Page 5 - DMTH402_COMPLEX_ANALYSIS_AND_DIFFERENTIAL_GEOMETRY

CONTENT

Unit 1: Complex Numbers 1
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Unit 2: Complex Functions 9
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Unit 3: Elementary Functions 21
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Unit 4: Integration 30
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Unit 5: Cauchy s Theorem 41
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Unit 6: Cauchy s Integral Formula 47
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Unit 7: Transformations and Conformal Mappings 59
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Unit 8: Series 79
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Unit 9: Taylor and Laurent Series 90
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Unit 10: Residues and Singularities 99
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Unit 11: Rouche s Theorem 108
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Unit 12: Fundamental Theorem of Algebra 114
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Unit 13: Schwarz’s Reflection Principle 136
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Unit 14: Notation and Summation Convention 150
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Unit 15: Tensors in Cartesian Coordinates 159
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Unit 16: Tensor Fields Differentiation of Tensors 175
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Unit 17: Tensor Fields in Curvilinear Coordinates 186
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Unit 18: Theory of Space Curves 198
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