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MTH632 : Complex Analysis and Differential Geometry

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Course Info
Course Category	Mathematics
Course Level	Undergraduate
Credit Hours	3
Pre-requisites	N/A
Instructor	Dr. Sohail Iqbal Doctor of Philosophy in Mathematics University of Warwick, Coventry, UK

Course Contents
Complex Numbers Algebra and Geometry of Complex Numbers Conjugates of Complex Numbers Exponential Form of Complex Numbers Roots of Complex Numbers Complex Plane Complex Functions Mappings: Geometry Limits and Continuity The Reciprocal Transformation Derivative The Cauchy–Riemann Equations Analytic Functions Harmonic Functions Sequences and Series Ratio Test and Root Test Power Series Functions Complex Exponential Functions Complex Logarithmic Functions Complex Trigonometric Functions Hyperbolic and Inverse Functions Contours Complex Integrals Contour Integrals The Cauchy-Goursat Theorem Fundamental Theorem of Integration Tangent Space Vector Fields Directional Derivatives Curves Frenet Approximation Curvature Frenet Serret Frame Frenet Serret Formula