Complex Analysis
47 videos • 3,059 views • by IK Knowledge Orchard
1
Why we need complex numbers? | Complex Plane | Algebraic Properties of complex numbers
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2
Modulus of Complex Numbers || Commutative Associative, Distributive Property of Complex Numbers
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3
Further Important Properties of Complex Numbers
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4
Reduction of complex quotient and complex powers to real numbers
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5
Geometrical Interpretation and important properties of Modules and Conjugate of Complex Numbers
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6
Triangle Inequality and Reverse Triangle Inequality Proof | Some Counter example of result of Moduli
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7
Vector and Moduli Representation of Complex number their sum, difference by vectors in complex plane
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8
Important results related to complex numbers proofs by using modules and Conjugate properties
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9
Polar Form of complex Numbers | Relationship between cartesian and polar form of complex numbers
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10
Complex Analysis identity proof by mathematical induction
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11
Find argument by using modulus condition | Complex Analysis
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12
Proof complex expression by writing individual factor in exponential form then change to rectangular
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13
Complex Analysis very important result conversion prove by converting in exponential form
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14
Use de Moivre's formula to derive trigonometry identities of Cos 3x and Sin 3x
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15
Roots of complex numbers | Square roots of complex numbers | cube, fourth roots of complex numbers
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16
Interior ponts | Exterior points | Boundary points | Open sets | Close sets in complex Analysis
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17
How to draw complex numbers on plane? | Connected set , Domain , Region concept in complex Analysis
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18
How to find closure in complex Analysis? | How to sketch closure on complex plan?
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19
Graphing of complex functions || Domain of definition of complex functions || Complex Analysis
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20
Comparison of limit in Real plane and Complex plane | Limit in complex Analysis | Complex Analysis
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21
Criteria for non-existance of limit? with counter example || How to find limit of complex function ?
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22
Criteria for Continuity of Complex Functions | Properties of continuous functions | Complex Analysis
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23
Properties or complex limits || Evaluation of complex limit || Complex Analysis
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24
Criteria for Continuity of Complex Functions | Properties of continuous functions | Complex Analysis
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25
Differentiability of complex functions || Every continuous is not differentiable || Complex Analysis
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26
Analytic Function ||Holomorphic Functions || Regular Functions || Entire Function || Singular Points
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27
Differentiabilty implies Continuity but converse may not be true counter example | Complex Analysis
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28
Cauchy Riemann Equations ( CR-Eq's ) || Differentiability implies CR-Eq's hold || Complex Analysis
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29
Criteria for Non-Analytic Function with Exp| Necessary & Sufficient condition for Differentiability
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30
Sufficient condition for Analytic with Example || Analytic function | CR equation | Complex Analysis
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31
When derivative exists of complex functions? || Sufficient Condition for Differentiability
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32
CR equation in polar and cartesian form relationship || Differentiability || Analytic || CR Eq's
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33
CR equation in polar and cartesian form relationship || Differentiability || Analytic || CR Eq's
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34
Entire Function with Examples || Relationship between Differentiability, Analyticity and Entire
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35
Types of singularities || Isolated Singularity || Removable Singularity || Essential singularity
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36
Def. And Exp's of Translation || Rotation || Magnification || Complex Mapping || Complex Analysis
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37
Complex Integral part 1 || Complex Analysis || Contour integration || By Iqra zareef Maan
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38
Complex Integral part 2 || Complex Analysis || Contour integration || By Iqra zareef Maan
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39
Arc || Simple Arc || Closed Arc || Jordan Arc || Differentiable Arc || Arc Length || Unit Tangent
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40
Laplace Equation || Harmonic Function || Every Analytic Function is harmonic | Complex Analysis ||
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41
Contour Integral part 1 || Complex integration over Circle and Semi Circles || Complex Analysis ||
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42
Contour Integral part 2 || Complex integration over Circle and Semi Circles || Complex Analysis
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43
Contour Integral part 3| Upper Bound for Moduli of Contur Integral | ML- Inequality Complex Analysis
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44
Cauchy Theorem For Countour Integral || Cauchy Goursat Theorem For Countour Integral || Complex
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45
Evaluation of integral along a Parametric Curve || Real Integral Part 1 || Conplex Analysis by Zill
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46
Evaluation of integral along a function & figure || Real Integral Part 2 || Conplex Analysis by Zill
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47
Orientation of Curve || Evaluation of line Integral along a Parametric Curve and Explicit Functions
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