Euler form - Study guides, Revision notes & Summaries

1.1 Prove that there is no largest prime. Proof : Suppose p is the largest prime. Then p!+1 is NOT a prime. So, there exists a prime q such that q |p! + 1 ) q |1 which is impossible. So, there is no largest prime. Remark: There are many and many proofs about it. The proof that we give comes from Archimedes 287-212 B. C. In addition, Euler Leonhard (1707-1783) find another method to show it. The method is important since it develops to study the theory of numbers by analytic method. The r...

Problem 1.1: Newton’s second law can be expressed as F = ma (1) where F is the net force acting on the body, m mass of the body, and a the acceleration of the body in the direction of the net force. Use Eq. (1) to determine the mathematical model, i.e., governing equation of a free-falling body. Consider only the forces due to gravity and the air resistance. Assume that the air resistance is linearly proportional to the velocity of the falling body. Solution: From the free-body-diagram ...