Each of the following problems are related with my recent research. All these problems are the zeroth order steps to reach what I am working on now-a-days.

Basic:

• Digitize a traveling wave on a vibrating string [An interactive example!]

• What is(are) the normal mode(s) of 4-coupled spring-mass-system arranged in the form of a square?

• Solve this functional differential equation: x′(t) = - x(t-τ). Feel free to choose your own initial conditions.

• Write down a simple computer program to solve one-dimensional random-walk-problem on a periodically compressed (and stretched) rubber-band.

• Develop a baby program (in Fortran or C++) to solve a system of nonlinear equations. [Hint: Use this Algorithm 10.3 @ page 658]

• Factorize a number, (for example: {15: 1, 3, 5, 15}), using a computer algorithm that takes polynomial time. [Hint: Use  Shor's algorithm and Qiskit architecture]

Intermediate:

• If you were a computer, how will you identify, whether a thread/string  is 'knotted' or not?

• Sketch an algorithm that can distinguish between a 'one-sided-surface' (Möbius strip) and a standard 'two-sided-closed-surface'.

• Given a thin current carrying wire of arbitrary shape, can you find the magnetic field at a distance? [Write down a small computer program!]

• Can you do the inverse problem, that is, given a prescribed magnetic field profile, can you find the configuration of the current carrying wire? [-do-]

• How will you measure the electromagnetic radiation from a current carrying tube of arbitrary shape? [-do-]

Advanced:

• If I ask you to write down a simple advection solver using third-order upwind difference scheme, which flux-limiter will you prefer to use and why?

• Where is the global-minimum of this function: f(x) = sin(x) - exp(- x^2) [Which optimization method will you choose and why?]

• Take a Fourier transform with "pencil-decomposition". [Hint: Use FFTW library]

• What is that equation, whose solution is:  x(t) = A cos (ω t + φ) [Write down a small computer program in support of your claim!]