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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

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Date Posted: Jan 8, 2021
Review by: Cristian Mojica
Student Email: comojica@ucdavis.edu
Courses Completed: Probability Theory
Review: A fantastic course! I was able to complete it in about half a year (with a few gaps) alongside other coursework I was completing. There are no deadlines except the one-year mark after registering, so you work at your own rate and schedule. Probability Theory is required for me to apply to Master's programs in Statistics, so I was glad when I found Distance Calculus. While the course was slightly less difficult than I originally expected, there were parts that definitely slowed me down and made me think. (Also, although calculus is not everywhere in the course, it is everywhere in normal and exponential variables and beyond, so make sure to review derivatives and integrals (single and double)!) I used Mathematica for my software, and it helped speed along calculations and proved to be the perfect stage and tool for this material. I think visual learners will absolutely revel in how the material is presented in this course. (I know I did!) As there is plenty of writing and calculation to do, you have many opportunities to develop and strengthen your voice as a mathematician. The modern format of 80% electronic notebook work and 20% handwritten work is an excellent mixture for studying probability theory and grasping its core ideas. Dr. Curtis is clear in his answers to any questions and concerns you may have and is highly responsive to email and chat, and to responses you leave in your notebooks. He truly wants to help you and to see you succeed, and he is always on your side. I highly recommend Probability Theory with Distance Calculus!



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Date Posted: Jan 12, 2020
Review by: Anonymous
Courses Completed: Calculus I, Calculus II
Review: I needed to brush up on my high school calculus and finally take Calc II before starting a graduate program that needed them as prereqs. This was perfect choice to fit in that summer. Got done at fast pace that I wanted and needed. Also had added bonus of one on one feedback and help when needed. Video lessons were better than many on campus instructors in large lecture settings. Recommend for anyone needing to satisfy prereqs at home institution.
Transferred Credits to: University of Michigan



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Date Posted: Jun 6, 2020
Review by: Douglas Z.
Courses Completed: Multivariable Calculus, Differential Equations, Linear Algebra, Probability Theory
Review: I loved these courses. So in depth and comprehensive. The mix of software and math curriculum was tremendously helpful to my future studies and career in engineering. I highly recommend these courses if you are bored of textbook courses.
Transferred Credits to: University of Massachusetts, Amherst