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Calculus III Online Course for Academic Credit

STEM Calculus III - DMAT 273 - is a SPECIAL BRIDGE COURSE in the freshman (engineering) calculus sequence (STEM: Science, Technology, Engineering, and Mathematics) which is NOT NEEDED by MOST STUDENTS.

Common Semester Sequence For Calculus

The common sequence for lower division calculus looks something like this at most colleges/universities in the U.S.:

YearSemesterCourseTopics
Freshman Fall Calculus I Differentiation
Beginning of Integration
Spring Calculus II Integration Techniques
Series, Sequences, Taylor's Theorem
Planes, Dot Product
Sophomore Fall Multivariable Calculus
= "Calculus III" or "Calculus IV"
3D Planes and Surfaces
Partial Derivatives
Vector Fields, Path Integrals
Double & Triple Integrals
Gauss, Green, Stokes, Divergence Theorem (GFTOC)
Spring Differential Equations
Linear Algebra
Ordinary Differential Equations
Matrix Algebra, Vector Spaces, Eigenvalues/vectors


Some U.S. Colleges/Universites are on the QUARTER System instead of the Semester System, additionally split their lower division Calculus sequence like this:

YearQUARTERCourseTopics
Freshman Fall Calculus I Differentiation
Winter Calculus II Integration
Spring Calculus III Series, Sequences, Taylor's Theorem
Planes, Dot Product
Partial Derivatives
Sophomore Fall Multivariable Calculus
= "Calculus IV"
3D Planes and Surfaces
Partial Derivatives
Vector Fields, Path Integrals
Double & Triple Integrals
Gauss, Green, Stokes, Divergence Theorem (GFTOC)
Winter Differential Equations Ordinary Differential Equations
Spring Linear Algebra Matrix Algebra, Vector Spaces, Eigenvalues/vectors

Special Bridge Course: DMAT 273 - Calculus III

For those students who are attempting to articulate to a Quarter-like Calculus sequence, we offer the Special Bridge Calculus III course, which, topic-wise, is 50% of our DMAT 263 - Calculus II course + 20% of our DMAT 355 - Multivariable Calculus course.

WARNING: If you are taking our standard Freshman and Sophomore Calculus sequence, you DO NOT NEED to take this DMAT 273 - Calculus III special bridge course.


All Students Applying To Enroll in DMAT 273 - Calculus III
will be screened to assure they are taking this extra course due to articulation needs at their college/university.


Completion of DMAT 273 - STEM Calculus II earns 3 academic credit semester hours with an official academic transcript from Roger Williams University, in Providence, Rhode Island, USA, which is regionally accredited by the New England Commission of Higher Education (NECHE), facilitating transfer of credits nationwide to other colleges and universities.



Course
DMAT 273 - STEM Calculus III
Credits
3 Semester Credit Hours
Delivery
Fully Online, Asynchronous, Self-Paced

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 Pennsylvania • Lipscomb University • Loma Linda University • London School of Economics • Loyola Marymount University • Luther College • Macon State College • Marian University • Marquette University • Mars Hill College • Marshall University • Mary Baldwin College • Massachusetts Maritime Academy • McHenry County College • Mercer University • Mercyhurst College • Meredith College • Mesa State College • Messiah College • Miami University • Michigan State University • Michigan Technological University • Middle Tennessee State University • Middlebury College • Millersville University • Missouri University of Science and Technology • Montana State University • Montana Tech • Montclair University • Morehead State University • Murray State University • Naval Post Graduate School • New Mexico Military Institute • New Mexico State University • New York University • North Carolina Agricultural and Technical State Univerisity • Northeastern University • Northern Arizona University • Northern Michigan University • Northwest Nazarene University • Northwestern University • Oberlin College • Occidental College • Oglethorpe University • Oklahoma Baptist University • Old Dominion University • Olympic College • Orange Coast College • Oregon State University • Pacific Lutheran University • Penn State University • Pennsylvania State University • Pepperdine University • Pomona College • Portland State University • Princeton University • Purdue University • Quinnipiac University • Randolph-Macon College • Regent University • Regis University • Rensselaer Polytechnic Institute • Rhode Island School of Design • Rice University • Robert Morris University • Rochester Institute of Technology • Roger Williams Univerity • Roger Williams University • Roosevelt University • Rowan University • Rutgers University • Saint Anselm College • Saint Joseph's University • Saint Louis University • Saint Michael's College • Salve Regina University • Samford University • San Diego State University • 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 Illinois • University of Kentucky • University of La Verne • University of Maine • University of Maryland • University of Massachusetts • University of Massachusetts, Amherst • University of Memphis • University of Michigan • University of Michigan: MBA, Medical Schools, Graduate Programs • University of Minnesota • University of Minnesota, School of Public Health • University of Minnesota, Twin Cities • University of Minnesota-Twin Cities • University of Mississippi • University of Missouri • University of Missouri, Columbia • University of Montana • University Of Mount Union • University of Nebraska • University of Nevada • University of New Hampshire Law School • University of New Haven • University of New Orleans • University of North Carolina • University of North Carolina at Chapel Hill • University of North Carolina, Chapel Hill • University of North Carolina, MBA • University of North Dakota • University of North Texas • University of Northern Iowa • University of Notre Dame • 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

STEM Calculus III Introductory Videos


STEM Calculus III Course Introduction

The third quarter/semester of 1st year Calculus is the preparatory course for all of the 2nd year courses (Multivariable Calculus, Differential Equations, Linear Algebra). Often referred to as "the last course on single-variable differential and integral calculus", STEM Calculus III contains the topics from the last half of our DMAT 263 - Calculus II course on sequences, series, Taylor's Theorem - via Splines - and first portion of the DMAT 355 - Multivariable Calculus & Vector Analysis.

STEM Calculus III is comprised of two distinct parts:

  • Taylor's Theorem
    The general concept of approximating functions using infinite polynomials, which requires the discussion on sequences, series, convergence, divergence, and error analysis.
  • Introduction to Multivariable Calculus
    A selection of topics from the Multivariable Calculus course, specially about planes, dot products, and partial derivatives, with these topics having very little to do with the Taylor's Theorem portion of the course, but added only because of historical and articulation needs. These topics are usually the last few chapters in the big, thick first year Calculus course textbook.

RWU Course Catalog - DMAT 273 • STEM Calculus III
Course
DMAT 273
Course Title
STEM Calculus III
Transcript Title
Calculus III
Credits
3 Semester Credit Hours
Description
A third course in the differential and integral calculus for engineering and science with emphasis on computational techniques, graphical analysis, and algebraic methods. Topics include splines, barriers, Taylor's Theorem, L'Hopital's Rule, infinite sequences and series, selected topics from three dimensional calculus and geometry.
Prerequisite
Successful completion (C- or higher) of Calculus II or equivalent, or consent of instructor.
E-Textbook
Calculus & LiveMath by Robert R. Curtis, Ph.D., adapted from Davis/Porta/Uhl Calculus&Mathematica courseware series
Software
LiveMath

DMAT 273 - Learning Outcomes

  1. To understand and compute parametric and Polar function integrals
  2. To understand and compute splines and polynomial approximations
  3. To understand and compute with Taylor's Theorem
  4. To understand and compute with L'Hopital's Rule and using expansions to compute limits
  5. To understand and compute sequences and series
  6. To understand and compute convergence or divergence of sequences and series
  7. To understand and compute 3D vector analysis, dot product, planes, and cross products
  8. To understand and compute partial derivatives and tangent planes to a surface

DMAT 273 - 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. Taylor’s Expansion of a Function
2.1 Splines and Smooth Splines
2.2 Points of Contact
2.3 Application: Landing an Airplane
2.4 Taylor Expansion
2.5 Recognizing Familiar Expansions
2.6 Using Expansions for Approximations
2.7 Derivatives and Integrals of Expansions
2.8 Expansions At Other Points
2.9 Newton’s Method
2.10 Calculating Limits: L’Hopital’s Rule
3. Sequences and Series
3.1 Sequences of Numbers
3.2 Series of Numbers
3.3 Convergence
3.4 Convergence of Taylor Expansions
3.5 Barriers: Radius of Convergence
3.6 Shared Convergence Intervals for Derivatives and Integrals of Functions
3.7 Applications: Drug Dosing
4. Power Series
4.1 Basic Definition
4.2 Convergence Intervals of Power Series
4.3 Ratio Test and Other Convergence Tests
4.4 Finding Series Convergence Values via Power and Taylor Series
5. Polar Coordinates
5.1 Basic Graphing
5.2 Recognizable Curves
5.3 Differentiation and Integration in Polar Coordinates
6. Vector Analysis
6.1 Vector Arithmetic
6.2 Dot Product, Cross Product
6.3 Planes
6.4 Partial Derivatives
6.5 Tangent Planes

Calculus III - Example Curriculum

Videotext - A Modern Replacement of the Textbook

What is a videotext? It is like a textbook, except instead of being based upon printed information, this "text" is based upon video presentations as the core method of explaining the course topics. Instead of a huge, thick 1000-page Calculus textbook to lug around in your backpack, all of this new "videotext" can be loaded into your iPods or iPhones (and soon, the iPad!).

Example Videos are in MP4/H.264 format, which play in most modern browsers without additional software. When additional software is required, a backup Flash player will play the video. As a backup to Flash, you may also use iTunes and/or VLC.

Although we are anywhere from a few miles to a few thousand miles apart, watching these screencast videos is like sitting next to the course instructor, watching his computer, learning the topics of Calculus at the same time as learning how to drive the computer algebra and graphing software LiveMath™. These LiveMath™ screencast videos make up the majority of the video presentations in the videotext.


Calculus III - Screencast Video Questions

One extremely powerful aspect of the Distance Calculus course technologies is the usage of screencast video (and audio) recordings made by the students and the instructors, exchanged just as easily as emails back and forth.

If a picture is worth a thousand words, then a screencast movie is worth a million words - and saves boatloads of time and effort.

Instead of trying to type out a math question about a particular topic or homework question, the ease of "turning on the screen recorder" and talking and showing your question - in the span of a few minutes - can save hours of time trying to convert your question into a typed (and coherent) narrative question.

Example Student/Instructor Question/Answer Movies

When a student asks a question in a homework notebook, sometimes the best way to explain the answer is via a screen movie. We utilize easy-to-use software to create screen movies with audio so that you can communicate with your instructor "as if they were sitting at the computer with you". Students don't ask questions like this everytime they have a question, but it is a good way to ask questions after text chats aren't working.

If a picture is worth a thousand words, and a movie is worth a thousand pictures, then a movie with audio is worth 1000*1000*1000 = 1,000,000,000 (billion) words!


Calculus III - Example Student Work and Grading

Course work occurs via LiveMath notebooks - interactive documents for mathematical computation. Students submit notebooks, instructors grade and give feedback, and notebooks go back and forth until mastery is achieved (typically 2-5 revisions).

Notebook #1
Notebook 1 example View PDF
Notebook #2
Notebook 2 example View PDF







Distance Calculus - Student Reviews

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
Chris M.★★★★★
Posted: May 7, 2025
Courses Completed: Multivariable Calculus, Differential Equations, Linear Algebra, Probability Theory
I've taken Multivariable Calculus, Linear Algebra, Differential Equations, and Probability Theory through Distance Calculus. All four courses were awesome. Dr. Curtis and the TA's were very responsive and helpful.
The biggest advantage of these courses, compared to taking a traditional course, is that in addition to the theory, I was forced to also think computationally. I have become quite adept at using LiveMath and Mathematica for doing calculations and plots.
All of the courses were accepted for credit transfer (Johns Hopkins University)
Email: chrismillermd@me.com
Transferred Credits To: Johns Hopkins University
Ian M.★★★★★
Posted: May 18, 2025
Courses Completed: Multivariable Calculus
Distance Calculus was a life saver! I needed an accredited program to complete multi-variable calculus for grad school and at the time was an American living in England. Being able to take the course on my own timeline, from my own home, was amazing! The content was thorough and the visualization exercises were very helpful for comprehension and understanding. This was an exceptionally, affordable, thorough, and convenient course that I found a lot of value in and I’m thankful it was available to me!
Transferred Credits To: Air Force Institute of Technology
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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