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Complex Analysis Online Course for Academic Credit

Complex Analysis covers analytic functions, contour integration, residue theory, and conformal mappings with computational visualization using Mathematica.

Course
DMAT 456 - Introduction to Complex Analysis
Credits
4 Semester Credit Hours
Delivery
Fully Online, Asynchronous, Self-Paced

RWU Course Catalog - DMAT 456 • Introduction to Complex Analysis
Course
DMAT 456
Course Title
Introduction to Complex Analysis
Transcript Title
Complex Analysis
Credits
4 Semester Credit Hours
Description
An introductory course on Complex Analysis, emphasizing the visual and computational aspects of the subject. Topics include moving from real numbers to the complex world, complex power series, complex elementary functions, multifunctions, branch points, complex function differentiation, conformal/analytic functions, Cauchy-Riemann equations, complex integration, poles, residues, and winding numbers, Cauchy-Riemann Formula, connections to vector fields.
Prerequisite
Successful completion with grade B or higher in Linear Algebra and Multivariable Calculus or equivalent, or consent of instructor.
E-Textbook
Complex Analysis by Mathews & Howell
Software
Mathematica and LiveMath

DMAT 456 - Learning Outcomes

  1. To understand the generalization of calculus from the real numbers to the complex number system
  2. To understand the generalization of differentiation and integration from freshman calculus to the field of complex numbers
  3. To understand the formulation of elementary trigonometric, exponential, and logarithmic functions in the field of complex numbers
  4. To understand the concepts of analytic / conformal complex functions
  5. To understand the Cauchy-Riemann equations
  6. To understand the concepts of winding numbers, poles, singularities
  7. To understand The Fundamental Theorem of Complex Calculus
  8. To understand Cauchy's Formula and the Calculus of Residues
  9. To understand the connections to vector field analysis
  10. To understand and utilize software tools to investigate visualization and computational aspects of the subject

DMAT 456 - Syllabus of Topics

1. Getting Started
1.1 Email and Chat
1.2 Learning About the Course
1.3 Required Hardware
1.4 Software Fundamentals
2. Complex Numbers
2.1 Origin of Complex Numbers
2.2 Algebra of Complex Numbers
2.3 Geometry of Complex Numbers
2.4 Topology of Complex Numbers
3. Complex Functions
3.1 Functions and Linear Mappings
3.2 Power Functions
3.3 Limits and Continuity
3.4 Branches of Functions
3.5 Reciprocal Transformation
4. Analytic and Harmonic Functions
4.1 Differentiability and Analytic Functions
4.2 The Amplitwist Concept
4.3 Cauchy-Riemann Equations
4.4 Analytic = Conformal
4.5 Harmonic Functions
4.6 Visual Differentiations
5. Sequences, Series, and Fractals
5.1 Sequences and Series
5.2 Julia and Mandlebrot Sets
5.3 Geometric Series and Convergence
5.4 Power Series Functions
6. Elementary Functions
6.1 Complex Exponential Function
6.2 Complex Logarithm
6.3 Complex Exponents
6.4 Trigonometric and Hyperbolic Functions
6.5 Inverse Trigonometric and Hyperbolic Functions
7. Complex Integration
7.1 Complex Integrals
7.2 Contours and Contour Integrals
7.3 Cauchy Theorem
7.4 Fundamental Theorem of Integration
7.5 Integral Representations
7.6 Liouville Theorem
8. Taylor and Laurent Series
8.1 Uniform Convergence
8.2 Taylor Series Representations
8.3 Laurent Series Representations
8.4 Singularities, Zeros, and Poles
8.5 Applications of Taylor and Laurent Series
9. Residue Theory
9.1 The Residue Theorem
9.2 Trigonometric Integrals
9.3 Improper Integrals of Rational Functions
9.4 Improper Integrals of Trigonometric Functions
9.5 Indented Contour Integrals
9.6 Integrands with Branch Points
9.7 The Argument Principle and Rouche Theorem
10. Conformal Mappings
10.1 Basic Properties of Conformal Mappings
10.2 Bilinear Transformations
10.3 Mappings Involving Elementary Functions
11. Harmonic Functions and Vector Fields
11.1 Vector Fields and Complex Functions
11.2 Fluid Flow
11.3 Sources and Sinks
11.4 Contour Integrals and Flow Along, Flow Across

Distance Calculus Referenced Colleges & Universities (29 Years - 393+ Institutions)

Distance Calculus students have transferred course credits to these colleges and universities:

Agnes Scott College • Aiken Technical College • Albany College of Pharmacy and Health Science • Alma College • American Graduate University • American Public University • American University • Andrews University • Arizona State University • Armstrong Atlantic State Univeristy • Athens State University • Auburn University • Auburn University MBA Program • Augusta State University • Austin Peay State University • Azusa Pacific University • Babson College • Baruch College • Baylor University • Belmont University • Beloit College • Bentley University • Berklee College of Music • Berry College • Bethany College • Binghamton University • Bloomsburg University • Bluefield State College • Bluegrass Community and Technical College • Borough of Manhattan Community College • Boston Conservatory • Boston University • Bryant University • Buena Vista University • California Lutheran University • California Polytechnic State University, San Luis Obispo • California state University • California State University Channel Islands • California State University, Dominguez Hills • California State University, Sacramento • Carleton College • Carnegie Mellon University • Cedarville University • Central Michigan University • Central Washington University • Champlain College • Chapman University • Charter Oak State College • Chicago State University • Clark University • Clarkson University • Clemson University • Cleveland State University • Coastal Carolina University • College of Santa Fe • College of William & Mary • Colorado Mesa University • Colorado State University • Columbia University • Columbia University School of Business • Cornell Univeristy • Cornell University • Covenant College • CUNY Medgar Evers College • Denison University • DePaul University • Drexel University • Duke University - Fuqua School of Business • Duke University School of Law • Duke University, Durham NC • Duke University, Fuqua School of Business, Law School, Graduate Programs • East Stroudsburg University • Eastern Illinois University • Eastern Kentucky University • Eastern Mennonite University • Eastern Nazarene College • Elon University • Embry Riddle Aeronautical University • Embry Riddle University • Endicott College • Evangel University • Excelsior College • Fairifield University • Fairleigh Dickenson University • Ferris State University • Florida A & M University • Florida Agricultural and Mechanical University • Florida Atlantic University • Florida Institute of Technology • Florida International University • Florida State College, Jacksonville • Florida State University • Fordham University • Fox Valley Technical College • Franklin University • Freed-Hardamen University • Fresno State University • Friends University • Gannon University • George Mason university • George Washington University • George Washington University School of Business • Georgetown University • Georgia Institute of Technology • Georgia State • Georgia State University • Georgia Tech • Gordon College • Governor's State University • Green Mountain College • Griffith University • Grinnell College • Grove City College • Hamline University • Hampshire College • Hampton University • Harvard University, Kennedy School of Government • Harvard University: Kennedy School of Government, Medical Schools • Hillsdale College • Hillsdale University • Hiram College • Hofstra University • Howard University • Huntingdon College • Illinois Institute for Technology • Illinois Institute of Technology • Indiana University • Iowa State University • Jacksonville State University • James Madison University • Jeff State Community College • Johns Hopkins Univerisity • Johns Hopkins University • Kalamazoo College • Kansas State University • Kaplan University • Kennesaw State University • Kentucky State University • Kettering University • Kings College, University of London • La Sierra University • Lebanon Valley College • Lee University • LeTourneau University • Liberty University • Lincoln University of 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Santa Fe Community College • Shepherd University • Smith College • South Dakota School of Mines and Technology • Southern Adventist University • Southern Methodist University • St. Anselm College • St. John's College • St. Mary's College of Maryland • Stanford University • Stanford University, MBA • State University at Buffalo Law School • State University at Buffalo, Law School • State University of New York • Stevens Institute of Technology • Strayer University • SUNY Binghamton • Swarthmore College • Syracuse University • Texas A&M University • Texas A&M • Texas A&M University • Texas Tech University • The Art Institute of Atlanta • The Catholic University of America • The Citadel • The Citadel, Military College of South Carolina • The College of New Jersey • The College of St. Scholastica • The George Washington University • The Master's College • The New England Institute of Art • The Ohio State Universtity • The University of Alabama • The University of South Carolina • The University of Texas at Austin • The University of Virginia • Thomas Edison State College • Trinity University • TUI University • Tulane University • Union University • United States Air Force Academy • United States Military Academy • Univeristy of Puget Sound • University of Alabama, Huntsville • University of Arizona • University of Arkansas, Little Rock • University of Auckland, New Zealand • University of California, Berkeley • University of California, Los Angeles • University of California, Santa Barbara • University of California, Santa Cruz • University of Central Florida • University of Central Oklahoma • University of Central Texas • University of Chicago • University of Cincinnati • University of Colorado • University of Colorado, Boulder • University of Colorado,Colorado Springs • University of Connecticut • University of Dallas • University of Findlay • University of Florida • University of Georgia • University of Hartford • University of Hawai'i-Manoa • University of 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University of Oklahoma • University of Otago • University of Pennsylvania • University of Pennsylvania Architectural School • University of Pennsylvania, Wharton School of Business • University of Phoenix • University of Pittsburgh • University of Portland • University of Redlands • University of Richmond • University of San Francisco • University of South Carolina • University of Southern California • University of Southern Indiana • University of Sussex • University of Tampa • University of Tennessee • University of Texas • University of Texas at Austin • University of Texas, Arlington • University of Texas, Austin • University of Texas, Brownsville • University of Texas, Dallas • University of Texas, Houston • University of Utah • University of Virginia • University of Warwick • University of West Alabama • University of West Florida • University of West Georgia • University of Wisconsin • University of Wisconsin, Madison • University of Wyoming • University West Florida • US Air Force Academy • Utah State University • Utah Valley University • Valdosta State University • Valley Forge Military College • Vanderbilt University • Villanova University • Virginia Military Institute • Virginia Tech • Walla Walla University • Washing State University • Washington and Lee University • Washington State University • Webster University • West Chester University • West Virginia University • West Virginia Wesleyan College • Western Governors University • Western Kentucky University • Western Michigan University • Westminster College • Wharton School of Business, University of Pennsylvania • Wheaton College • Wheaton College (IL) • Wheaton College Illinois • Whitman College • Whittier College • Widener University • William and Mary • William Jewell College • Winthrop University • Woodbury University • Wright State University • Yale University • Yeshiva University • Yonsei University





Distance Calculus - Student Reviews

Genevieve P.★★★★★
Posted: Sep 20, 2020
Courses Completed: Applied Calculus
I found out from my grad school after being accepted that I needed a Calculus course before starting their MBA program. I had less than 6 weeks to do it (and as a non-STEM undergrad no less). The video lectures were informative, the pre-calc refresher was great to get re-conditioned, and the asynchronous format worked so well as I did this at night/weekends after work. I completed it in 4 weeks. Professor Curtis was extremely responsive, graded assignments quickly, and a supportive guide providing constructive feedback to me to excel at the assignments. I highly recommend this course for those who need a pre-req in a hurry or like learning on their own schedule. Thanks, Distance Calculus and Professor Curtis!
Transferred Credits To: Massachusetts Institute of Technology (MIT)
Bradley R.★★★★★
Posted: May 18, 2025
Courses Completed: Probability Theory
A great way to learn probability theory through visualizations, code, and math. Rather than just solving equations through pencil and paper, this course helped me to see how how probability distributions form and behavior through simulations and visuals. I would recommend this course to anyone looking for a way a more interactive way to learn mathematics and at their own pace.
Transferred Credits To: none yet
Rebecca M.★★★★★
Posted: Mar 17, 2020
Courses Completed: Calculus II, Multivariable Calculus
Fantastic courses! I barely made it through Cal 1, and halfway through Cal 2 I found this program. I took Cal 2 and then Multivariable and I just loved it! SOOOOOOO much better than a classroom+textbook class. I highly recommend!
Transferred Credits To: Tulane University
M M.★★★★★
Posted: Feb 8, 2026
Courses Completed: Precalculus, Calculus I
The courses were excellent. Very flexible and engaging and the platform offers a lot of upper-level courses. Dr. Curtis is an outstanding professor and very responsive. I would take again.
Transferred Credits To: None yet
Tanja B.★★★★★
Posted: Jan 28, 2026
Courses Completed: Calculus I
After two failed attempts at my university, this course helped me understand Calculus. The live maths tool along with Dr. Curtis were especially helpful, allowing me to visualize concepts and expand my understanding. The explanations were clear, the examples practical, and I could learn at my own pace, which built my confidence. Thank you.
Transferred Credits To: University of Namibia
Henry F.★★★★★
Posted: Dec 18, 2025
Courses Completed: Differential Equations
Transferred Credits To: Saint Joseph High School
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