Complex Analysis Syllabus

Complex Analysis Syllabus Course

Course Title:	[COURSE TITLE]
Credits:	[CREDITS]
Instructor:	[INSTRUCTOR]
Schedule:	[SCHEDULE]
Location:	[LOCATION]
Textbook:	[TEXTBOOK]
Description:	[DESCRIPTION]
Assessments:	[ASSESSMENTS]
Grading:	[GRADING]
Office Hours:	[OFFICE HOURS]

1. Instructor Information

Organization: [YOUR COMPANY NAME]

Instructor: [YOUR NAME]

Contact: [YOUR EMAIL]

2. Course Description

This course will provide an introduction to complex analysis which involves the theory of complex numbers and complex functions. The main aim is to help students get a solid understanding of concepts like complex differentiation, integration, power series and residue theory. Complex analysis is a vivid subject that has an integral role in various areas of mathematics, engineering, and physics.

3. Learning Objectives

• To understand the fundamental concepts of complex numbers and complex functions.

• To master complex differentiation and integration.

• To solve problems using power series.

• To apply the principles of residue theory in practical applications.

• To develop problem-solving skills incorporating a wide range of complex analysis topics.

4. Course Schedule

Week	Topic	Readings
1	Complex Numbers	Introduction to Complex Numbers Basic Properties of Complex Numbers Operations with Complex Numbers
2	Complex Functions	Definition and Examples of Complex Functions Analytic Functions Complex Exponential Function
3	Limits and Continuity	Limit of Complex Functions Continuity of Complex Functions Differentiability in the Complex Plane
4	Complex Differentiation	Cauchy-Riemann Equations Differentiability and Analyticity Harmonic Functions
5	Complex Integration	Contour Integration Cauchy's Integral Theorem Cauchy's Integral Formula
6	Power Series	Taylor and Laurent Series Convergence of Power Series Singularities and Residues
7	Residue Theory	Residue Theorem Calculating Residues Applications of Residue Theory
8	Mapping and Conformal Mapping	Complex Mapping Conformal Mapping Examples of Conformal Mapping
9	Analytic Continuation	Analytic Continuation Riemann Surfaces Branch Cuts and Branch Points
10	Review	Comprehensive Review of Topics Practice Problems and Exercises Preparation for Final Exam

5. Required Reading and Materials

• "Complex Analysis" by Ahlfors, L. This book is the primary textbook for the course.

• "Visual Complex Analysis" by Needham, T. This is a supplemental book that provides a geometric view of complex analysis.

• "Functions of One Complex Variable" by Conway, J.B. This book is a deeper dive with emphasis on proofs.

• Additional papers and articles as assigned.

• Scientific calculator.

6. Assignments and Assessments

• Weekly problem sets. These assignments are designed to reinforce the concepts covered that week.

• Midterm Exam. This closed-book exam will cover everything taught in the first half of the course.

• Final Exam. The final exam is comprehensive and covers everything taught in the course.

• Final Project. Students will select a topic related to complex analysis for a deeper study and present it at the end of the course.

• Class Participation. Active participation in class discussions and problem-solving activities is encouraged.

7. Course Policy

• Attendance: Regular attendance is essential for understanding and mastering course materials.

• Homework: Homework assignments are due at the beginning of class. Late homework will not be accepted without a valid reason.

• Exams: All exams are closed-book and no electronic devices are allowed.

• Academic Integrity: Students are expected to maintain high standards of academic honesty and integrity.

• Accessibility: If you have a disability or require special accommodations, please let me know as soon as possible.

8. Grading Policy

Grades will be based on the combination of class participation (10%), homework (40%), midterm (20%), final exam (20%), and final project (10%).

9. Disclaimer

This syllabus, which serves as a course guide, may have alterations or adjustments in the future as deemed necessary. Should there be any updates, changes or modifications to the content or structure of this syllabus, it will be promptly and efficiently announced during the class. Furthermore, these changes will also be communicated using email so each student will be directly and personally informed about these revisions on the syllabus. Therefore, it's encouraged for all students to monitor their emails regularly to keep updated with any potential changes.

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