devotion & mathematics

                                                           Integration in  R 2   :    Line Integrals        contents :   1.plane curve in  R 2  2. Curve in  R 3  3. Curve in  R n                                                                                                                          Back  4.Closed Curve  5. Oriented Curve   6. Line Integral  7. Problems on Line integrals.                ...

EUCLIDEAN LINE, PLANE AND SPACES         We know about the real line or real number system R, R is one dimensional. Consider the two dimensional plane R 2 ={(a ,b)/ a ,b  Ꜫ  R}. In R 2  ,the elements of the form (a ,b) are called the ordered pairs of a & b. In R 2 , the addition and multiplication are defined as for x=( a 1 , b 1 ) , y=( a 2 , b 2 ) in R 2                                                                        x +y=(a 1+ a 2 ,b 1+ b 2  ) and x .y=(a 1. a 2  ,b 1. b 2 ) Here R 2  is called as an Euclidean  plane. Now consider the three dimensional space R 3 ={(a ,b ,c )/ a ,b ,c  Ꜫ  R}. In R 3 ,the elements of the form (a ,b ,c) are called ordered triples of a, b, c. The addition and multiplication in  R 3  are same...