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Calculus I Online Course for Academic Credit

Calculus I is the first course in the freshman (engineering) calculus sequence on an introduction to the mathematical concepts of differentiation and integration, culminating with the Fundamental Theorem of Calculus.

Completion of Math 213 - Calculus I earns 4 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.


Introductory Videos


Calculus I - Math 213 - Introduction

Calculus I is the gateway to collegiate mathematics. As such, Calculus I is often a prerequisite course for many majors, both science and non-science.

Calculus I introduces the fundamental concept of the derivative, geometrically demonstrated in this animation showing a limit of secant lines approaching a tangent line at a point on a curve y=f(x):

secants image

Calculus I also introduces the fundamental concept of the integral, geometrically demonstrated in this animation showing the accumulation of signed area under a curve y=f(x) of increasing accuracy:

area image
Math 213 - Calculus I course provides a thorough and demanding introduction to beginning calculus.
  • Intensive Precalculus Refresher
    Calculus I starts with an intensive 26 assignment refresher of precalculus including trigonometry, starting from scratch with solving basic equations, ranging then to functions, linear equations, polynomials, exponential, logarithmic, and trigonometric functions. This refresher aids students who have been away from academics for a while, as well as students with weaker mathematical backgrounds. For students with stronger math backgrounds, this refresher can be completed very quickly, and provides an excellent platform on which to learn the computer algebra software.
  • Analytic Geometry
    Calculus I usually includes an exploration of conic sections: parabola, hyperbola, ellipse. These topics are included for transferability requirements, as many schools in the U.S. still require these topics to be included in the Calculus I course, although many Precalculus courses are charged with presentation of these topics.
  • Introduction to Differential Calculus
    Calculus I begins with investigating the phenomena of growth of the various types of functions, culminating with the derivative as a measurement of growth. Limits of functions and their usage in formulating the algebraic rules for computing derivatives - Newton's "calculus" - are examined both in classical algebraic terms, and numerically and graphically with modern computer algebra and graphing tools. Applications of the derivative to "max/min" problems, differential equations, related rates, and parametric equations are then studied.
  • Introduction to Integral Calculus
    Calculus I studies the connection between integrals as measurement of signed area of regions defined by function curves, exploring the algebraic, graphical, and numerical aspects of integrals, in connection with introductory differential equations. Algebraic methods for computing basic integrals, followed by the introduction of the Fundamental Theorem of Calculus, along with the intial methods for computing integrals algebraically are then studied.


Roger Williams University Course Catalog Listing: Math 213 - Calculus I

Course Description: Covers the differential calculus of a single variable and introduces integration. Topics include limits and continuity, differentiation of algebraic and transcendental functions, applications of derivatives to rates of change, optimization, and curve sketching, and the Fundamental Theorem. The laboratory component involves use of computer algebra software. (4 credits)

Prerequisite: Precalculus with Trigonometry
Detailed Course Syllabus in PDF


Different Names for Calculus I

"Calculus I" is best described as the first semester of the lower-division calculus sequence, which often has these names:

Sometimes Calculus I is referred to as "Freshman Calculus" or even "1st Year Calculus".

It is important to note that Calculus I is the higher track of Calculus, in comparison to the lower Applied Calculus track for (primarily) non-science majors.

If you are not a science major (e.g. MBA, Nursing/Pharmacy, Other Graduate), check out the Applied Calculus page for more information on that lower-level course. If your need for a "one semester course of differential and integral calculus" will be satisfied in the lower Applied Calculus course, it is best to enroll in that lower course.


Prerequisites for Math 213 - Calculus I

Calculus I provides an introduction to differential and integral calculus, usually in preparation for completing the Calculus II second semester of Calculus, and perhaps higher sophomore-level Calculus sequence courses (Vector/Multivariable Calculus, Differential Equations, Linear Algebra, Probability Theory).

Calculus I course has the prerequisites of College Algebra and Trigonometry, or the combined Precalculus course.

The main topical differences between the lower Applied Calculus and the higher (Engineering) Calculus I course are described in the table below.

Topic Applied Calculus Calculus I
Trigonometry No Yes
Functions Polynomials, Roots, Exponential, Logarithmic Polynomials, Roots, Exponential, Logarithmic, Trigonometric, Composite, Integral Functions
Limits Mainly Graphical, Numerical Algebraic, Graphical, Numerical
Derivatives Simple Algebraic Rules Rigorous Rule Development, Application
Applications Economics, Finance, Easier Physics, Economics, Rates, Challenging
Introduction to Differential Equations No Yes
Derivatives and Integrals of Parametric Curves/Functions No Yes
Displacement, Velocity, Acceleration Minimal Yes
Integration Basic Integration Rules Algebraic Integration, Integral Functions, Integration via Substitution, Preparation for Calculus II

The Applied Calculus course does include more applications to business, finance, economics, etc. than does the Engineering Calculus I course.


TYPICAL STUDENTS IN CALCULUS I - Example Student Profiles


Case 1: Returning To Graduate School

Kelly is planning to go to graduate school in Economics, and the degree program she wishes to enroll in requires her to complete Calculus I, Calculus II, and Differential Equations. Kelly took a Calculus course back in her undergraduate days, but it has been too many years to rely upon that course information to move forward in the Calculus sequence.

How fast can Kelly finish the MAT 2610 - Calculus I course?

Graduate school-bound students tend to be highly motivated, and they usually have a timeline they need to follow to complete these courses.

Common Completion Timelines for MAT 2610 - Calculus I
Hours DedicatedMath SkillsDedicationCompletion TimeAdvisory
5-10 hours/weekWeaker1-2 hours/day16 weeksReasonable
7-12 hours/weekModest2-3 hours/day12 weeksReasonable
10-15 hours/weekStronger3-4 hours/day8 weeksReasonable
15-20 hours/weekStrong5-6 hours/day6 weeksStretched
20-25 hours/weekStrong5-7 hours/day4 weeksStretched
25-35 hours/weekStrong6-8 hours/day3 weeksWorld's Record

Case 2: Undergraduate Student Needs Calculus I

Jim is an undergraduate student at a university. Jim attempted the Calculus I course at his school, but he was not successful. He wants to take Calculus I via Distance Calculus to get back on track with his major requirements.

What are some issues Jim should consider?

Lack of success in a traditional course can be caused by many factors, some of which include:

  • Classroom Lecture Structure
    Some students are very good at the classroom lecture paradigm, some are not. 100+ students in a big lecture hall is not the best learning environment for many students.
  • Traditional Course Pace
    In a traditional course, the student must keep pace with the rest of the class. If a student has weakness in a particular area (e.g. trigonometry), the student is expected to kick into "high gear" to make up the distance. Sometimes this re-doubling of effort is not enough to stay on pace with the lectures and the homework due dates.
  • Too Many Other Classes
    Often traditional undergraduate students find themselves taking 5 courses concurrently. When the scheduling pressure reaches critical with exams and papers due, often one course will suffer. Ambitious scheduling for a "tough semester" will sometimes not follow the planned path. Courses that require ample amounts of time and effort - like Calculus I - can fall by the wayside.
In these above cases, looking towards Calculus I via Distance Calculus is an excellent alternative. Jim could plan to take Calculus I over the summer months, or during December/January while on winter break, to allow for a single-focus concentrated effort towards the Calculus I course.

Adding Calculus I via Distance Calculus in addition to a full-load of 4-5 other traditional courses is usually not advised.


Case 3: High School Student & AP Calculus

Alicia is an ambitious high school student. Alicia is taking a number of AP courses, but the AP Calculus course has a time conflict at her high school. Alicia plans to take Calculus I via Distance Calculus instead of the AP Calculus course.

What are some issues that Alicia should consider?

There are positive and negative issues to consider with such a plan. Most often, our ambitious high school students are successful in Distance Calculus, as these students are successful in all tasks they engage in.

Positive Aspects

  • Collegiate Calculus I While in High School
    Although the content of the AP Calculus course is at the collegiate level, most AP Calculus courses are still offered just like other high school courses. The parameters of collegiate courses - expectations of additional written work, thorough solution presentations, challenging problems and approaches to concepts - are often not found in the AP Calculus courses, which are set towards the successful completion of the AP Calculus exam.
  • AP Calculus Exam Not Required
    As the Calculus I via Distance Calculus is a real collegiate-level, academic-credit-earning course, the AP Calculus exam is not required to earn the collegiate credit hours. Some students do not like high-stakes exams like the AP Calculus exam.
  • Asychronous Course & High School Class Schedule
    High school students have an expected 8am-3pm school day, which makes it difficult to attend a traditional college lecture course, except for night courses. As Distance Calculus is asynchronous, high school students will be able to complete the course without impacting their regular daytime class schedule.

Negative Aspects

  • Lack of AP-Inflated GPA
    At many high schools, AP courses award GPA points with an inflated multiplier - often 1.3. In this way, ambitious students are able to inflate their GPAs, often higher than 4.0, which is beneficial to collegiate applications. Distance Calculus courses do not offer this kind of GPA help.
  • Academic Immaturity
    The first real collegiate course a high school student takes is often a bit shocking. High school courses tend to be very "answer-centered", while a collegiate course is usually less so, and more "open ended". In Distance Calculus, there is no "answer key" to check your answers, as many high school math courses are geared for. For these reasons, some high school students experience an unfamiliar sense of unsuccessfulness at the beginning of the course, which is disconcerting for many.

Case 4: Non-Science Major, But Applied Calculus Is Not Acceptable

Rashida is a pharmacy student, looking towards pharmacy school, which requires a "single semester introductory Calculus course." Rashida checks with her pharmacy school, and they tell her that the lower Applied Calculus course is not acceptable for their program, but the higher Calculus I course is acceptable.

What are some issues Rashida should consider?

The Calculus I course is the higher, more rigorous, more challenging course when compared to the lower Applied Calculus course. But the two courses are built from the same core e-textbook, so the higher level of difficulty should be thought of as more challenging, rather than "impossible".

Rashida should consider these items:

  • Precalculus & Trigonometry
    The Calculus I course has a prerequisite of Precalculus with Trigonometry. Rashida remembers that she never took trigonometry in high school. That means Rashida will need to start with the Precalculus course before moving forward into the Calculus I course.
  • Extra Time for Calculus I
    As Calculus I is more challenging than the lower Applied Calculus, Rashida will need to plan for taking a bit longer to complete the Calculus I course. The 8-12 week completion plan is probably the fastest that Rashida will be able to complete Calculus I (which does not include another 6-8 weeks to complete the Precalculus course first).
  • Courseload Considerations
    Rashida is finishing up her undergraduate work, and has a full load of senior-level classes. Adding Calculus I to this full-load is not advisable. It may be best for Rashida to wait for her current semester to end and to take up Calculus I as her single-focus course.

Case 5: Working Parent Planning for Graduate Studies Needs Calculus I

Amelia is a parent of three children who also works full-time. Amelia has ambitious plans to return to graduate school in the next year to advance her career. Amelia cannot take a traditional classroom math course due to her schedule constraints.

How fast can Amelia finish the MAT 2610 - Calculus I course?

We have many students like Amelia who are quite successful in Distance Calculus!

Amelia will probably do her math homework after her kids are asleep for the night, in the 10pm-midnight timeframe. The Mastery Learning format for Distance Calculus serves Amelia well, where she is able to spend extra time on those topics that are more challenging for her, without penalty or "falling behind" as she would in a traditional course.

When the children get sick and stay home from school, or life and work commands extra time, Amelia is able to take a break from Distance Calculus - usually for a few weeks, but perhaps for a few months, if needed - and return to her studies when her schedule permits. While such breaks do cause slower completion times, and "getting back in the swing of things" does require extra time and effort for Amelia, the flexibility of the asynchronous course format allows Amelia to finish the course when she can.


Case 6: 18-22 Year Old Student With Full Course Load Needs To Finish Calculus I

James is an undergraduate student at a university, carrying 15 semester credits - a full course load. James wants to add the Applied Calculus course to his course schedule, in order to complete a general education requirement.

What are the challenges that James will face with this plan?

In our experience, when a student is faced with "too many courses" at the same time, it is the asynchronous distance course that almost always is the course to suffer a lack of attention. With other synchronous course deadlines and examinations, it is natural that an asynchronous course such as Distance Calculus becomes the "pressure valve".

Students in these situations nearly always finish their Distance Calculus course during the winter break (December, January), spring vacation (April), and/or the summer vacation months (May-August). Even with the best of intensions, it is very difficult to complete a Distance Calculus course while taking 4 or 5 other courses simultaneously.

Younger students also have more difficulty with the flexible schedule of Distance Calculus. It is very easy to put off your course work "until all day Saturday" or "next week after my Philosophy exam", which snowballs into a huge amount of work leftover to an increasingly short amount of time. Planning for vacation times is the best approach for students in this category.


Distance Calculus Referenced Colleges/Universities

Over the past 24 years, Distance Calculus has enrolled thousands of students who successfully complete the Calculus I course, and use this course record towards undergraduate and graduate programs at various colleges and universities in the U.S. and throughout the world.

Below is a list of schools (most recently, from just 2010-2013) that Distance Calculus - Calculus I students have listed as their Home Institution:

  • Agnes Scott College
  • Aiken Technical College
  • Albany College of Pharmacy and Health Science
  • Alma College
  • American Public University
  • Andrews University
  • Arizona State University
  • Athens State University
  • Auburn University
  • Augusta State University
  • Austin Peay State University
  • Baylor University
  • Belmont University
  • Beloit College
  • Bentley University
  • Berry College
  • Bethany College
  • Binghamton University
  • Bloomsburg University
  • Borough of Manhattan Community College
  • Boston Conservatory
  • Boston University
  • Bryant University
  • Buena Vista University
  • California state University
  • Carleton College
  • Central Washington University
  • Champlain College
  • Chicago State University
  • Clemson University
  • Cleveland State University
  • Coastal Carolina University
  • College of Santa Fe
  • Colorado Mesa University
  • Colorado State University
  • Columbia University
  • Cornell Univeristy
  • Covenant College
  • Drexel University
  • Duke University School of Law
  • Duke University, Durham NC
  • East Stroudsburg University
  • Eastern Illinois University
  • Elon University
  • Embry Riddle Aeronautical University
  • Excelsior College
  • Ferris State University
  • Florida Agricultural and Mechanical University
  • Florida Atlantic University
  • Florida International University
  • Florida State University
  • Fordham University
  • Fox Valley Technical College
  • Freed-Hardamen University
  • Friends University
  • George Mason university
  • George Washington University
  • Georgetown University
  • Georgia State
  • Griffith University
  • Grinnell College
  • Grove City College
  • Hampshire College
  • Hampton University
  • Hillsdale College
  • Hiram College
  • Huntingdon College
  • Illinois Institute for Technology
  • Indiana University
  • Iowa State University
  • Jacksonville State University
  • Jeff State Community College
  • Johns Hopkins Univerisity
  • Kalamazoo College
  • Kennesaw State University
  • Kentucky State University
  • Kettering University
  • Lebanon Valley College
  • Lee University
  • LeTourneau University
  • Liberty University
  • Lincoln University of Pennsylvania
  • Marian University
  • Mary Baldwin College
  • Massachusetts Maritime Academy
  • McHenry County College
  • Mercer University
  • Mercyhurst College
  • Meredith College
  • Miami University
  • Michigan Technological University
  • Middle Tennessee State University
  • Millersville University
  • Montana State University
  • Montana Tech
  • Naval Post Graduate School
  • New York University
  • Northeastern University
  • Northern Arizona University
  • Northern Michigan University
  • Northwest Nazarene University
  • Northwestern University
  • Oberlin College
  • Oglethorpe University
  • Oklahoma Baptist University
  • Old Dominion University
  • Olympic College
  • Orange Coast College
  • Pacific Lutheran University
  • Pennsylvania State University
  • Pepperdine University
  • Pomona College
  • Randolph-Macon College
  • Regent University
  • Regis University
  • Rhode Island School of Design
  • Robert Morris University
  • Rochester Institute of Technology
  • Roger Williams University
  • Roosevelt University
  • Rutgers University
  • Saint Anselm College
  • Saint Joseph's University
  • Salve Regina University
  • Shepherd University
  • Southern Methodist University
  • St. Anselm College
  • St. John's College
  • State University of New York
  • Stevens Institute of Technology
  • Swarthmore College
  • Texas A&M University
  • The Citadel
  • The New England Institute of Art
  • The University of South Carolina
  • Trinity University
  • Tulane University
  • University of Wisconsin
  • University of Auckland, New Zealand
  • University of California, Santa Cruz
  • University of California, Los Angeles
  • University of Central Texas
  • University of Colorado
  • University of Connecticut
  • University of Dallas
  • University of Florida
  • University of Georgia
  • University of Hawai'i-Manoa
  • University of Illinois
  • University of Michigan
  • University of Minnesota
  • University of Mississippi
  • University of Missouri
  • University of Nevada
  • University of New Haven
  • University of New Haven
  • University of North Carolina
  • University of Northern Iowa
  • University of Oklahoma
  • University of Otago
  • University of Pennsylvania
  • University of Pittsburgh
  • University of Southern California
  • University of Southern Indiana
  • University of Sussex
  • University of Tennessee
  • University of Texas
  • University of Utah
  • University of West Alabama
  • University of West Georgia
  • University of Wisconsin
  • University West Florida
  • US Air Force Academy
  • Utah Valley University
  • Villanova University
  • Virginia Military Institute
  • Virginia Tech
  • Washington State University
  • Webster University
  • West Chester University
  • West Virginia University
  • West Virginia Wesleyan College
  • Western Kentucky University
  • Western Michigan University
  • Wheaton College
  • Wheaton College (IL)
  • William and Mary
  • William Jewell College
  • Wright State University
  • Yale University
  • Yonsei University


CALCULUS I: ACADEMICS

80% Computer Algebra, 20% Pencil/Paper, 0% Multiple Choice

Through the usage of a computer algebra system like LiveMath™ - you will never miss a minus sign again!

Although the driving of a computer algebra system requires some up-front time to learn and master, once completed (rather quickly for most students), the time saved from having to be a "minus sign accountant" adds to the productivity of your study time. If you have ever spent hours looking for that "little numerical error", you know what we mean.

Command of a computer algebra software system is a modern-day necessity of mathematical academics. It is important, however, to retain a meaningful command of paper/pen/pencil manual computations as well. Our blend of curriculum strives for an 80%/20% split between computer algebra usage and manual computation and written skills. With each module in our curriculum, a concluding Literacy Sheet assignment ensures that each student has written mathematical competency in the subject area.

The proctored final exam is a written exam away from the computer. It is these Literacy Sheet assignments, and the continuing bridge from modern computer algebra software back to classical, manual mathematics that prepares the student from this written final exam.

We do not have any multiple-choice work. We are a real collegiate-level course program - not a "canned" set of multiple-choice question sheets which are common from large publishers and degree-mill schools.


Calculus I 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.

Our videotext features two main types of videos:

  • Screencast Videos using LiveMath™ Play Video

    example view video

    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.

  • ChalkTalk Videos: Manual Calculations Play Video

    example view video

    While using a computer algebra software package is a very cool way to do Calculus computations and investigations, we must also pay attention to the classical side of Calculus, and the computations that can be completed by hand with paper/pen/pencil. To be a well-rounded Calculus student, you need to be able to do calculations in both technical and manual methods.


Calculus I 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 Instructor Question/Answer Movie

When a student asks a question in a homework notebook, sometimes the best way to explain the answer is via a screen movie.


Calculus I Example Student Work and Grading

The majority of course work occurs via the exchange of LiveMath™ notebooks - think Word Processing Files, but for mathematical computations instead of just text.

The student will "Hand-In" a notebook, and one of the instructors will grade, correct, give feedback, and/or give hints on the work in the notebook, and return the notebook to the student in his/her "GetBack" folder, where the student will view the instructor comments.

Sometimes the notebook is deemed "Complete" on the first revision. Sometimes the notebook must go back and forth between the student and instructor a number of times - 2, 3, 4, 5 times is rather common.

Coupled with the screencast video mechanism, sometimes the instructor or the student will submit a screen movie with the notebook, giving further explanation or questions in audio/video format.

Below are some example notebooks from actual students, showing the progression from starting notebook to completed notebook.








Distance Calculus - Student Reviews

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Date Posted: Mar 16, 2020
Review by: Malia K.
Courses Completed: Applied Calculus
Review: Course was good and fast. I don't like math so I can't say it was fun or anything. Grader was very nice. Software was ok.
Transferred Credits to: University of Maine





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Date Posted: Jan 12, 2020
Review by: Anonymous
Courses Completed: Calculus I
Review: This course is amazing! I took it as a requirement for admission to an MBA program, and couldn't have been happier with the quality and rigor of the course. I previously took calculus two times (at a public high school and then a large public university commonly cited as a "public ivy"), this course was by far the best and *finally* made the concepts click. Previously I had no idea what was going on because terrible PhD students were teaching the course and saying stuff like "a derivative is the slope of a tangent line" - ??? but what does that mean ???, but the instructors in the Shorter University course explain everything in ways where it FINALLY made sense (e.g., "imagine a roller coaster hitting the top of a hill, there's a moment where it shifts momentum and you're not accelerating or decelerating, that's what a 0 rate of change is - that's when the derivative would be zero"). They explain everything in multiple ways and relate it to other concepts. It all made perfect sense when I finally had a good instructor. Really recommend this class
Transferred Credits to: The Wharton School, UPenn





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Date Posted: Dec 20, 2019
Review by: Bill K.
Courses Completed: Calculus I, Calculus II, Multivariable Calculus, Linear Algebra
Review: I took the whole calculus series and Linear Algebra via Distance Calculus. Dr. Curtis spent countless hours messaging back and forth with me, answering every question, no matter how trivial they might seem. Dr. Curtis is extremely responsive, especially if the student is curious and is willing to work hard. I don't think I ever waited much more than a day for Dr. Curtis to get a notebook back to me. Dr. Curtis would also make videos of concepts if I was really lost. The course materials are fantastic. If you are a student sitting on the fence, trying to decide between a normal classroom class or Distance Calculus classes with Livemath and Mathematica, my choice would be the Distance Calculus classes every time. The Distance Calculus classes are more engaging. The visual aspects of the class notebooks are awesome. You get the hand calculation skills you need. The best summary I can give is to say, given the opportunity, I would put my own son's math education in Dr. Curtis's hands.
Transferred Credits to: None