Introduction to c++ programming and object orientation
How to write scientific reports
Linear algebra and eigenvalue problems. (Lecture notes chapters 6.1-6.5 and 7.1-7.5 and projects 1 and 2).
Ordinary differential equations (Lecture notes chapter 8 and projects 3 and 4 )
Monte Carlo methods in physics (Lecture notes chapters 11, 12 and 13, project 4)
How to handle vectors and matrices
Gaussian elimination and LU decomposition (project 1)
How to solve linear equations (project 1)
How to obtain the inverse and the determinant of a real symmetric matrix
Cubic spline
Tridiagonal matrix decomposition (project 1)
Householder's tridiagonalization technique and finding eigenvalues based on this
Jacobi's method for finding eigenvalues (project 2)
Random walks and Markov chains
Generation of random numbers
Monte Carlo integration
Probability distributions and their properties
Errors in Monte Carlo calculations (statistical errors)
Metropolis algorithm (project 4)
Applications to statistical physics systems (project 4)
Brief excursion into quantum mechanical systems (project 4)
Euler's method and improved Euler's method, truncation errors (projects 3 and 4)
Runge Kutta methods, 2nd and 4th order, truncation errors (projects 3 and 4)
Leap-frog and Verlet algoritm (projects 3 and 4)
How to implement and solve a second-order differential equation, both linear and non-linear.
How to make your equations dimensionless.
Set up diffusion, Poisson and wave equations up to 2 spatial dimensions and time
Set up the mathematical model and algorithms for these equations, with boundary and initial conditions. The stability conditions for the diffusion equation.
Explicit, implicit and Crank-Nicolson schemes, and how to solve them. Remember that they result in triangular matrices (project 4).
Diffusion equation in two dimensions.
Select the project you liked the most among projects 2-4. Alternatively, if there are other topics of relevance you would like to present, feel free to suggest (send me an email however). Your presentation (bring your own laptop) should include
Introduction with motivation
Give an overview of the theory and numerical algorithms employed
Discuss the implementation of your algorithm and how you verified it and validated it. Discuss for example various tests you made.
Present and discuss your results
Summary, conclusions and perspectives
Anything else you think is important. Useful to have backup slides
In total your talk should have a duration of 20-25 minutes, but longer is also ok. The style for the final presentation follows very much the layout your reports.