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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.


Free Complex Analysis Books PDF | Download University Textbooks

Theory of Functions of Complex Variable by A. Forsyth
Discover complex analysis, power series, multiform functions, and advanced function theory in Forsyth’s seminal work on complex variables.
Complex Integration & Cauchy's Theorem - G.N. Watson | PDF
Explore G.N. Watson’s Complex Integration and Cauchy's Theorem, a concise guide to complex analysis, contour integration, and residue calculus.
Functions of Two Complex Variables by A. Forsyth | PDF
Study functions of two complex variables, double power series, and multiform functions in Forsyth’s foundational complex analysis text.
Theory of Functions - Harkness & Morley | PDF
Study complex analysis, singularities, and conformal mappings in Harkness and Morley’s authoritative treatise on analytic functions.
Elements of Complex Variable Theory - H. Durege
Understand the basics of complex numbers, analytic functions, and series expansions in Dürrège’s Theory of Functions of a Complex Variable.

Mathematics Book Categories

Algebra & Trigonometry
Precalculus
Basic Algebra
Trigonometry
Calculus
Calculus with Analytical Geometry
Single Variable Calculus
Differential Calculus
Integral Calculus
Multivariable Calculus
Advanced Calculus
Calculus of Variation
Geometry
Elementary Geometry
Analytic Geometry
Differential Geometry
Algebraic Geometry
Non Euclidean Geometry
Computational Geometry
Topology
Linear Algebra
Linear Algebra (Introduction)
Matrix Algebra
Discrete Mathematics
Probability & Statistics
Introductory Statistics
Probability & Stochastic
Mathematical Statistics
Statistical Learning
Bayesian Statistics
Applied Statistics
Abstract Algebra
Number Theory
Applied Mathematics
Mathematical Methods
Differential Equations
Computational Mathematics
Numerical Analysis
Mathematical Modeling
Mathematical Physics
Engineering Mathematics
History of Mathematics

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