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 an accessible, application-oriented textbook developed for undergraduate courses in complex analysis. Serving as a core text for mathematics, physics, and engineering students, this guide functions as an essential resource for complex analysis contour integration problem solving practice.
The course notes systematically cover complex numbers, analytic functions, Cauchy’s theorem, Laurent series, residue calculus, and conformal mapping. By blending rigorous proofs with geometric intuition and physical engineering applications, Orloff enables readers to execute essential complex variables mathematical proof derivations with absolute logical accuracy.
Widely utilized in university coursework for its clear explanations and practical examples, this text is an invaluable companion for self-study and review. Orloff’s structured approach provides scholars with core analytical tools needed for mastering modern complex analysis principles across technical fields.
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 Lecturer in the Department of Mathematics at the Massachusetts Institute of Technology (MIT), recognized for his contributions to undergraduate mathematics education and digital curriculum design.
Throughout his teaching career at MIT, Dr. Orloff has focused on developing intuitive, student-friendly learning materials that bridge abstract mathematical theory with applied engineering for undergraduate complex variables study guides.
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