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A complete course on Complex Analysis.
Rating: 4.0 out of 5(15 ratings)
109 students
Created byDr. Piyusha Somvanshi
Last updated 11/2021
English

What you'll learn

  • In this course every concept of the subject is discussed in easy but in detailed manner. This course is very useful for the students of science and engineering.
  • Detailed study of Analytic functions.
  • Residue theorem and its applications.
  • Contour Integration.

Explore related topics

Course content

3 sections • 20 lectures • 5h 28m total length

  • Introduction1:45

    This is an brief introduction of the course in which students will be able to know what they are going to learn in each lecture.

  • Analytic Functions | Cauchy Riemann Equations13:40

    This video lecture contains concept of function of complex variables, entire function, singular point, analytic function and Cauchy Riemann equations with its proof.

  • Some examples of C-R equations23:41

    This video lecture contains some problems based on Cauchy Riemann equations with their solutions.

  • Milne Thomson method23:16

    In this lecture we have discussed about Milne Thomson method with some examples. Milne Thomson method is a method to construct analytic function.

  • Rectifiable curve and Jordan Arc8:13

    In this lecture  some basic concepts and terminologies related to complex integration are explained like partition and norm, rectifiable curve, Jordan arc and contour.

  • Cauchy's Integral Theorem20:47

    In this lecture students will learn about simply and multiply connected regions and Cauchy's theorem with its proof. Again extension of Cauchy's theorem is given for multiply connected region.

  • Examples of Cauchy's Integral Theorem24:26

    In this lecture some examples of Cauchy's Integral Theorem is discussed so that he students can better understand applications of the theorem.

  • Cauchy's Intrgral Formula12:36

    This video lecture contains explanation of Cauchy's integral formula with its derivation. Derivatives of an analytic function is also discussed.

  • Examples of Cauchy's Integral Formula20:48

    In this lecture some examples of Cauchy's integral theorem are illustrated to explain application of the formula. Also difference between Cauchy's integral theorem and Cauchy's integral formula is explained through some examples so that students will not get confused with their usage.

  • Morera's Theorem15:59

    This lecture contains simple and easy proof of Morera's Theorem which is converse of Cauchy's Theorem.

  • Power Series and Radius of Convergence18:44

    This lecture contains the concepts of power series, absolute and conditional convergence, circle and radius of convergence and some examples based on radius of convergence.

Requirements

  • Students must be acquainted with Mathematics of Senior High School level.

Description

This is a complete course on complex analysis in which all the topics are explained in detailed but simple and easy manner. This course is designed for university and college level students of science and engineering stream as well as for the students who are preparing for various competitive exams . The whole curriculum is divided into two parts.

Part 1

  • Functions of Complex variables, Analytic Function, Cauchy Riemann Equations

  • Some examples of Cauchy Riemann Equations

  • Milne Thomson Method to construct Analytic function

  • Simply and Multiply Connected Domains, Cauchy's theorem and its proof, extension of Cauchy's theorem for multiply connected domain

  • Some examples of Cauchy's theorem

  • Cauchy's Integral Formula with its proof

  • Some examples of Cauchy's integral formula

  • Morera's Theorem

  • Power series and Radius of Convergence

Part 2

  • Taylor's series and Laurent's series and some examples based on these

  • Residues and Cauchy's Residue Theorem

  • Some applications of Cauchy's residue theorem

  • Poles and Singularities

  • Contour Integration

  • Bi linear or Mobius Transformation

Complex numbers are just extension of real numbers. In complex Analysis mostly we discuss about complex variables. This course on Complex Analysis is taught to the students of science and engineering with the task of meeting two objectives : one, it must create a sound foundation based on the understanding of fundamental concepts and development of manipulative skills, and second it must reach far enough so that the student who completes such a course will be prepared to tackle relatively advanced applications of the subject in subsequent courses that utilize complex variables.



Who this course is for:

  • Univesity and college level students.

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