The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style employed is more accessible and concise, in keeping with the needs of engineering students.
The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows students to write simple programs for solving common mathematical problems with numerical methods in the context of engineering and science courses. The emphasis is on generic algorithms, clean program design, the use of functions, and automatic tests for verification.
Table of contents
- The First Few Steps
- 1.1 What Is a Program? And What Is Programming?
- 1.2 A Python Program with Variables
- 1.3 A Python Program with a Library Function
- 1.4 Importing from Modules and Packages
- 1.5 A Python Program with Vectorization and Plotting
- 1.6 Plotting, Printing and Input Data
- 1.7 Error Messages and Warnings
- 1.8 Concluding Remarks
- 1.9 Exercises
- A Few More Steps
- 2.1 Using Python Interactively
- 2.2 Variables, Objects and Expressions
- 2.3 Numerical Python Arrays
- 2.4 Random Numbers
- 2.5 Exercises
- Loops and Branching
- 3.1 The for Loop
- 3.2 The while Loop
- 3.3 Branching (if, elif and else)
- 3.4 Exercises
- Functions and the Writing of Code
- 4.1 Functions: How to Write Them?
- 4.2 Programming as a Step-Wise Strategy
- 4.3 Exercises
- Some More Python Essentials
- 5.1 Lists and Tuples: Alternatives to Arrays
- 5.2 Exception Handling
- 5.3 Symbolic Computations
- 5.4 Making Our Own Module
- 5.5 Files: Read and Write
- 5.6 Measuring Execution Time
- 5.7 Exercises
- Computing Integrals and Testing Code
- 6.1 Basic Ideas of Numerical Integration
- 6.2 The Composite Trapezoidal Rule
- 6.3 The Composite Midpoint Method
- 6.4 Vectorizing the Functions
- 6.5 Rate of Convergence
- 6.6 Testing Code
- 6.7 Double and Triple Integrals
- 6.8 Exercises
- Solving Nonlinear Algebraic Equations
- 7.1 Brute Force Methods
- 7.2 Newton's Method
- 7.3 The Secant Method
- 7.4 The Bisection Method
- 7.5 Rate of Convergence
- 7.6 Solving Multiple Nonlinear Algebraic Equations
- 7.7 Exercises
- Solving Ordinary Differential Equations
- 8.1 Filling a Water Tank: Two Cases
- 8.2 Population Growth: A First Order ODE
- 8.3 Spreading of Disease: A System of First Order ODEs
- 8.4 Oscillating 1D Systems: A Second Order ODE
- 8.5 Rate of Convergence
- 8.6 Exercises
- Solving Partial Differential Equations
- 9.1 Example: Temperature Development in a Rod
- 9.2 Finite Difference Methods
- 9.3 Exercises
| Pages : | 350 |
| Size : | 7.3 MB |
| Downloads: | 112 |
| Created: | 2022-02-03 |
| License: | CC BY |
| Author(s): | Svein Linge, Hans Petter Langtangen |
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