Free Download A Bootcamp to Complex AnalysisLast updated 9/2024
Created by Shyamkant Anwane
MP4 |
Video: h264, 1280x720 |
Audio: AAC, 44.1 KHz, 2 Ch
Level: Beginner |
Genre: eLearning |
Language: English + subtitle |
Duration: 40 Lectures ( 9h 1m ) |
Size: 2.58 GB
History & developments of Complex Numbers
Roots of complex numbers
Topology in complex plane
Complex Functions, graphing it, iteration of function and Julia sets
Complex sequences, limit, continuity and derivatives of complex functions
Analytic functions, Cauchy-Riemann equations
RequirementsYou can learn this subject without any prior knowledge.
The basics of real analysis that we learn in school level mathematics are reviewed before entering in Complex Analysis.
DescriptionThis course A Bootcamp to Complex Analysis provides an introduction to the theory of complex functions of a complex variable. It opens by introducing the complex plane, followed by the algebra and geometry of complex numbers. Like in Real Analysis, we will make our way through algebraic processing, topology, complex dynamics, Julia sets, the relationship of exponential function and the imaginary unit i, analytic function etc. In this course, we are going to learn different concepts than the ones we have already learned in school as Real Analysis. In real numbers, we can approach infinity by either heading towards the right side or left side on the number scale while in the complex plane, we have infinite ways of approaching infinity. Likewise, with the aid of the Residue theorem, which is the pinnacle of this learning concept, with a technical advantage we shall be able to solve integrals that real analysis is not capable of. Complex analysis has real-life applications spread over all science subjects, all fields of engineering disciplines, and industrial applications too. The course is divided into 5 sections that are spread over 40 video lectures with embedded quizzes for self-assessment and self-evaluation.The optional homework/practice assignments are for advanced learners to take up their skills via stages: Remembering-Understanding-Application-Evaluation-Creation, the cognitive domain of Bloom's Taxonomy. Infact, a significant amount of your learning will happen while completing the homework assignments that will need pen and paper. We anticipate basic knowledge of algebra, geometry, and calculus. However, amateurs can also take this as a primary course for building a level of creative application.Course OutcomesDefinition of CN,It's algebraic processing,Topology,Complex Dynamics,Plotting of complex functions,Iteration - Julia Sets, Limit & Continuity,Exponential function and complex numbers - Euler's Identity,Analytic Functions.
Who this course is forStudents who wants to apply knowledge for creative outcomes
Engineering and Science Students
Anyone who is wants to learn applied part Physical Sciences requires knowledge of Complex Analysis.
Complex variables are a fundamental part of QM as they appear in the Wave Equation.
Complex Analysis shows up in abundance in String theory.
Physics students use Complex Analysis in electrical signals study
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