Complex Variables with Applications by Jeremy Orloff
Complex Variables with Applications - Table of Contents
1. Complex Algebra and the Complex Plane
2. Analytic Functions
3. Multivariable Calculus
4. Line Integrals and Cauchy’s Theorem
5. Cauchy Integral Formula
6. Harmonic Functions
7. Two-Dimensional Hydrodynamics and Complex Potentials
8. Taylor and Laurent Series
9. Residue Theorem
10. Definite Integrals Using the Residue Theorem
11. Conformal Transformations
12. Argument Principle
13. Laplace Transform
14. Analytic Continuation and the Gamma Function
What You Will Learn in Complex Variables with Applications
"Complex Variables with Applications" by "Jeremy Orloff" is a clear and practical introduction to complex analysis, written for undergraduate students in mathematics, engineering, and the physical sciences. The book focuses on helping readers understand how complex variables work and why they are useful, combining theory with real-world motivation. Its friendly style and logical structure make it accessible even to students encountering complex analysis for the first time.
The text covers essential topics such as complex numbers and functions, analytic functions, complex integration, Taylor and Laurent series, and residue theory. A strong emphasis is placed on "applications", showing how "complex variables" are used to evaluate real integrals, solve problems in physics, and model phenomena in engineering. Visual intuition, examples, and step-by-step explanations help readers grasp abstract ideas more easily.
One of the strengths of the book is its balance between "theory and applications". While it introduces key theorems of "complex analysis", it avoids unnecessary abstraction and focuses on practical understanding. Often used in university courses and shared through open educational platforms, the book is also well suited for self-study. Overall, "Complex Variables with Applications" provides a solid foundation for students who want both conceptual clarity and practical skills in complex analysis.
Book Details & Specifications
Title:
Complex Variables with Applications by Jeremy Orloff
Publisher:
MIT OpenCourseWare
Year:
2018
Pages:
150
Type:
PDF
Language:
English
ISBN-10 #:
0073383171
ISBN-13 #:
978-0073383170
License:
CC BY-NC-SA 4.0
Amazon:
Amazon
About the Author: Jeremy Orloff
The author
Jeremy Orloff
is a mathematician and educator known for his clear, application-driven approach to "Complex Analysis". He taught the well-known MIT course "Complex Variables with Applications", where his lecture notes became the foundation for the textbook. The book reflects Orloff’s focus on practical understanding, connecting theory with engineering and scientific problems. Shared through "MIT OpenCourseWare", it supports "Mathematics Education" by offering accessible, well-structured material for undergraduate students learning complex variables.
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