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Complex Analysis 4 | Holomorphic and Entire Functions

📝 Find more here: https://tbsom.de/s/ca 👍 Support the channel on Steady: https://steadyhq.com/en/brightsideofm... Other possibilities here: https://tbsom.de/sp You can also support me via PayPal: https://paypal.me/brightmaths Or via Ko-fi: https://ko-fi.com/thebrightsideofmath... Or via Patreon:   / bsom   Or via other methods: https://thebrightsideofmathematics.co... Join this channel on YouTube:    / @brightsideofmaths   💬 Access to the community forum: https://thebrightsideofmathematics.co... 🕚 Early access for videos: https://thebrightsideofmathematics.co... ❓ FAQ: https://thebrightsideofmathematics.co... 🛠️ What tools do you use: https://thebrightsideofmathematics.co... Please consider to support me if this video was helpful such that I can continue to produce them :) Each supporter gets access to the additional material. If you need more information, just send me an email: https://tbsom.de/s/mail Watch the whole video series about Complex Analysis and download PDF versions and quizzes: https://tbsom.de/s/ca Supporting me via Steady is the best option for me and you. Please consider choosing a supporter package here: https://tbsom.de/s/subscribe 🌙 There is also a dark mode version of this video:    • Complex Analysis 4 | Holomorphic and ...   🔆 There is also a bright mode version of this video:    • Complex Analysis 4 | Holomorphic and ...   🔆 To find the YouTube-Playlist, click here for the bright version:    • Complex Analysis   🌙 And click here for the dark version of the playlist:    • Complex Analysis [dark version]   🙏 Thanks to all supporters! They are mentioned in the credits of the video :) Thanks to all supporters who made this video possible! They are mentioned in the credits of the video :) This is my video series about Complex Analysis. I hope that it will help everyone who wants to learn about complex derivatives, curve integrals, and the residue theorem. Complex Analysis has a lof applications in other parts of mathematics and in physics. In particular, we can solve real integrals by going to the complex realm. For any questions, please leave a comment or come to the community forum of the Bright Side of Mathematics: https://tbsom.de/s/community x 00:00 Intro 00:28 How to define a holomorphic function? 02:29 Essential properties of holomorphic functions 04:21 Example 1. A complex polynomial 06:11 Example 2. A 'rational function' for polynomials #ComplexAnalysis #Analysis #Calculus #Mathematics #curveintegral #integration (This explanation fits to lectures for students in their first or second year of study: Mathematics, Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on) The Bright Side of Mathematics has whole video courses about different topics and you can find them here https://tbsom.de/s/start For questions, you can contact me: https://steadyhq.com/en/backend/messa...