What is Complex Variables and Transfroms?

A Quick Intro

Complex variables and transforms are key concepts in the field of complex analysis, which is a branch of mathematics dealing with functions of a complex variable and the application of transforms. This area is crucial for solving problems in engineering, physics, and applied mathematics.
A complex variable is a variable that can take on the value of a complex number. Complex numbers are numbers of the form z=x+iy , where x and y are real numbers, and i is the imaginary unit with the property i² = −1.
Transforms are mathematical operations that convert a function from one domain to another, often to simplify analysis and solve differential equations.

All of the topics are covered in detail in our Complex Variables and Transfroms Course.

https://www.youtube.com/watch?v=g8fjQokhhkM&list=PLrtzypMWdxDGIOVbWIs3hpux-0EOeHiz1&pp=iAQB

The following sections contain links to our full lessons on all the topics listed below.

Complex Variables and Transfroms:

• Complex Numbers, Complex Conjugates, Complex Plane (Z-Plane or Argand Diagram) with Solved Examples.
• Triangular Inequality, Upper Bound, Lower Bound with Solved Examples.
• Polar Form of Complex Numbers, Principal Arguments, Arguments of “z” with Solved Examples.
• Euler Formula in Complex Variables and Transfroms with Solved Examples.
• Integer Powers of “z”, De-Moivre’s Theorem with Solved Examples.
• Powers and Roots of Complex Numbers with Solved Examples.
• Describe the set of points “z” in the Complex Plane with Solved Examples.
• Complex Functions, Real and Imaginary Parts of Complex Functions with Solved Examples.
• Complex Functions in Polar Coordinates, Complex Exponential Functions, Periodicity of e^z with Solved Examples.
• Complex Function as Mappings with Solved Examples.
• Limits, Criterion for non-existence of Limit with Solved Examples.
• Limits at Infinity, Continuity of Function with Solved Examples.
• Derivative of Complex Function with Solved Examples.
• Analytic Functions, L’ Hospital Rule with Solved Examples.
• Cauchy-Rieman Equations (CR-Eqs) with Solved Examples.
• Harmonic Functions, Harmonic Conjugate Function with Solved Examples.
• Complex Logarithm Function, Principal Value of Complex log with Solved Examples.
• Complex Powers, Principal Value of z^α with Solved Examples.