- Organizational details, introduction to the lab at UB third floor.
- What is scientific computing?
- An Ancient calculation of sqrt(2): Sumerian tablet YBC7289
- Working with various bases: Number Systems
- Simulated flow trajectoris during the Deepwater Horizon Oil Spill. NOAA
- Supercomputing the climate NASA
- Patriot disaster GOA report
- Heron's Original paper Newton's Original paper Raphson's Original paper Newton's Method
- Tree of Life Demo
- Floating Point Arithmetic Computer arithmetic

**Binary digits:**Determine the binary representation of the decimal number 9.4. Compute the first 8 binary digits of the famous number sqrt(2). Please show your computational steps.**Can you beat Newton?**Enter the difference equation x1 -> x1 - 0.21*(x1*x1 - 2) into PHASER. Iterate the initial condition x0 =2.24 and observe that it approaches to sqrt(2). Compare the rate of convergence of this method of computing sqrt(2) with that of Newton's method x1-> 0.5*(x1 + 2/x1). To make a fair comparison, use the same initial condition in both iterations. How many iterations are required to get 13 correct digits of sqrt(2) in each iteration?**Small angle approximation:**In physics, it is often convenient to use the 'small angle approximation' by replacing sin(x) with x when x is small. Use Newton-Raphson method to find a value of x which satisfies the equation sin(x) - x = 0.016. How many such x can you find? Draw the stair-step diagram of the iteration process. How many fixed points do you see?**Trouble with Newton:**Using Newton's method, with starting value x = 1, try to find a root of the function f(x) = -x^4 + 3x^2 + 2. Does the iteration converge? Can you explain what is going wrong? Can you find other initial conditions that converge to a root? How many (real) roots can you find?**Your favorite computer trouble:**Write a short report (half a page?) about your favorite, or scariest, hardware, software, security, etc. problem. Please indicate your sources.