Complex Analysis 1 by Dennis G Zill Solution||lec#11||Ch#1||inverse & example#3||#complexanalysis

Complex Analysis 1 by Dennis G Zill Solution|lec # 11|Ch#1|inverse & example #3|#complexanalysis
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Complex Analysis 1 by Dennis G Zill Solution|lec # 10|Ch#1|division & example # 2|#complexanalysis

Complex Analysis 1 by Dennis G Zill Solution|lec # 9|Ch#1|properties of conjugate|#complexanalysis

Complex Analysis 1 by Dennis G Zill Solution|lec # 8|Ch#1|conjugate|#complexanalysis

Complex Analysis 1 by Dennis G Zill Solution|lec # 7|Ch#1|zero and unity|#complexanalysis

Dear students in this lecture we will discuss First Chapter of Complex Analysis By Dennis G Zill.
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Course Name: Complex Analysis By Dennis G Zill Solutions Course Intstructior:
Malik Ali Junaid ( Math Pointers)

Objectives:
The main objectives of this course are to:
• Get firm grip on basic ideas of complex numbers and their basic operations with examples.
• Apply and use the concepts of analytic functions and limits.
• Know concretely about elementary functions and their properties.
• Understand ideas of complex integration and power series expansion.
• Use concept of residues.

Course Outline:
Complex Numbers: Complex Numbers and their Algebraic Properties, Cartesian and Polar Coordinates Analytic Functions: Limits, Continuity, Continuity in a Region, Uniform Continuity, Derivatives, Cauchy-Riemann Equations Elementary Functions: Exponential, Logarithmic, hyperbolic functions Complex and Contour Integrations: Definite Integrals, Contours, Line Integrals, The CauchyGoursat Theorem, Proof of the Cauchy-Goursat Theorem, Simply and Multiply Connected Domains, Indefinite Integrals, The Cauchy Integral Formula, Morera's Theorem, Maximum Moduli of Functions, The Fundamental Theorem of Algebra and its applications, Liouvilles theorem. Power Series: Convergence of Sequences and Series, Taylor Series, Laurent Series, Uniform Convergence, Integration and Differentiation of Power Series The Calculus of Residues: Zeros of Analytic functions, Singularities and its types, Poles, Residues at Poles, Cauchy’s Residue Theorem and its application in computing improper integrals.

Recommended Books:
• Churchill, R. (2008). Complex Variables and Applications. McGraw –Hill.
• Pennissi, L. (1976). Elements of Complex Variables, Rinchart and Winston
• Mark J. Ablowitz and Fokas A.S, Complex Variables, Cambridge University Press.
• Shabat, B.V.(1992), Introduction to Complex Analysis, American Mathematical Society.

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