Process Simulation and Mathematical Techniques for Chemical Engineers

Table of Contents

• Intro
• Python
• NumPy
• Real Analysis
  • Real Analysis
• Taylor’s theorem
  • Bonus Slide Lecture
  • Mathematical Preliminaries and Error Analysis
    • Introduction
    • Review of Calculus
    • Round-Off Error and Computer Arithmetic
    • Errors in Scientific Computation
  • Approximations with Taylor Series
  • Discussion on Errors
• Root finding in one dimension, bisection, Newton-Raphson for root finding
  • Root Finding
  • Solutions of Equations of One Variable
    • Introduction
    • The Bisection Method
  • Newton’s Method
  • Root Finding Problem Statement
  • Tolerance
  • Bisection Method
  • Newton-Raphson Method
  • Root Finding in Python
• Big-O notation
  • Big-O
  • Complexity and Big-O Notation
  • Complexity Matters
  • The Profiler
• Interpolation, Lagrange polynomials, cubic splines
  • Interpolation
  • Interpolation and Polynomial Approximation
    • Introduction
    • Lagrange Polynomials
  • Spline Interpolation
  • Interpolation Problem Statement
  • Linear Interpolation
  • Cubic Spline Interpolation
  • Lagrange Polynomial Interpolation
• Numerical integration and differentiation
  • Integration & Differentiation
  • Basic Quadrature Rules
  • Numerical Differentiation
  • Numerical Differentiation Problem Statement
  • Finite Difference Approximating Derivatives
  • Approximating of Higher Order Derivatives
  • Numerical Differentiation with Noise
  • Numerical Integration Problem Statement
  • Riemann’s Integral
  • Trapezoid Rule
  • Simpson’s Rule
  • Computing Integrals in Python
• PRNG Secrets
• Intro to IVPs
  • ODE Initial Value Problem Statement
  • Reduction of Order
  • Numerical Error and Instability
• Euler’s method
  • Introduction; Taylor Methods
  • The Euler Method
• Better IVP Methods
  • Intro to IVPs & RK4
  • Python ODE Solvers
  • Advanced Topics
• RK4
  • Runge-Kutta Methods
  • Predictor-Corrector and Runge Kutta Methods
• IVP systems, RK4 for systems
  • IVP Systems Final
  • Methods for Systems of Equations
  • Final IVPs
• Predictor-corrector & adaptive methods for IVPs
  • Predictor-Corrector Methods
  • Adaptive Techniques
  • Stiff Differential Equations
• Gaussian elimination, inverting & factoring
  • Linear Systems
  • Linear Systems
  • Linear Systems 2
  • Gaussian Elimination
  • Direct Methods for Solving Linear Systems
    • Linear Algebra and Matrix Inversion
    • Matrix Factorization
    • Techniques for Special Matrices
  • Basics of Linear Algebra
  • Linear Transformations
  • Systems of Linear Equations
  • Solutions to Systems of Linear Equations
  • Solve Systems of Linear Equations in Python
• Matrices & graph theory for chemistry
• Markov chain generative models for text & polymers (uses matrices)
• Norms, eigenvalues, eigenvectors & iterative matrix solvers
  • Iterative Methods for Solving Linear Systems
  • Matrix Inversion
  • Summary and Problems
• Intro to optimization
  • Optimization
  • Optimization 2
  • Error Bounds and Iterative Refinement
  • The Steepest Descent Method
• Iterative search, condition numbers
• Steepest descent search direction, nonlinear solvers, Newton, quasi-Newton
  • Systems of Nonlinear Equations
• Midterm Review

Text Files

All PDFs converted to text using OCR. Use cases:

• Compatible with the search engine, so it can find search queries. Just confirmed this isn’t allowed on the midterm however.
• Find a search query using command + F.
• Copy + paste. Useful for code blocks to run in Colab.

Faires & Burden

• adaptive-techniques.txt
• basic-quadrature-rules.txt
• error-bounds-iterative-refinement.txt
• gaussian-elimination.txt
• introduction-bisection.txt
• introduction-convergence-vectors-eigenvalues-eigenvectors.txt
• introduction-larange-polynomials.txt
• introduction-taylor-methods.txt
• linear-algebra-matrix-inversion-matrix-factorization-techniques-special-matrices.txt
• mathematical-preliminaries-error-analysis.txt
• methods-systems-equations.txt
• newton-method.txt
• numerical-differentiation.txt
• predictor-corrector-methods.txt
• runge-kutta-methods.txt
• spline-interpolation.txt
• steepest-descent-method.txt
• stiff-differential-equations.txt
• systems-nonlinear-equations.txt

Lecture Slides

Note: The bonus slide has not been converted because it’s a .png so cannot be read by the OCR software.

• 352LectureSlides01-Intro.txt
• 352LectureSlides02-Python.txt
• 352LectureSlides03-NumPy.txt
• 352LectureSlides04-Real-Analysis.txt
• 352LectureSlides05-BigO.txt
• 352LectureSlides06-Root-Finding.txt
• 352LectureSlides07-Interpolation.txt
• 352LectureSlides08-Integration-Differentiation.txt
• 352LectureSlides09-Intro-to-IVPs.txt
• 352LectureSlides10-IVPs-RK4.txt
• 352LectureSlides11-IVP-systems.txt
• 352LectureSlides12-Final-IVPs.txt
• 352LectureSlides13-Linear-Systems.txt
• 352LectureSlides14-Linear-Systems2.txt
• 352LectureSlides15-Optimization.txt
• 352LectureSlides16-Optimization2.txt
• 352LectureSlides17-MidtermReview.txt