Complex analysis by dennis g zill solutions- Lecture#7 Exercise# 1.3 Quetions#1 to 12 - Math Tutor 2

Complex analysis by denni g zill solutions- Lecture#7 Exercise# 1.3 Quetions#1 to 12 - Math Tutor 2
Dear students in this lecture we will discuss Exercise questions of 1.3 ( Questions 1 to 12). If you found any mistake while solving problems then ingore it.

Course Name: Complex Analysis By Dennis G Zill Solutions
Course Intstructior: Malik Aqeel ( Math Tutor-2)
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.

PDF link:https://drive.google.com/file/d/1xJDi...

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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_________________________Complex Analysis Lectures series____________________________

https://www.youtube.com/watch?v=Wc6h9...

https://www.youtube.com/watch?v=w1nEv...

______________________Real Analysis lecture series_____________________________________

https://www.youtube.com/watch?v=mF40Z...

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