low Guess My Number Game
  • 1.9. Modules and Files
  • 1.10. Linear Algebra with Numpy and Scipy
  • 1.11. Visualization with matplotlib
  • 1.12. Manipulating Data with Pandas
  • 1.13. Functions as Arguments
  • 1.14. Testing and Debugging in Python
  • 1.15. Preparing Publication Quality Figures in Python
• 2. Advanced Python

Numerical Methods

• 3. Linear Algebra Primer
  • 3.1. Chapter 1: Math Fundamentals
  • 3.2. Chapter 2: Intro to Linear Algebra
  • 3.3. Chapter 3: Computational linear algebra
  • 3.4. Chapter 4: Geometric Aspects of Linear Algebra
  • 3.5. Chapter 5: Linear Transformations
  • 3.6. Chapter 6: Theoretical Linear Algebra
• 4. Applied Linear Algebra
  • 4.1. Modeling Systems of Linear Equations
  • 4.2. Gaussian Elimination
  • 4.3. Invertible Matrix Theorem and Gaussian Elimination Example
  • 4.4. LU Decomposition
  • 4.5. Errors in Linear Systems
  • 4.6. Example: Mass Balances and Linear Algebra
  • 4.7. Linear Algebra Review and SciPy Basics
• 5. Algorithm Building Blocks
  • 5.1. Taylor Series Approximations
  • 5.2. Finite Difference Derivative Approximations
  • 5.3. Example: Heating a Metal Slab
• 6. Nonlinear Systems of Equations
  • 6.1. Modeling Systems of Nonlinear Equations: Flash Calculation Example
  • 6.2. Newton-Raphson Method in One Dimension
  • 6.3. More Newton-Type Methods
  • 6.4. Convergence Analysis for Newton-Raphson Methods
  • 6.5. Newton-Raphson Methods for Systems of Equations
  • 6.6. Newton Methods in Scipy
• 7. Numeric Integration
  • 7.1. Introduction and Newton-Cotes
  • 7.2. Gauss Quadrature
  • 7.3. Scipy Library: Adaptive Methods for Newton-Cotes and Gauss Quadrature
  • 7.4. Application: Inertial Navigation Systems
  • 7.5. Forward and Backward Euler Methods
  • 7.6. Crank-Nicolson (Trapezoid Rule)
  • 7.7. Stability Analysis
  • 7.8. Explicit Range Kutta Method
  • 7.9. Systems of Differential Equations and Scipy
  • 7.10. Example: Reaction Rates
• 8. Continuous Optimization
  • 8.1. Pyomo Basics
  • 8.2. Electricity Market Optimization
  • 8.3. Flash Calculations in Pyomo

Data Analysis

• 9. Descriptive Statistics and Visualization
  • 9.1. Sampling
  • 9.2. Summary Statistics
  • 9.3. Visualizing Data
• 10. Probability Theory
  • 10.1. Basic Ideas of Probability
  • 10.2. Random Variables
  • 10.3. Jointly Distributed Random Variables
  • 10.4. Jointly Continuous Random Variables
  • 10.5. Practice Problems
• 11. Common Probability Distributions
  • 11.1. Bernoulli Probability Distribution
  • 11.2. Binomial Probability Distributions
  • 11.3. Poisson Probability Distributions
  • 11.4. Normal Probability Distributions
  • 11.5. Summary
• 12. Uncertainty and Error Propagation
  • 12.1. Measurement Error
  • 12.2. Error Propagation
  • 12.3. Measuring Flowrate Example
  • 12.4. Car and Incline Example
  • 12.5. Simulation
  • 12.6. Monte Carlo Error Propagation
  • 12.7. Practice Problems
• 13. Statistical Inference
  • 13.1. Central Limit Theorem
  • 13.2. Standard Normal Distribution
  • 13.3. Confidence Intervals
  • 13.4. Student’s t-Distribution
  • 13.5. Hypothesis Testing Basics
  • 13.6. Flavors of Hypothesis Testing
  • 13.7. Type I and Type II Errors
  • 13.8. Statistical Power Basics
  • 13.9. Statistical Power in Python
  • 13.10. Statistical Power Practice Problems
  • 13.11. Bootstrap Confidence Intervals
• 14. Multivariate Linear Regression
  • 14.1. Correlation, Covariance, and Independence
  • 14.2. Simple Least Squares
  • 14.3. Ordinary Least Squares Linear Regression
  • 14.4. Residual Analysis
  • 14.5. Regression Assumption Examples
  • 14.6. Uncertainty Analysis and Statistical Inference
  • 14.7. Multivariate Linear Regression
  • 14.8. Linear Regression Practice Problems
• 15. Nonlinear Regression
  • 15.1. Transformations and Linear Regression
  • 15.2. Weighted Linear Regression
  • 15.3. Nonlinear Regression
  • 15.4. Nonlinear Regression Practice Problem
  • 15.5. Monte Carlo Uncertainty Analysis for Nonlinear Regression
  • 15.6. Nonlinear Regression Case Study: Adsorptive Nanoporous Membranes
• 16. Design of Experiments
  • 16.1. Model-Based Design of Experiments

Extra Information

• Fall 2022
  • Syllabus
  • Fall 2022 Schedule
  • Project 1: Computating for Problem Solving (Fall 2022)
  • Project 2: Data Analysis (Fall 2022)
• Fall 2023
  • Syllabus
  • Schedule
  • Semester Project
  • Problem Set 1
  • Problem Set 2
  • Problem Set 3
  • Problem Set 4
  • Problem Set 5
  • Problem Set 6
• Contributed Examples
  • Estimating the Entrance Length of Channel Flow
  • Non-Isothermal Packed Bed Reactor
  • Solving Fick’s Second Law Using Numeric Integration
  • Stochastic Simulation of Chemical Reactions
  • Spaghettification of the Magic School Bus
  • Alcohol Pharmacokinetics and Blood Alcohol Content % Modeling
  • Plotting McCabe-Thiele diagram through computational methods
  • Example of Mass Balance Problem in Wastewater Treatment Units
  • Filtration of a Yeast Suspension
  • Calculating Fraction of Molecular Collisions