Chemical and Biomedical Engineering Calculations Using Python

Presents standard numerical approaches for solving common mathematical problems in engineering using Python

Python is a clear and powerful object–oriented programming language, comparable to Perl, Ruby, Scheme, or Java. The Python program language is ideal due to its rapid growth and strong recent interest amongst practitioners in areas as diverse as numerical modeling, data science, and bioinformatics.  Chemical and Biological Engineering Calculations Using Python presents standard numerical approaches for solving common mathematical problems in engineering.

The book covers the most common engineering calculations used by students and utilizes the freely available Python software and its supporting libraries. Chemical and Biological Engineering Calculations Using Python features topics on:

Programming in Python  Common External Libraries for Engineering Plotting  Symbolic Mathematics Linear Systems Regression  Nonlinear Equations  Statistics  Numerical Differentiation and Integration  Initial Value Problems  Boundary Value Problems  Partial Differential Equations Finite Element Method

Chemical and Biological Engineering Calculations Using Python is written to be accessible to engineering students in a numerical methods or computational methods course as well as for practicing engineers that want to learn to solve common problems using Python. Also included is an electronic download of the Python codes presented in the book.

Jeffrey J. Heys is currently the department head in Chemical and Biological Engineering at Montana State University.  He has taught numerous courses in Chemical and Biological Engineering for 15 years.  He also taught courses in Applied Mathematics at the University of Colorado at Boulder, including Numerical Analysis, for three years.  Jeff has been creating mathematical models of biological systems for approximately 20 years, published more than 40 peer reviewed papers, and has programmed extensively in FORTRAN, C, C++, MATLAB, and Python.

Preface

Chapter 1: Problem Solving in Engineering

1.1 Equation Identification and Categorization

Problems

Additional resources

Chapter 2: Programming with Python

2.1 Why Python?

2.2 Getting Python

2.3 Python Variables and Operators

2.4 External Libraries

Problems

Additional Resources

Chapter 3: Programming Basics

3.1 Comparitors and Conditionals

3.2 Iterators and Loops

3.3 Functions

3.4 Debugging or Fixing Errors

3.5 Top 10+ Python Error Messages

Problems

Additional Resources

Chapter 4: External Libraries for Engineering

4.1 Numpy Library

4.2 Matplotlib Library

4.3 Application: Gillespie Algorithm

Problems

Additional Resources

Chapter 5: Symbolic Mathematics

5.1 Introduction

5.2 Symbolic Mathematics Packages

5.3 An Introduction to SymPy

5.4 Factoring and Expanding Functions

5.5 Derivatives and Integrals

5.6 Cryptography

Problems

Additional Resources

Chapter 6: Linear Systems

6.1 Example Problem

6.2 A Direct Solution Method

6.3 Iterative Solution Methods

Problems

Additional Resources

Chapter 7: Regression

7.1 Motivation

7.2 Fitting Vapor Pressure Data

7.3 Linear Regression

7.4 Nonlinear Regression

7.5 Multivariable Regression

Problems

Additional Resources

Chapter 8: Nonlinear Equations

8.1 Introduction

8.2 Bisection Method

8.3 Newton s Method

8.4 Broyden s Method

8.5 Multiple Nonlinear Equations

Problems

Additional Resources

Chapter 9: Statistics

9.1 Introduction

9.2 Reading Data from a File

9.3 Statistical Analysis

9.4 Advanced Linear Regression

9.5 U.S. Electrical Rates Example

Problems

Additional Resources

Chapter 10: Numerical Differentiation and Integration

10.1 Introduction

10.2 Numerical Differentiation

10.3 Numerical Integration

Problems

Additional Resources

Chapter 11: Initial Value Problems

11.1 Introduction

11.2 Biochemical Reactors

11.3 Forward Euler

11.4 Modified Euler Method

11.5 Systems of Equations

11.6 Stiff Differential Equations

Problems

Additional Resources

Chapter 12: Boundary Value Problems

12.1 Introduction

12.2 Shooting Method

12.3 Finite Difference Method

Problems

Additional Resources

Chapter 13: Partial Differential Equations

13.1 Finite Difference Method for Steady–State PDEs

13.2 Convection

13.3 Finite Difference Method for transient PDEs

Problems

Additional Resources

Chapter 14: Finite Element Method

14.1 A Warning

14.2 Why FEM?

14.3 Laplace s Equation

14.4 Pattern Formation

14.5 Further Reading

Problems

Additional Resources

Index