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Complex Analysis for Real Analysis,Engineering Math Students

Name: Complex Analysis for Real Analysis,Engineering Math Students
Rating: 3.7 (15 reviews)

Complex Analysis with Complex Numbers for all Algebra, Calculus, Engineering Math, Physics, Real Analysis Students

Created byMath Reddy

Last updated 6/2022

English

English [Auto],

What you'll learn

Introduction to Complex Numbers [ Updated ( MARCH - 2022 ) with new Video lectures ]
Complex Differentiation
Cauchy Reimann Equations
Analytic function
Laurent Series
Power Series
Taylor Series
Complex Integration
Singular Points
Types of Singularities
Poles
Cauchy's Theorem
Zero’s and Poles
Cauchy Residue
Cauchy Reside Theorem
Bilinear or Mobius Transformation

Course content

12 sections • 63 lectures • 3h 31m total length

30-Day Money-Back Guarantee and 3 more benefits1:04
What you'll learn in this Complex Analysis course0:10
Download - PDF - Complex Analysis1:14

Basic Concepts Part 10:05
Complex Function0:39
Basic Concepts Part 112:17
Define a function as a binary relation between two sets that assigns exactly one element of the second set to every element of the first set.
Basic Concepts Part 214:42
Solved Problem 19:20
The lecture shows solving for F(3), F(4), and F(5) by substituting into F(x) = x + 1, and clarifies the function definition, domain, and range.
Solved Problem 28:17

Limit of Complex Function6:21
Continuity of Complex Function6:51
Examine continuity of complex functions through the epsilon-delta definition, proving that for every epsilon there exists delta with |f(z) - f(z0)| < epsilon whenever |z - z0| < delta.
Differentiability of Complex Function5:23
Explore the differentiability of complex functions by checking when the complex limit exists. Learn how the derivative of a complex function is defined and denoted.
What are CR equations?2:51
This lecture introduces the Cauchy-Riemann equations and demonstrates checking a function f(z)=u(x,y)+i v(x,y) by applying partial derivatives with respect to x and y.
Solved example problem on CR equations6:12
Verify the Cauchy-Riemann equations for the given function by computing partial derivatives with respect to x and y and confirming the exponential and trigonometric components satisfy the relations.
What is Analytic function?1:44
Identify analytic functions by applying the Cauchy-Riemann equations to a complex function with real and imaginary parts. Verify the partial derivatives with respect to x and y to confirm analyticity.
Zero’s of Analytic Functions0:07
The Complex Derivative0:04
Analytic Function:Solved Example problem8:04
Verify analyticity by applying the Cauchy–Riemann equations to a given complex function. This solved example computes partial derivatives of the real and imaginary parts to confirm CR conditions hold.
Every Analytic Function is Differential0:02
Holomorphic functions0:02
Harmonic function0:02
Entire Function0:03
Harmonic Conjugate0:05

Laurent series0:06
What is residue?0:04
Represent a circle with complex numbers0:16
The Residue Theorem in Complex Analysis0:05
Finding Residues in Complex Analysis0:05
Formula to find Residues in Complex Analysis7:05
Learn to compute residues in complex analysis, covering simple poles and higher-order poles, and apply the standard residue formulas to evaluate them.
Solved Problem on Evaluating Integrals via the Residue Theorem19:15
Solve the given integral via the residue theorem by identifying poles inside the circle and summing the residues.

Introduction0:02
Cauchy-Goursat theorem0:14
Cauchy Integral Formula0:01
Cauchy Integral Formula3:44
Explore the Cauchy integral formula within simply connected domains, using contour integrals to relate function values to interior points and clarify when a point lies inside the contour.
Solved problem on Cauchy Integral Formula9:55
Solve a problem using the Cauchy integral formula by analyzing the circle and denominator to determine the integral’s value. The lecture uses equation comparisons to derive the result.
Solved Problem 218:09

Conformal mapping0:06
Linear Mapping0:07
Bilinear or Mobius transformation0:13
What is Bilinear Transformation?10:11
Problem 1: Finding Fixed Point10:13
Compute the three fixed points of a complex-valued function by forming a quadratic equation through cross-multiplication and solving with the quadratic formula.
Problem 2: Finding Fixed Point8:30
Find fixed points of the given transformation by solving w = f(w) through cross multiplication, showing when no real solutions exist and identifying two complex fixed points.
Problem 3: Finding Fixed Point9:17
Determine fixed points of a given transformation by equating a transformed form to x^2+Bx+C=2, compare coefficients, and solve for x via the quadratic formula.

Requirements

Be able to read Complex number System

Description

This course comes with a 30 day money back guarantee! If you are not satisfied in any way, you'll get your money back. Plus you will keep access to the Notebooks as a thank you for trying out the course.

Updated ( MARCH - 2022 ) : New Video lectures are added.

Hi,

I am Kishore Reddy. I have 11 years experience of teaching

Complex Analysis for Real Analysis, Engineering Math Students

Dear students, How are you studying? Hope you are doing well.

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HERE IS WHAT SOME STUDENTS OF THIS COURSE HAVE TOLD ME:

"It's soo clear and fully satisfied, video clarity is also good" - Madhu

"This Complex analysis course is explained in easy way. This Mathematics course has assignment which is helped to practice.

Thank you " - Ravi

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In this course, you are going to learn about Complex Analysis.

In lower classes, you learnt about number SYSTEM from Natural Numbers, Whole numbers, Real Numbers.

And also you learnt Calculus concepts like Differentiation and Integration.

Now, in this course, you will learn about

Complex analysis, traditionally known as the theory of functions of a complex variable. Complex Analysis is the branch of mathematical analysis that investigates functions of complex numbers.

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In this course you will learn about

Complex Number
Cauchy Reimann Equations
Analytic function
Poles
Power Series
Contour Integrals
Cauchy's Theorem
Zero’s and Poles
Cauchy Reside Theorem
Singularly
Bilinear Transformation

Learn above concepts from this course

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***Mathematics in my point of view: "Mathematics/Math: Math is a simply a language. In School grade/Classes, covered Algebra, Trigonometry, Geometry, and Precalculus. In College, covered Algebra 2,College Algebra, Probability, Statistics, Calculus: Calculus 1,Calculus 2,Calculus 3(Multivariable Calculus like Differential Equations, Engineering Mathematics), And University Math topics are Abstract Algebra, Linear Algebra, Discrete Mathematics, Number Theory, Real Analysis, Complex Analysis, Functional Analysis, Matlab. In Test Prep: SAT, Act, GRE,GMAT,LSAT are with Quantitative Aptitude Section. Application of Math: Engineering, Physics, Science, Computer sciences like in Games development, Programming, Machine learning, Data science".***

Udemy is great platform to learn.

You'll Also Get:

✔ Lifetime Access to course updates

✔ Fast & Friendly Support in the Q&A section

✔ Udemy Certificate of Completion Ready for Download

So, enroll today in this "Complex Analysis-

Complex Analysis for All Level students.

All the best,

Thank you

Kishore Reddy

Who this course is for:

Who want to learn Engineering Mathematics
Electrical Engineering Students
BSc Students
Engineering Students
MSc Maths Students
Math Majors
University Math Students

Complex Analysis for Real Analysis,Engineering Math Students

What you'll learn

Explore related topics

Course content

The 4 Benefits | Complex Analysis3 lectures • 2min

Introduction to Complex Numbers2 lectures • 4min

Complex Functions6 lectures • 45min

Complex Differentiation14 lectures • 38min

Power series5 lectures • 1min

Laurent Series and the Residue Theorem7 lectures • 27min

Complex Integration6 lectures • 32min

Singularity and Cauchy Residue theorem in Complex Analysis8 lectures • 3min

Contour integration3 lectures • 1min

Conformal Mapping in Complex Analysis7 lectures • 39min

Requirements

Description

Who this course is for: