Computational Physics

Lecture 1

Aims

  • Teach the techniques of computational physics and numerical methods
  • side benefit: develop familiarity with python

Syllabus

  • Numerical Differentiation: Learn methods for approximating derivatives when analytical solutions are not feasible or too complicated.
  • Numerical Integration: Techniques for estimating the integral of functions that cannot be integrated using elementary calculus will be explored.
  • Numerical Solution of ODEs: Understand methods to solve Ordinary Differential Equations that appear in various scientific and engineering disciplines.
  • Monte Carlo Techniques & Random Walks: We will delve into probabilistic algorithms used for simulations in diverse applications like finance and molecular modeling.
  • Function Minimization and Optimization: Learn the key methods for finding optimum points of a function, a crucial task in machine learning, economics, and engineering.

Organisation

Contact

email: will.yeadon@durham.ac.uk

office: TLC033

Office Hour: Friday 2-4.55 starting week 2, either in person in my office PHY304 or via Teams.

Lectures

  • Fri 12-13. This week half the lecture is covering organisation, from next week onwards this section will be to go over the previous weeks assignment and as a Q&A session.
  • The technical material will also be available as videos on learn ultra which can be watched while trying the programing.
  • Adaptable format depending on people's needs. Currently the lectures are directly on this site so that you can easily refer to them.

Workshops

  • Mon, Tue, Thu, Fri 17-18
  • Attendence is not monitored
  • Cannot change the day
  • In ENGEX1

Computing environment

  • We will use Jupyter notebooks for all the works in this course
  • System introduced to you last year:
    • electronic submission, marking and feedback
    • easier interaction with python
    • better integration of plots and animations
    • accessible from anywhere
  • Please report problems!
  • Manual available at https://notes.dmaitre.phyip3.dur.ac.uk/notebooks/

Jupyter platform

  • log in to the server using your CIS username and password: https://compphys-2324.notebooks.danielmaitre.phyip3.dur.ac.uk/
  • go to the “Assignment” tab
  • select the assignment and “fetch” it
  • open the assignment section and select the notebook to use. It will open in a new tab.
  • work on the assignment
  • your work is automatically saved
  • you can also save your work with the “save icon” or the File menu

Programming environment

  • we use Python 3
  • all packages you need should be installed on the server
    • if you think a package would be useful but is not installed let me know

Saving your work

  • your work is automatically saved every few minutes
  • save your work with the “save icon” or the File menu
  • your python session will be closed after 1-2 hours of inactivity
    • the text and output in the notebook will be saved
    • the state of the python interpreter will not be saved:
      • you need to reevaluate all cells to restore the state
      • use “Kernel” -> “Restart and run all”
      • it is useful to do this occasionally to make sure the notebook runs as written and does not rely on code executed previously and edited since
  • can save a copy of your notebooks using “File” -> “Download as” -> “Notebook”
  • backup every hours of saved files
    • only in emergencies: you have to ask me to restore the file
  • you can make copies of notebooks “File” -> “Make a copy” but for the assessment only the original file will be considered!

Working on the server

  • Feel free to create new notebooks to experiment and play
  • I can see everything you do on the server so:
    • follow the CIS usage policy
    • don’t use the resources for other purposes than academic ones
    • don’t try to trick the marking system

Assessments

  • 8 assessments
  • distributed through the notebook server
  • submitted through the notebook server
  • deadline: Mondays 14:00 (starting Week 3, i.e. 1st assignment due 16th October)
  • the last submission counts! Submit partial work to avoid having no submission in time at all.
  • if your first submission is after the deadline no marks will be awarded!
  • Each assessement will be composed of one or more notebooks
  • Each notebook will have a description of the tasks to perform
  • It will be in the form of either:
    • a piece of code to provide
    • a task (for example producing a plot)
    • a free text question

Assessment: piece of code

  • if you are asked to provide a piece of code the location will be marked by a # YOUR CODE HERE marker
def double(x):
    # YOUR CODE HERE
    raise NotImplementedError()

Assessment: piece of code

  • replace the marker (and the raise statement) with a valid piece of code:
def double(x):
    return 2*x
  • code tasks will typically be followed by a test that helps you check that your code’s functionality is correct
assert double(4) == 8

Assessment: piece of code

  • when you click on the “validate” button in the notebook or in the assignment list the notebook is run and checks that all these assert tests pass, you will get a warning if they don’t.
  • these tests are part of the assessment: if they don’t pass you won’t get all marks!

Assessment: free text question

A free text question will be followed by a cell with the text

YOUR ANSWER HERE

You can double click on it and edit the text. You can use $\LaTeX$

Feedback

Feedback will be made available on the notebook server.

I will demonstrate it after your first assignment’s feedback is ready.

Getting help

Useful packages

  • matplotlib: Plotting and Data Visualization
    • Why It's Useful: Data visualization is crucial for understanding data trends, making predictions, or presenting your findings. matplotlib provides a comprehensive range of plotting tools, from basic line and scatter plots to complex 3D visualizations.
    • Key Features: Customizable plots, support for various formats like PNG, PDF, and SVG, and integration with Jupyter notebooks for real-time data visualization.
  • numpy: Fast Numerical Calculations with Arrays
    • Why It's Useful: Numerical computing is the backbone of data science, machine learning, and scientific computing. numpy offers a fast and efficient multidimensional array object that dramatically speeds up numerical calculations.
    • Key Features: Element-wise operations, broadcasting, linear algebra functions, and tight integration with other scientific libraries.
  • scipy: Collection of Scientific Functions
    • Why It's Useful: While numpy provides the foundational building blocks for numerical computation, scipy goes a step further by offering a large set of algorithms and utility functions for specialized scientific computing tasks.
    • Key Features: Optimization, signal processing, integration, interpolation, eigenvalue problems, and more.
  • sympy: Symbolic Calculation
    • Why It's Useful: Unlike numerical computing, which provides approximate solutions, symbolic computing deals with mathematical objects analytically. sympy allows for algebraic manipulation, equation solving, and calculus operations in symbolic form.
    • Key Features: Symbolic algebra, calculus, equation solving, and pretty printing of mathematical expressions.

See new L1 python resource for more on these packages

Useful tips

  • tab completion
  • inline help (append ? to a command)
  • execution can be interrupted using the $\rm {\blacksquare}$ button