Complex Variables and Transforms

BY
Udemy

Learn about the basic principles and strategies associated with transforms, and complex variables, such as the Laplace transform.

Mode

Online

Fees

₹ 1999

Quick Facts

particular details
Medium of instructions English
Mode of learning Self study
Mode of Delivery Video and Text Based

Course overview

Yasir Amir - University Professor established the Complex Variables and Transforms online certification, which is delivered through Udemy and is aimed at participants who wish to learn college-level mathematics and calculus. The Complex Variables and Transforms online course by Udemy focuses on teaching participants how to utilize complex numbers and how to discover the singular points of an analytic function through the creation of a series.

Complex Variables and Transforms online classes are subdivided into two parts, with the first dealing with complex numbers, complex variables, and functions, and the second with transforms and series. Participants will receive more than 30.5 hours of digital learning resources in this course, which will cover numerous tactics and methodologies for analyzing issues involving functions of complex variables, transformations, series, limits, continuity, and differentiability.

The highlights

  • Certificate of completion
  • Self-paced course
  • 30.5 hours of pre-recorded video content
  • Learning resources

Program offerings

  • Online course
  • Learning resources. 30-day money-back guarantee
  • Unlimited access
  • Accessible on mobile devices and tv

Course and certificate fees

Fees information
₹ 1,999
certificate availability

Yes

certificate providing authority

Udemy

Who it is for

What you will learn

After completing the Complex Variables and Transforms certification course, participants will be introduced to the foundational principles of complex variables and transforms. Participants will study the Laplace transform, Fourier transform, Cauchy-Reimann equation, De Moivre's theorem, Heaviside expansion formula, convolution theorem, and Argand's diagram, among other theories relating to variables and transforms. Participants will learn about ideas related to complex functions, such as analytical and harmonic functions, as well as line integrals and other integral approaches. Participants will also learn about the properties of the region of convergence, inverse Laplace transform, and the solution of the ordinary differential equation.

The syllabus

Introduction

  • Introduction
  • Complex Numbers Continued
  • Complex Numbers with Numerical problems
  • Worked Problems and Vectors

More About Complex Numbers

  • Modulus, Triangle Inequality and Complex Conjugate with Worked Problems
  • Complex Conjugate Properties and Worked Exercise Problems
  • Exponential Form of Complex Numbers
  • de Moivre's Formula and Exercise Problems
  • Roots of Complex Numbers

Functions of Complex Variables

  • Basics of functions of complex variables
  • Functions of complex variables- Theorems of Limits - Continuity
  • Trigonometric Functions
  • Hyperbolic Functions and Numerical Problems
  • Hyperbolic Functions and Numerical Problems continued
  • Logarithmic Functions
  • Logarithmic Inverse Trigonometric and Hyperbolic Functions & worked problems
  • More about Inverse Trigonometric and Hyperbolic Functions with examples
  • Exercise problems related to inverse trigonometric and hyperbolic funcs
  • Differentiation and Integration of complex-valued functions
  • Differentiation and Integration of complex-valued functions II
  • Methods of Integration of complex-valued functions & Cauchy Riemann equations
  • Integration (continued)
  • Cauchy's Integral Theorem and Independence of Path
  • Previous Lecture worked problems and Cauchy's Integral Formula with numerical

Series and Sequence of Complex Numbers

  • Sequence and Series of Complex Numbers and Convergence
  • Convergence of Infinite Series
  • Sequence and Series Exercise Problems
  • Taylor and Maclaurin Series for Complex Numbers
  • Worked examples related to Taylor and Maclaurin Series
  • More worked examples related to Taylor and Maclaurin Series
  • Harmonic Functions
  • Harmonic Functions numerical problems

Series and Transforms

  • Fourier Series
  • Fourier Series continued
  • Half Range Fourier Series and Even Odd Functions
  • Exponential Fourier Series
  • Fourier Transform
  • Properties of Fourier Transform
  • Inverse Fourier Transform and Parseval's Theorem
  • Laplace Transform
  • Inverse Laplace Transform and example problems
  • Laplace Transform properties, solving differential equations and
  • examples
  • z Transforms

Instructors

Mr Yasir Amir

Mr Yasir Amir
Professor
Freelancer

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