FLAC/FLAC3D Short course at Tongji university

Itasca Software Training Course

Computations in Science and Engineering Python3

• 1. Overview
• 2. Basic python usage
  • 2.1. Basic math
  • 2.2. Advanced mathematical operators
  • 2.3. Creating your own functions
  • 2.4. Defining functions in python
  • 2.5. Advanced function creation
  • 2.6. Lambda Lambda Lambda
  • 2.7. Creating arrays in python
  • 2.8. Functions on arrays of values
  • 2.9. Some basic data structures in python
  • 2.10. Indexing vectors and arrays in Python
  • 2.11. Controlling the format of printed variables
  • 2.12. Advanced string formatting
• 3. Math
  • 3.1. Numeric derivatives by differences
  • 3.2. Vectorized numeric derivatives
  • 3.3. 2-point vs. 4-point numerical derivatives
  • 3.4. Derivatives by polynomial fitting
  • 3.5. Derivatives by fitting a function and taking the analytical derivative
  • 3.6. Derivatives by FFT
  • 3.7. A novel way to numerically estimate the derivative of a function - complex-step derivative approximation
  • 3.8. Vectorized piecewise functions
  • 3.9. Smooth transitions between discontinuous functions
  • 3.10. Smooth transitions between two constants
  • 3.11. On the quad or trapz'd in ChemE heaven
  • 3.12. Polynomials in python
  • 3.13. Wilkinson's polynomial
  • 3.14. The trapezoidal method of integration
  • 3.15. Numerical Simpsons rule
  • 3.16. Integrating functions in python
  • 3.17. Integrating equations in python
  • 3.18. Function integration by the Romberg method
  • 3.19. Symbolic math in python
  • 3.20. Is your ice cream float bigger than mine
• 4. Linear algebra
  • 4.1. Potential gotchas in linear algebra in numpy
  • 4.2. Solving linear equations
  • 4.3. Rules for transposition
  • 4.4. Sums products and linear algebra notation - avoiding loops where possible
  • 4.5. Determining linear independence of a set of vectors
  • 4.6. Reduced row echelon form
  • 4.7. Computing determinants from matrix decompositions
  • 4.8. Calling lapack directly from scipy
• 5. Nonlinear algebra
  • 5.1. Know your tolerance
  • 5.2. Solving integral equations with fsolve
  • 5.3. Method of continuity for nonlinear equation solving
  • 5.4. Method of continuity for solving nonlinear equations - Part II
  • 5.5. Counting roots
  • 5.6. Finding the nth root of a periodic function
  • 5.7. Coupled nonlinear equations
• 6. Statistics
  • 6.1. Introduction to statistical data analysis
  • 6.2. Basic statistics
  • 6.3. Confidence interval on an average
  • 6.4. Are averages different
  • 6.5. Model selection
  • 6.6. Numerical propagation of errors
  • 6.7. Another approach to error propagation
  • 6.8. Random thoughts
• 7. Data analysis
  • 7.1. Fit a line to numerical data
  • 7.2. Linear least squares fitting with linear algebra
  • 7.3. Linear regression with confidence intervals (updated)
  • 7.4. Linear regression with confidence intervals.
  • 7.5. Nonlinear curve fitting
  • 7.6. Nonlinear curve fitting by direct least squares minimization
  • 7.7. Parameter estimation by directly minimizing summed squared errors
  • 7.8. Nonlinear curve fitting with parameter confidence intervals
  • 7.9. Nonlinear curve fitting with confidence intervals
  • 7.10. Graphical methods to help get initial guesses for multivariate nonlinear regression
  • 7.11. Fitting a numerical ODE solution to data
  • 7.12. Reading in delimited text files
• 8. Interpolation
  • 8.1. Better interpolate than never
  • 8.2. Interpolation of data
  • 8.3. Interpolation with splines
• 9. Optimization
  • 9.1. Constrained optimization
  • 9.2. Finding the maximum power of a photovoltaic device.
  • 9.3. Using Lagrange multipliers in optimization
  • 9.4. Linear programming example with inequality constraints
  • 9.5. Find the minimum distance from a point to a curve.
• 10. Differential equations
  • 10.1. Ordinary differential equations
  • 10.2. Delay Differential Equations
  • 10.3. Differential algebraic systems of equations
  • 10.4. Boundary value equations
  • 10.5. Partial differential equations
• 11. Plotting
  • 11.1. Plot customizations - Modifying line, text and figure properties
  • 11.2. Plotting two datasets with very different scales
  • 11.3. Customizing plots after the fact
  • 11.4. Fancy, built-in colors in Python
  • 11.5. Picasso's short lived blue period with Python
  • 11.6. Interactive plotting
  • 11.7. key events not working on Mac/org-mode
  • 11.8. Peak annotation in matplotlib
• 12. Programming
  • 12.1. Some of this, sum of that
  • 12.2. Sorting in python
  • 12.3. Unique entries in a vector
  • 12.4. Lather, rinse and repeat
  • 12.5. Brief intro to regular expressions
  • 12.6. Working with lists
  • 12.7. Making word files in python
  • 12.8. Interacting with Excel in python
  • 12.9. Using Excel in Python
  • 12.10. Running Aspen via Python
  • 12.11. Using an external solver with Aspen
  • 12.12. Redirecting the print function
  • 12.13. Getting a dictionary of counts
  • 12.14. About your python
  • 12.15. Automatic, temporary directory changing
• 13. Miscellaneous
  • 13.1. Mail merge with python
• 14. Worked examples
  • 14.1. Peak finding in Raman spectroscopy
  • 14.2. Curve fitting to get overlapping peak areas
  • 14.3. Estimating the boiling point of water
  • 14.4. Gibbs energy minimization and the NIST webbook
  • 14.5. Finding equilibrium composition by direct minimization of Gibbs free energy on mole numbers
  • 14.6. The Gibbs free energy of a reacting mixture and the equilibrium composition
  • 14.7. Water gas shift equilibria via the NIST Webbook
  • 14.8. Constrained minimization to find equilibrium compositions
  • 14.9. Using constrained optimization to find the amount of each phase present
  • 14.10. Conservation of mass in chemical reactions
  • 14.11. Numerically calculating an effectiveness factor for a porous catalyst bead
  • 14.12. Computing a pipe diameter
  • 14.13. Reading parameter database text files in python
  • 14.14. Calculating a bubble point pressure of a mixture
  • 14.15. The equal area method for the van der Waals equation
  • 14.16. Time dependent concentration in a first order reversible reaction in a batch reactor
  • 14.17. Finding equilibrium conversion
  • 14.18. Integrating a batch reactor design equation
  • 14.19. Uncertainty in an integral equation
  • 14.20. Integrating the batch reactor mole balance
  • 14.21. Plug flow reactor with a pressure drop
  • 14.22. Solving CSTR design equations
  • 14.23. Meet the steam tables
  • 14.24. What region is a point in
• 15. Units
  • 15.1. Using units in python
  • 15.2. Handling units with the quantities module
  • 15.3. Units in ODEs
  • 15.4. Handling units with dimensionless equations
• 16. GNU Free Documentation License
• 17. References
• 18. Index

(Source: https://kitchingroup.cheme.cmu.edu/pycse/pycse.html#orge7cc054)