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Complex Analysis By Dr. P.K. Srivastava

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Publisher Vayu Education
ISBN 9789383137497
Author: Dr. P.K. Srivastava
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Preface
About The Book
Syllabus Math 1.3 Complex Analysis I Block I Complex Numbers. 1. Arithmetic operations. Conjugation, Absolute value, Inequalities. 2. Geometric addition and multiplication. the binomial equation, the spherical representation. 3. Lines and Circles. 4. Limits and Continuity. Block II Analytic functions and power series. 1. Analytic functions, Cauchy Riemann equations. Harmonic functions, rational functions. 2. Elementary theory of power series, sequences, uniform convergence, Abel s limit theorem. 3. The exponential, logarithmic and trigonometric functions. 4. Toplology of the complex plane. Linear transformations, elementary conformal mappings. Block III Comple Integration. 1. Line integrals, rectifiable arcs 2. Cauchy s theorem for a rectangle. Cauchy s theorem in a disc. 3. The index of a point with respect to a closed curve. Cauchy s integral formula, Liouville s theorem. The fundamental theorem of Algebra. 4. Removable singularities, Taylor s theorem, zeros and poles, The maximum principle.
Contents Preface ...............................................................................................................v BLOCK 1 1. Arithmetic operations ....................................................................................3 1.1 Introduction .............................................................................................. 3 1.2. Complex Numbers ....................................................................................3 1.3. Equality of Complex Numbers ..................................................................4 1.4. Complex Conjugate ................................................................................... 4 1.5. Graphical Representation of a Complex Number .....................................4 1.6. Absolute of the Complex Number ............................................................5 1.7. Conjugation ...............................................................................................6 1.8. Inequalities ................................................................................................7 1.9. Properties of the Arguments ................................................................... 10 2. Geometric Operations .................................................................................. 12 2.1 Geometric of complex numbers ............................................................. 12 2.2 Subtraction of Complex Numbers .......................................................... 12 2.3 Multiplication of Complex Numbers ....................................................... 12 2.4 Division of Complex Numbers ................................................................ 13 2.5 Some Properties of Complex Numbers .................................................. 13 2.6 Polar Form of Complex Numbers .......................................................... 16 2.7 Product of Complex Numbers In Polar Form ........................................ 17 2.8 Quotient of Complex Numbers In Polar Form .......................................18 2.9 The Binomial Equation ............................................................................ 18

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