Introduction to Mastering Complex Integration and Cauchy's Theorem

This course provides an in-depth exploration of complex integration and the critical role of Cauchy's Theorem in complex analysis. Designed to deepen understanding and proficiency in handling complex integrals, the course tackles essential concepts, techniques, and applications related to complex functions. Through comprehensive explanations, interactive examples, and practical problem-solving exercises, students will gain a robust grasp of the foundational principles and tools used in higher mathematics.


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Last update: 04/2024
English

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Course Overview

5 sections . 18 lessons .

Introduction to Complex Numbers and Functions

Visualizing Complex Functions 14:32
Understanding Complex Numbers 1:22:11
Functions of a Complex Variable 25:20
Elementary Functions in the Complex Plane 22:04
Introduction to Complex Numbers and Functions Quiz 20 min

Techniques of Complex Integration

Integration Formulas and Examples 29:00
Line Integrals in the Complex Plane 41:29
Contour Integration Techniques 14:05
Analyzing Singularities and Residues 24:51
Techniques of Complex Integration Quiz 20 min

Cauchy's Integral Theorem and Its Proof

Proof of Cauchy's Integral Theorem 9:39
Statement of Cauchy's Integral Theorem 9:39
Implications and Consequences 2:13
Cauchy's Integral Theorem Quiz 20 min

Extensions of Cauchy's Theorem and Applications

Generalizations of Cauchy's Theorem 13:35
Cauchy's Integral Formula 9:20
Applications to Series and Products 44:04
Practical Applications in Physics and Engineering 8:51
Extensions of Cauchy's Theorem and Applications Quiz 20 min

Advanced Problem Solving in Complex Integration

Challenging Problems in Complex Integration 40:45
Strategies for Complex Problem Solving 16:19
Case Studies and Real-World Scenarios 16:39
Advanced Problem Solving in Complex Integration 30 min

Instructor

32 published courses

9 courses sold

Instructor ratings

4.25 (4 ratings)
Goal

Course Objectives

Understand the basic concepts of complex functions and their properties.

Develop proficiency in computing complex integrals using various techniques.

Learn and apply Cauchy's Integral Theorem and its extensions.

Explore the applications of complex integration in physics and engineering.

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Prerequisites

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Familiarity with basic calculus, including differentiation and integration.

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An understanding of basic concepts in complex numbers.

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Some exposure to differential equations is helpful but not necessary.

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5 lessons

USD 1.00

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