devotion & mathematics

                                                             CANTOR SET                  INTRODUCTION :                                      We have learn about open sets and its characterization on the real line.  We now consider the structure of its closed sets. Among the simplest closed sets on the real line are the closed intervals and finite union of closed intervals. Finite sets are also include the single point set which is a closed interval with equal end-points.    Now we are going to study the character of the most general closed sets on the real line.    One of the most general proper closed subset of the real line is obtained by removing a countable disjoint c...

  LINE INTEGRALS - PROBLEMS &SOLUTIONS :       We have discussed about the definitions and development of line integrals .  Here we going to solve some problems regarding line integrals.  PROBLEM 1 :  .   Evaluate  ∫ dx/(x+y),  Where C  is the curve x=at 2 ,y=2at, 0 ≤ t ≤ 2. SOLUTION :                          PROBLEM 2 :   Show that ∫ xy dx  =4/5, where C is the arc of the parabola y 2 =x from (1,-1) to   (1,1). SOLUTION :                         3.   PROBLEM 3 :  Show that ∫  [ (x-y) 3 dx+(x-y) 3 dy]=3 πa 4 , where C Is the circle x 2 +y 2 =a 2  in       the counter clockwise sense.         SOLUTION :                                ...