complex analysis - ahlfors
mathematics - arnold - complex analysis
... lim z↑0 e 1/z = 0. COMPLEX ANALYSIS 1 Douglas N. Arnold 2 References: John B. Conway, Functions of One Complex Variable, Springer-Verlag, 1978. Lars V. Ahlfors, Complex Analysis, McGraw-Hill, 1966. Raghavan ... consequences of simple-connectivity. Recall that every analytic function on a simply-connected region admits a primitive. It follows that if f is a nowhere-vanishing function...
Ngày tải lên: 27/03/2014, 11:51
complex analysis
... lim z↑0 e 1/z = 0. COMPLEX ANALYSIS 1 Douglas N. Arnold 2 References: John B. Conway, Functions of One Complex Variable, Springer-Verlag, 1978. Lars V. Ahlfors, Complex Analysis, McGraw-Hill, 1966. Raghavan ... consequences of simple-connectivity. Rec all that every analytic function on a simply-connected region admits a primitive. It follows that if f is a nowhere-vanishing functio...
Ngày tải lên: 27/03/2014, 11:51
complex -analysis
... is connected iff it is path connected. COMPLEX ANALYSIS 16 Proposition 4.6 Let f : D → C be holomorphic where D is a region. If f = 0, then f is constant. COMPLEX ANALYSIS 17 5 Cauchy’s Theorem Proposition ... constant. Theorem 7.3 (Fundamental theorem of algebra) Every non-constant polynomial with complex coefficients has a zero in C. COMPLEX ANALYSIS 26 Theorem 7.4 Let D be a d...
Ngày tải lên: 27/03/2014, 11:51
g12can complex analysis
... g can only be complex differentiable at 0. Since the partial are continuous and the Cauchy-Riemann equations are satisfied at (0,0), our function g IS complex differentiable - 17 - at 0. It is ... we have met so far. 4.1 Complex Series Let a p , a p+1 , a p+2 , be a sequence (i.e. a non-terminating list) of complex numbers. For n p, define s n = k=p ∑ n a k , - 25 - the...
Ngày tải lên: 27/03/2014, 11:51
real hypersurfaces and complex analysis
... irresistible. In this de- sire to generalize, there were two ways to pro- ceed. One was to focus on functions of several complex variables as the generalization of func- tions of one complex variable. ... of R 2n with C n . We call M a real hypersurface of the complex space C n to dis- tinguish it from a complex hypersurface, that is, a complex n − 1 dimensional submanifold of C...
Ngày tải lên: 27/03/2014, 11:52
A First Course in Complex Analysis pptx
... sentence “The complex number x + iy has absolute value r and argu- ment φ" now becomes the identity x + iy = re iφ . The left-hand side is often called the rectangular form, the right-hand side ... definition of the derivative of a complex function, we consider functions which have a derivative of 0. One of the first applications of the Mean-Value Theo- rem for real-valued functions, T...
Ngày tải lên: 31/03/2014, 12:20
complex analysis - cain
... y. This is simply the set of all points on the cross formed by the two straight lines -2 -1 0 1 2 3 4 -3 -2 -1 1 2 3 x Exercises 10. At what points is the function f given by fz x 3 i1 ... Contents Chapter One - Complex Numbers 1.1 Introduction 1.2 Geometry 1.3 Polar coordinates Chapter Two - Complex Functions 2.1 Functions of a real variable 2.2 Func...
Ngày tải lên: 31/03/2014, 15:12