Complex Integration And Cauchys Theorem
Complex Integration And Cauchys Theorem
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Then 2 j (z r+1 - z r ) \ is less than or equal to the sum r = of the total variations of x (t) and y (t) as t varies from t to t n+1 .
Since the modulus of a sum does not exceed the sum of the moduli, it follows that 3 |(* r+1 -* r )|= 2 l{(^, -^) + e(y r+1 - r co [X(t r ^}-X(t r )}\ + S \{y(t r +i)-y(t r )}\. R=0 r-0 But t r+l ^t r, since the points z 0t z l} z 2, ... Are in order; and nsequently the first of these summations is less than or equal to the total variation of x (t), and the seco...nd summation is less than or equal to the total variation of y (t) ; that is to say, 2 (z r+l - z r ) \ is less than or equal to the sum of the total variations of x (t) and y (t).
10. We are now in a position to give a formal definition of a complex integral and to discuss its properties. The notation which has been introduced in 2, 4 and 5 will be employed throughout.
DEFINITION. Let AB be a simple curve with limited variations drawn in the Argand diagram.. Let f(z) be a function of the complex variable z which is continuous on the curve AB.
What to read after Complex Integration And Cauchys Theorem?
You can find similar books in the "Read Also" column, or choose other free books by G N George Neville Watson to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Then 2 j (z r+1 - z r ) \ is less than or equal to the sum r = of the total variations of x (t) and y (t) as t varies from t to t n+1 .
Since the modulus of a sum does not exceed the sum of the moduli, it follows that 3 |(* r+1 -* r )|= 2 l{(^, -^) + e(y r+1 - r co [X(t r ^}-X(t r )}\ + S \{y(t r +i)-y(t r )}\. R=0 r-0 But t r+l ^t r, since the points z 0t z l} z 2, ... Are in order; and nsequently the first of these summations is less than or equal to the total variation of x (t), and the seco...nd summation is less than or equal to the total variation of y (t) ; that is to say, 2 (z r+l - z r ) \ is less than or equal to the sum of the total variations of x (t) and y (t).
10. We are now in a position to give a formal definition of a complex integral and to discuss its properties. The notation which has been introduced in 2, 4 and 5 will be employed throughout.
DEFINITION. Let AB be a simple curve with limited variations drawn in the Argand diagram.. Let f(z) be a function of the complex variable z which is continuous on the curve AB.
What to read after Complex Integration And Cauchys Theorem?
You can find similar books in the "Read Also" column, or choose other free books by G N George Neville Watson to read onlineMoreLess
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