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Differential Equations - The Modern Approach

Differential Equations is a sophomore-level course in the calculus sequence, taken after the Calculus II course (integration theory with Taylor Series, Sequences, et al.)

Classical Differential Equations is all about being presented with a type of differential equation, and then learning the paper and pencil techniques to solve the given type differential equation. Classically, you run out of easy differential equations very quickly, and the second half of the course is usually tasked with generalizing functions to Power Series representations, and finding - by hand! - the power series definitions that solve the next level of more difficult differential equation types.

A modern approach to differential equations is forget all of that paper and pencil classical technique - after all, is it really important to learn how to calculate the square root of 3 by hand? Our Modern approach to Differential Equations via the Calculus&Mathematica curriculum is to look at differential equations as what they mean - not how to solve the (rather trivial) cases you can do by hand. Having a powerful tool like Mathematica means you can obtain the solution of a differential equation (if there is one!), but what does the solution mean? How do you interpret it? What does its graph mean? What if the differential equation changes just slightly? What is a driving term?

This modern approach to Differential Equations is a superior approach for physics, economics, and data science. Instead of having a bag of "here's how you solve this differential equation by hand", students leave the course with an appreciation to engage against any differential equation!

Here is a video on the Differential Equation course:

Differential Equation Course



Data Science and Distance Calculus



 





Distance Calculus - Student Reviews

Louisa A.★★★★★
Posted: Dec 9, 2019
Courses Completed: Calculus I
My microeconomics class required college-level calculus as a prerequisite, and I didn't want to wait until next year to take the class. So, I took DC's Calculus I class over the summer, so I could register for econ when I got back to school this fall. I actually think I got more help taking the class online than I would have in the huge lecture classes here. Prof. Curtis was really clear in explaining concepts and talking me through the topics that I was having trouble with. It took me about 10 weeks to finish the class, which didn't seem too long and didn't feel rushed. My friends who are in calculus now, trying to finish the prereq, are pretty jealous!
Christopher K.★★★★★
Posted: May 19, 2025
Courses Completed: Precalculus, Calculus I
Well organized and well explained content. Professor did a great job. I learned a lot.

Dist Calc saved a ton of hassle and time having to take calc at a local community college, which realistically would have delayed my entrance to BU LEAP by at least a year.

Would strongly recommend it.
Transferred Credits To: Boston University
Jessica M.★★★★★
Posted: Feb 25, 2020
Courses Completed: Applied Calculus
I highly recommend this course. I started the Kennedy School at Harvard with a last-minute admission, but my application required the Liberal Arts calculus course, so I had to finish the course in 3 weeks. Diane was an awesome instructor! The class was surprisingly interesting. If you need to take calculus fast, this is the program to use.
Transferred Credits To: Kennedy School of Government, Harvard University
Ryan★★★★★
Posted: Aug 28, 2026
Courses Completed: Finite Math
I will preface this review by saying that if you are looking to take the easiest course possible, cheat through it, and learn as little as possible, this is not the course for you. Below, I will provide my uncensored opinions to this course:

First, this course uses software called LiveMath. This software can be a little bit challenging to get the hang of, but once you do get the hang of it, it's super easy. Remember that for all new things, it takes a bit to get used to it. Overall, I was highly satisfied with this course. I thought that the instructions were extremely detailed, including a video and a textbook explaining every different concept. In addition, this course offered exposure to a lot of different aspects of finite math. I think that many would agree with me on the following, that, you know, when a teacher is passionate about what they are teaching, it is so much more enjoyable, and you can definitely see that in this course. This course can be challenging at times. Maybe it'll be easy for you, maybe it'll be hard, but I think it's important to remember that the things that challenge us are, you know, the things that make us learn and the things that make us better. There's also a math chat option for if you need help or if you have any questions. Overall, I would recommend this course. I actually initially went into this course looking for an easy course to just help me get the credit requirements, but it ended up being an amazing learning experience and completely shifted my perspective on math overall. And another thing that I thought was great in this course is throughout so many different lectures, the professor would explain how each different thing can be applicable in life. And I think that, you know, that is a lot of what people think about when they are learning something. They're like, will I ever use this? Do I need to learn this? And a lot of this actually is really applicable. And I think that even if, you know, you may not be doing these math equations in your future, I think that, you know, the psychology behind these and the rules can be applied to so many different fuacets of life.
Transferred Credits To: GWU
Aiden B.★★★★★
Posted: Jul 29, 2026
Courses Completed: Calculus II, Multivariable Calculus, Differential Equations, Linear Algebra
After completing all the math offered by my highschool, I switched over to Roger Williams for Calculus II and onward. Overall, it has been a pretty great way to understand the topics online, with transferrable college credits. The exams are not terrible, and the courses cover the vast majority (if not all) of topics covered by traditional courses, with some unique ones added to. So far, I have taken four courses, with another one or two before I graduate.

The only problem with the course is the lack of pen and paper work. This shouldn't come as a crazy surprise with an online course, but there is not much emphasis on symbolic computation. Mathematica or other software does most of the heavy computation for you. The lectures usually show how to solve the problems through paper, but those skills are rarely put into practice. Literacy Sheets act as a way to do some of that (especially with the Calculus II & III course).

All in all, this isn't a huge issue. I just memorize and practice things like double integration, Laplace, ODE solving, matrix diagonalized form, row operations, etc. With a little outside work, this resolves itself. Without Roger WIlliams, I probably would not have been able to take any of these math courses in highschool.

So overall, a great choice for highschool advanced math, especially with transferrable credits.
Email: abarger@protonmail.com
Lucas L.★★★★★
Posted: Jun 25, 2026
Courses Completed: Multivariable Calculus
The professor as well as the TAs give great feedback when you need help with problems and the videos are great at explaining concepts. Return time on work is good and the work is not too much to handle.
Transferred Credits To: University of Wisconsin
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