Programming for Computations - Python

• 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