# 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

*Date Posted: May 21, 2020*

Review by: Chester F.

Courses Completed: Calculus I, Calculus II

Review: I did not enjoy Calculus I at my school. I retook Calculus I, and then Calculus II, over the summer via Distance Calculus and it was awesome. I started my sophomore year back on track and ready for my physics classes. I struggled with the MathLive software but I guess it was alright.

Transferred Credits to: University of North Carolina

*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

*Date Posted: Apr 30, 2020*

Review by: Hannah J.

Courses Completed: Probability Theory

Review: Probability Theory was a great course. Very very thorough. I thought it would never end :). I was very prepared for my coursework in economics. Excellent refereshher of derivatives and integrals - really forced me to remember that stuff from freshman cal.

Transferred Credits to: Boston University

## Distance Calculus - Curriculum Exploration

### Systems of Equations

- P10: Systems of Equations:
- P10.1: Systems of Linear 2D Equations
- P10.1.a: Graphing
- P10.1.b: Solving by Substitution
- P10.1.c: Using Matrix Notation
- P10.1.d: Homework Problems
- P10.2: Matrices
- P10.2.a: Matrix Addition
- P10.2.b: Matrix Multiplication
- P10.2.c: Determinants
- P10.2.d: Matrix Inverse
- P10.2.e: Solving Linear Matrix Equation
- P10.2.f: Homework Problems
- P10.3: Systems of Linear 3D Equations
- P10.3.a: Graphing
- P10.3.b: Solve via Substitution
- P10.3.c: Solve Using Matrix Methods
- P10.3.d: Different Solution Cases in 3D
- P10.3.e: Homework Problems
- P10.4: Non-Linear Systems