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Applied Calculus Online Course for Academic Credit

"Applied Calculus" is best described as a "single college-level course in differential and integral calculus". This type of single-semester course has many equivalent names:

Sometimes Applied Calculus is referred to as "Junior Calculus" or even "Baby Calc" - distinguishing Applied Calculus as the lower track of Calculus, in comparision to the higher track of Engineering-level Calculus I.

Completion of Math 207 - Applied Calculus 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.

Applied Calculus is offered in the Fall, Winter, Spring, and Summer semesters with "revolving enrollment", which means you may enroll at any time, and start your course whenever you wish, independent of the traditional academic calendar.


Applied Calculus Introductory Video


Different Names for Applied Calculus

Sometimes Applied Calculus is referred to as "Junior Calculus" or even "Baby Calc" - distinguishing Applied Calculus as the lower track of Calculus, in comparision to the higher track of Engineering-level Calculus I.

For more information on the different names for Applied Calculus, see this page.


Lower Applied Calculus vs. Higher Engineering Calculus I

Both Applied Calculus and (Engineering) Calculus I provide an introduction to differential and integral calculus.

Applied Calculus provides a lighter, more general introduction to the introductory topics of Calculus, while the higher Calculus I course expects students to have strong fundamentals the limit definition, definition of continuity, derivatives of functions, integrals, and applications of calculus to more difficult and challenging problem sets, in preparation for continuation to the higher Calculus II course in the first year Calculus sequence. Applied Calculus is "a notch or two easier" than the Engineering Calculus I course

Applied Calculus does not include nor require trigonometry. High School Algebra II is sufficient prerequisite for Applied Calculus, while the higher Calculus I course requires College Algebra, Trigonometry, and/or Precalculus.

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
Analytical Geometry No Conic Sections, Parametric Functions
Functions Polynomials, Roots, Exponential, Logarithmic Polynomials, Roots, Exponential, Logarithmic, Trigonometric, Composite, Integral Functions
Limits, Definition of Continuity Mainly Graphical, Numerical Algebraic, Graphical, Numerical
Derivatives Simple Algebraic Rules Rigorous Rule Development, Application
Applications of Calculus 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 course.

Roger Williams University Course Catalog Listing

Math 207: Applied Calculus
[3 credit hours]

Course Description: This course covers fundamental notions of differentiation and integration of algebraic, exponential and logarithmic functions, with problems drawn from principally from business situations. Topics include optimization, related rates, and simple applications and methods of integration. While covering traditional analytic methods, this course also emphasizes graphical and numerical approaches. This course may not be taken for credit by mathematics majors, minors or core concentrators. No credit will be given to students who have previously received credit for MATH 213. (3 credits)

Prerequisite: High School Algebra
Detailed Course Syllabus in PDF


Will Applied Calculus Suffice For Your Program?

The keywords to look for in your academic program's description is

"a single course on introductory differential and integral calculus"
Such a sentence almost always indicates that the lower Applied Calculus course will meet the requirements for this academic program.

Academic programs that usually will accept the lower Applied Calculus course include:

  • MBA & Business Schools
    Many MBA & EMBA programs accept Applied Calculus to satisfy their calculus course requirement.
  • Pharmacy, Nursing, or Pre-Med Schools
  • Architecture
  • Baccelaureate General Education Requirements
  • Other Graduate School Programs
  • Primary/Secondary Education Teacher Certification

Academic programs that usually require the higher (Engineering) Calculus I course include:

  • Science Majors
    Physics, Mathematics, Engineering, Computer Science, Chemistry
  • Economics Majors/Degrees
    Programs in Economics tend to be more mathematically oriented, and usually require Calculus I and beyond
  • Special Military Training
    Advanced military training programs, such as Test Pilot School, usually the higher Calculus I course

Transferring Credits vs. Satisfying Program Prerequisites

Many of our Applied Calculus students are seeking to satisfy the prerequisites for a graduate program of study, which is distinctly different than planning to transfer academic credits to a home institution. Some of the differences include:

  • Prerequisite Satisfaction: Minimal Grade
    Students using the Applied Calculus course to satisfy a prerequisite in another academic program will be required to achieve a minimal grade. For some programs the minimal required grade is a "B", and for others a "C" grade will suffice.
  • Prerequisite Satisfaction: Course Approval
    For Prerequisite Satisfaction, often only the graduate program (usually an admissions officer) must give approval for usage of the Distance Calculus course. For transferring of academic credits, often others, such as the Registrar, must also give approval to transferring credits.
  • Transferring Credits: Grades May or May Not Transfer
    When Transferring Credits, many institutions will accept the academic credits in transfer, but not the letter grade earned. In these cases, earning an "A" in the course is no different than earning a "B" or a "C". Often this type of situation gives the student guidance on which Grade Path to choose for Distance Calculus.

In either case, it is important to check with your graduate program to make sure the Applied Calculus course will satisfy their prerequisite requirements, and to make sure the Distance Calculus course is acceptable to them.


Applied Calculus Course Content & Syllabus

The Applied Calculus course provides a general (and lighter) introduction to beginning calculus.

  • Intensive Algebra Refresher
    Applied Calculus starts with an intensive 20 assignment refresher of high school Algebra I/II, starting from scratch with solving basic equations, ranging then to functions, linear equations, polynomials, and then exponential and logarithmic 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.
  • Introduction to Differential Calculus
    Applied Calculus begins with investigating the phenomena of growth of the various types of functions, culminating with the derivative as a measurement of growth. Algebraic rules for computing derivatives of functions are explored and utilized. Applications of the derivative to "max/min" problems are the final set of topics in the study of differential calculus.
  • Introduction to Integral Calculus
    Applied Calculus studies the connection between integrals as measurement of signed area of regions defined by function curves, concentrating on the graphical and numerical aspects of integrals. Algebraic methods for computing basic integrals, followed by the introduction of the Fundamental Theorem of Calculus, conclude the course.
  • Application of Calculus
    Applied Calculus is less about "rigourous calculus development" and more about learning various topics to study with the tools of Calculus - mathematical models involving calculus: applications of calculus in finance, applications of calculus in computing area and volume, applications of calculus in physics, applications of calculus in epidemiology. This Applied Calculus course is not "applied" in the sense of only being about these applications, but there are many problem sets about such applications so students learn working knowledge of how calculus is applied in many disciplines.


Roger Williams University Course Catalog Listing - Math 207 - Applied Calculus

Course Description: This course covers fundamental notions of differentiation and integration of algebraic, exponential and logarithmic functions, with problems drawn from principally from business situations. Topics include optimization, related rates, and simple applications and methods of integration. While covering traditional analytic methods, this course also emphasizes graphical and numerical approaches. This course may not be taken for credit by mathematics majors, minors or core concentrators. No credit will be given to students who have previously received credit for MATH 213. (3 credits)

Prerequisite: High School Algebra
Detailed Course Syllabus in PDF

Nearly all collegiate students have completed "high school algebra". There is no mathematics placement exam. The Applied Calculus course starts with a very thorough "warm up" module on the important topics of high school algebra, with the added usage of the LiveMath software, which makes for an excellent "refresher" for student who have maybe be away from academic mathematics for some time.


Applied Calculus - Academic Caveats

Some issues to consider when determining if Applied Calculus is for you.

  • Terminal Course
    Applied Calculus does not lead to the higher Calculus sequence, and is not equivalent to the higher Calculus I course. Applied Calculus is usually the last math course a student takes as an undergraduate.
  • No Trigonometry
    Applied Calculus does not include nor require Trigonometry. If your academic program requires a calculus course that includes trigonometry, you need to take the Calculus I course instead.
  • No Multivariable Calculus
    Applied Calculus does not branch into the multivariable calculus topics - required by some majors/programs, especially Economics. If you need Multivariable/3D Calculus topics, you'll need to go through the higher Calculus I/II + Multivariable Calculus sequence.

Applied Calculus Student Academic Goals

One way to determine if Applied Calculus is the right course for you is to align yourself with examples of student profiles we usually encounter.

  • Prepare for MBA or Other Graduate Program
    Many graduate programs, such as MBA's, have prerequisites that include "a single college-level Calculus course". The majority of our Applied Calculus students are seeking to satisfy such prerequisite requirements prior to starting their graduate school program. Our MBA-bound students tend to be highly-focused, goal-oriented students who complete their course work under very tight deadlines.
  • Pharmacy, Nursing, Pre-Med
    Often these academic and training programs require "a single college-level Calculus course" as a prerequisite. Many students in these programs have strong mathematical skills, which aid them in completing the Applied Calculus course quickly. Some students in this category do have weaker mathematical backgrounds, requiring more time to achieve mastery and success in the Applied Calculus course.
  • General Education Requirement
    Many students have "one more class" to finish to earn their baccelaureate degree, and Applied Calculus fits the bill for them.
    Warning: Many colleges/universities have a senior residency requirement where the last set of credits (usually 20-30 credits) must be completed at the college/university granting the degree, and cannot be "transferred in" from another school. Make sure you check with your college/university about such rules.
  • Teacher Re-Certification
    Primary and secondary educators often are required to take courses for their certification and/or re-certification programs.
    Warning: Distance Calculus courses do not carry graduate-level credits. Some recertification programs require their teachers to complete graduate level credits. Calculus courses are inherently undergraduate-level courses.


Applied Calculus Example Student Profiles

Case 1: MBA-Bound Student Needs Applied Calculus

Sally just got her acceptance letter from her MBA graduate school, but with notification that she needs to finish "a single collegiate-level differential and integral calculus course" by the start of MBA courses.

How fast can Sally finish the Math 207 - Applied Calculus course?

MBA students tend to be highly-motivated and deadline-centered students, ready to "do what it takes" to get finished by the required date. Here are some scenarios for Sally:

Common Completion Timelines for Math 207 - Applied Calculus
Hours Per Week 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
20-25 hours/weekStrong6-8 hours/day3 weeksUnreasonable, But Has Been Done
30-40 hours/weekVery Strong8-10 hours/day2 weeksUnreasonable, But Has Been Done
40-50 hours/weekVery Strong10-12 hours/day9 daysWorld's Record

Case 2: Pharmacy Student Needs Applied Calculus

Marc is planning to go to Pharmacy School in a few months, and needs to finish the Applied Calculus course prior to the start of school. Marc has been away from academic mathematics for many years, and does not have a strong mathematics background, but makes up for such weaknesses with drive, energy, and dedication to achieving his goals.

How fast can Marc finish the Math 207 - Applied Calculus course?

Marc will need to plan for extra time, especially at the beginning of the course, to get back into the swing of academic mathematics. The high school algebra review portion of the course (20 assignments) will be time well spent for Marc, as he revisits topics from high school that previously he did not have much success with. Marc is able to dedicate himself to the task, and is able to move more quickly through the Calculus curriculum (50 assignments). Here are some scenarios for Marc:

Common Completion Timelines for Math 207 - Applied Calculus
Hours Per Week DedicatedMath SkillsDedicationCompletion TimeAdvisory
8-10 hours/weekWeaker1-2 hours/day15 weeksReasonable
15-20 hours/weekWeaker2-3 hours/day10 weeksReasonable
20-25 hours/weekWeaker3-4 hours/day8 weeksReasonable
20-25 hours/weekModest2-3 hours/day8 weeksReasonable
25-30 hours/weekModest4-5 hours/day6 weeksStretched
30-35 hours/weekModest5-6 hours/day4 weeksStretched

Case 3: Working Parent Planning for Graduate Studies Needs Applied Calculus

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 Math 207 - Applied Calculus 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 4: 18-22 Year Old Student With Full Course Load Needs To Finish Applied Calculus

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.

Applied Calculus Referenced Colleges/Universities

Over the past 24 years, Distance Calculus has enrolled thousands of students who successfully complete the Applied Calculus courses, 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 that Distance Calculus students have utilized their Applied Calculus course credits earned towards these programs:

  • University of Pennsylvania, Wharton School of Business
  • London School of Economics
  • Harvard University: Kennedy School of Government, Medical Schools
  • Duke University, Fuqua School of Business, Law School, Graduate Programs
  • Columbia University School of Business
  • University of Pennsylvania Architectural School
  • University of Michigan: MBA, Medical Schools, Graduate Programs
  • Stanford University, MBA
  • University of California, Berkeley
  • Auburn University MBA Program
  • University of North Carolina, MBA
  • George Washington University School of Business
  • Roger Williams University
  • University of Minnesota, School of Public Health
  • Montclair University
  • Baylor University
  • Eastern Illinois University
  • University of Minnesota, Twin Cities
  • University of Memphis
  • State University at Buffalo, Law School
  • Westminster College
  • University of Mississippi
  • Georgia Tech
  • Wharton School of Business, University of Pennsylvania
  • Harvard University, Kennedy School of Government
  • Duke University - Fuqua School of Business
  • Stanford University
  • Princeton University
  • University of California, Berkeley
  • University of California, Santa Barbara
  • University of Southern California
  • Pennsylvania State University
  • College of William & Mary
  • University of Texas at Austin
  • Drexel University
  • University of Massachusetts
  • Cornell University
  • University of Wisconsin, Madison
  • Carnegie Mellon University
  • University of North Carolina, Chapel Hill
  • Kings College, University of London
  • Indiana University
  • Rice University
  • University of Georgia
  • University of South Carolina
  • University of Minnesota-Twin Cities
  • Baylor University
  • Loma Linda University
  • University of Maryland
  • Georgetown University
  • University of West Florida
  • Eastern Illinois University
  • University of Virginia
  • University of Maryland
  • University of Nebraska
  • University of Missouri
  • University of Georgia
  • Florida Atlantic University
  • Washington State University
  • University of New Orleans
  • California State University, Sacramento
  • California State University, Dominguez Hills
  • Babson College
  • Wheaton College
  • Middlebury College
  • George Washington University
  • Roger Williams University
  • Texas A&M University
  • Oregon State University
  • Illinois Institute of Technology
  • Montclair University
  • Hillsdale University
  • Evangel University
  • The Art Institute of Atlanta
  • New Mexico Military Institute
  • Athens State University
  • American Graduate University
  • Kaplan University
  • University of Warwick
  • Gordon College
  • University of Memphis
  • Endicott College
  • University Of Mount Union
  • Mesa State College
  • Azusa Pacific University
  • Thomas Edison State College
  • State University at Buffalo Law School
  • Murray State University
  • University of Phoenix
  • Webster University
  • Northern Michigan University
  • Western Michigan University
  • Central Michigan University
  • Fairleigh Dickenson University
  • Whitman College
  • Fairifield University
  • Jacksonville State University
  • University of Redlands
  • Westminster College
  • University of San Francisco
  • Strayer University
  • Vanderbilt University
  • Howard University
  • Middlebury College
  • Valdosta State University
  • American University
  • Clarkson University
  • Howard University
  • Green Mountain College
  • Whittier College
  • Florida A & M University
  • James Madison University
  • Franklin University
  • Woodbury University
  • Quinnipiac University
  • Webster University
  • Western Michigan University


Applied Calculus: 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.


Applied Calculus 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 play 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 play 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.

Applied Calculus 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.


Applied Calculus 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: Jan 12, 2020
Review by: Mark Neiberg
Courses Completed: Calculus I, Calculus II, Multivariable Calculus
Review: Curriculum was high quality and allowed student to experiment with concepts which resulted in an enjoyable experience. Assignment Feedback was timely and meaningful.





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Date Posted: Jan 18, 2021
Review by: Coury Gaffney
Student Email: courygaffney@gmail.com
Courses Completed: Linear Algebra
Review: The program used gives an amazing insight into everything that's happening, that you wouldn't get in a traditional course. All of the lessons are clear and clean, and the professor is very helpful along the way. I learned a lot and am happy with taking this course
Transferred Credits to: Virginia Tech





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Date Posted: Jun 21, 2020
Review by: Abdul J.
Courses Completed: Applied Calculus
Review: This was the best class! So much more interesting doing the computer math than a boring lecture class. Diane was so responsive and helpful. I recommend this course.
Transferred Credits to: Villanova University





Frequently Asked Questions

Yes, Applied Calculus, Business Calculus, Survey of Calculus - all are different names for the same level of "lower calculus", in the sense of being lower than the Engineering Calculus I course.

Yes, Applied Calculus is certainly easier than the Engineering Calculus I course, although the topics look similar when you look at a syllabus of both courses.

Yes, All Distance Calculus courses are offered through Roger Williams University in Providence, Rhode Island, USA, which is regionally accredited (the highest accreditation) through New England Commission of Higher Education (NECHE).

Yes, the majority of our Applied Calculus students are either enrolled or applying to an MBA program

Yes, the prerequisite for Applied Calculus is Algebra II from high school, which most university students have taken already. Trigonometry is not part of the prerequisite for Applied Calculus